Research ArticleGame Models on Optimal Strategies in a TourismDual-Channel Supply Chain

Lei Yang1 Jingna Ji1 and Kebing Chen2

1School of Economics and Commerce South China University of Technology Guangzhou Guangdong 510006 China2Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing Jiangsu 210016 China

Correspondence should be addressed to Lei Yang yangscuteducn

Received 1 March 2016 Accepted 21 April 2016

Academic Editor Luca Guerrini

Copyright copy 2016 Lei Yang et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper explores a two-echelon tourism supply chain consisting of a hotel and an online travel agency The upside hotel roomscan be sold through the downside hotel alliance and online travel agency The hotel alliance selling rooms at a lower price is adirect sale platform with a negligible entry fee Notwithstanding the online travel agency sells the room at a higher price withrelated personalized service Customers will be refunded partially in case of their cancellation or no-show An integrated modeland two decentralizedmodels based on Bertrand and Stackelberg games are developed respectivelyThe results show that when thewholesale price is lower than a certain value both the hotel and the online travel agency can gain more profit from the Stackelberggame than that from the Bertrand game In the case that the hotel allows overbooking the optimal overbooking quantity is obtainedIf the overbooking proportion is too high overbooking is profitable for the hotel only when the overbooking cost is lower than acertain value At the end of the study some experiments are conducted to analyze the sensitivity of the optimal prices and profitsin the light of certain parameters

1 Introduction

The improvement of transport infrastructure has significantlyreduced the trip cost and promoted the development oftourism [1] In recent years the tourism industry has evolvedconsiderably and plays an essential role in local economicdevelopment In the supply chain management specificallytourism has never been so much concerned by academicresearchers and industry practitioners since it provides anew perspective for the tourism firms to improve theircompetitiveness As we all know supply chain managementis a kind of process to increase the efficiency of a supply chainnetwork via conducting and integrating fund informationand goods flows from suppliers to end customers [2] Thetourism supply chain is defined as a network of tourismorganizations engaged in different activities ranging fromthe supply of tourism products or services such as flightsand accommodation to the distribution andmarketing of thefinal tourism product at a specific tourism destination [3] InChina for example the hotel industry is one of the fastest

growing worldwide with revenue increasing 18 times duringthe period from 2000 to 2009 [4] Therefore we study thetourism supply chain involving hotels

The development of Internet has provided a strongincentive for manufacturers to engage in direct sales Theproviders of tourism products are also inclined to build dual-channels By the end of December 2015 China has had 688million Internet users among which there are 260 milliononline travel product users (httpcnniccngywmxwzxrdxw2015201601W020160122639198410766pdf) On theother hand in 2014 the online tourism market transac-tions totaled 30779 billion yuan which increases by 389comparing with the same period in 2013 (httpreportiresearchcnreport2015042341shtml) The Internet hasbeen widely used by travelers as a crucial channel for bookinghotel rooms [5] Hotels therefore usually provide two book-ing channels the online travel agency (OTA) and the hotelalliance (HA)

OTA as an intermediary between hotels and customersplays an essential role in the tourism supply chain such as

Hindawi Publishing CorporationDiscrete Dynamics in Nature and SocietyVolume 2016 Article ID 5760139 15 pageshttpdxdoiorg10115520165760139

2 Discrete Dynamics in Nature and Society

Ctripcom eLongcom andMangocitycomHowever a com-mon phenomenon is that hotels must pay high commissionfor each sold room [6 7] In order to reduce commissionfees and sell rooms to customers directly hotels join a HAwhere the HA can be regarded as a direct sales platform Forinstance WeChat public platform and alitripcom offer thedirect selling platforms for hotels Comparedwith developingofficial websites joining HA can help the hotels reducecost Hotels have not been benefited much from websitedevelopment investment [8] Take for example Four Seasonshotel it has invested 18 million for its new website whileonline revenue only increases by 2 in five years [9] On thecontrary hotels can pay 0 to 15000 yuan per year to join thealitripcom so as to deal with orders through this websitedirectly Generally speaking the reservation price throughthe alliance is up to 20 to 70 of the rack rate In the light ofthe uncertain factors such as time city room type and roomquantity the discount is not fixed In most cases the priceof HA is 10 to 30 lower than OTA except for a plan ofpromotion with the extent to which the price will be equalto that of OTA Pricing competition exists between the twochannels Therefore how to determine the pricing decisionshas much practical significance for hotels

Customer cancellations and no-show occur frequentlyin the yield management of hotel reservations [10] Oncecustomers cancel the reservation or fail to show up thehotel will suffer loss for the rooms That is because roomsare perishable products In order to deal with this case thehotel usually permits overbooking However overbookingwill bring a risk that the actual booking quantity is greaterthan the number of hotel rooms As a result the overbookingcosts must be paid A question therefore arises as to how ahotel determines the overbooking quantity so as to keep abalance between the vacancy lost and the overbooking costs

Since more and more hotels employ dual-channel struc-ture we develop a two-echelon tourism supply chain modelinvolving one hotel and one OTA to study hotel room pricingstrategies with whichOTAprovides related service Bertrandand Stackelberg game models are both analyzed Further-more this paper considers customersrsquo no-show phenomenonin a dual-channel setting under tourism supply chain Theresults of the study will assist hotels to manage and optimizetheir pricing decisions

The remainder of this paper is organized as followsSection 2 provides a literature review and Section 3 presentsnotations Section 4 analyzes the integrated tourism supplychain Section 5 shows the Bertrand and Stackelberg gamemodels respectively The overbooking situation is illustratedin Section 6 Section 7 conducts numerical experiments toprovide more insights Conclusions and outlooks are finallypresented in Section 8 To make the paper more readable allproofs are presented in Appendix

2 Literature Review

This research is closely related to tourism supply chainpricing strategies in dual-channel supply chain and revenuemanagement To highlight our contributions we review only

the literature that is representative and particularly relevantto our study

21 Tourism Supply Chain Management Tourism supplychain management has been studied since the 1990s Forexample Yang et al [11] utilized game theory to investigate thecooperation and competition between two tourism supplychains which consist of service providers a theme parkoperator and accommodation providers They concludedthat in order to optimize performance the decision makersof the two tourism supply chains are expected to adoptappropriate product differentiation strategies Differentlywe highlight the comparison between the Bertrand andStackelberg game in a two-echelon tourism supply chainHuang et al [12] did research on competition strategies ina tourism supply chain network consisting of theme parksaccommodation providers and tour operators which areinvolved in producing and providing package holidays Theyanalyzed the differences between the impacts of quantity andprice competitions Huang et al [13] studied the impact of theinvolvement of tour operators in a tourism supply chain withmultiple hotels and travel agencies and showed that when themarket size of travel agencies is lower than a certain levelboth travel agencies and the hotel can benefit more fromthe presence of a tour operator in a tourism supply chainSimilarly we focus on the supply chain involving hotels andtour operators However our contributions are directed toformulating a dual-channel environment by considering theno-show phenomenon Furthermore Lee and Fernando [14]developed a model for the medical tourism supply chain andshowed that supply chain coordination and information shar-ing have a direct effect on organizational performance Weaim to contribute to this stream of literature by consideringhotelsrsquo pricing decisions under dual-channel structure

22 Pricing Strategies in Dual-Channel Supply Chain Theresearch on dual-channel supply chain management hasgained much attention among the marketing and supplychain management In particular the studies focusing onpricing strategies are closely related to our study In thisaspect Chiang et al [15] make a great contribution Theyconstructed a price-setting game between a manufacturerand its independent retailer They pointed out that thedirect sales channel can help the manufacturer improveoverall profitability by reducing the degree of inefficientprice double marginalization Tsay and Agrawal [16] foundthat the manufacturer can coordinate the supply chain andachieve a win-win situation through adjusting the directprice Q-H Li and B Li [17] studied a dual-channel supplychain in which the retailer provides value-added servicesto products Their results indicate that the entire supplychain cannot be coordinated with a constant wholesale pricewhen the retailer provides value-added services and hasfairness concerns Similarly we also assume that the OTAadds additional value to the tourism product Panda et al[18] explored pricing and replenishment policies for a high-tech product in a dual-channel supply chain that consistsof a brick-and-mortar channel and an internet channel

Discrete Dynamics in Nature and Society 3

Liu et al [19] investigated the pricing decisions under dual-channel structure In their model fairness and free-ridingbehavior are considered They detected that manufacturerrsquosequilibrium price based on channel fairness is below its equi-librium price ignoring fairness More related articles on thisissue have been presented by Chen et al [20] Ding et al [21]and Rodriguez and Aydin [22]

23 RevenueManagement Revenuemanagement whichwasoriginated in the airline industry is also widely used in thehotel industry That is because airline and hotel have similarcharacteristics (eg perishable service or product fixedcapacity distinct customer segmentation and price differen-tiation) In this aspect the room pricing decision has beenstudied extensively since price has an important influence oncustomerrsquos accommodation selection decisions [23] It is alsorelevant to our study

Chen et al [24] examined the impact of hotel pricing onguest satisfaction Their results imply that at the low pricelevel room price and food and beverage price lead to anincrease in guest satisfaction whereas the high price levelcould have just the opposite effect Ling et al [6] consid-ered the case that customers can make reservations directlythrough the distribution channel of the hotel or indirectlythrough the OTA Although the background of the studyis similar to that in our model they aim to find a methodfor hotels to manage their room availability for cooperativeOTAs Espinet et al [25] analyzed how hotel characteristicsaffect seasonality in prices and find that more hotel servicesand higher star ratings are associated with fewer seasonalvariations in hotel prices Juaneda et al [26] investigated theprice component of physical characteristics and the locationof apartments and hotels and compare their effect on thefinal price of both types of accommodation Abrate et al [27]collected data from almost 1000 hotels in Europe to analyzethe dynamic pricing strategies of hotels they showed thatthe intertemporal pricing structure primarily depends on thetype of customer the star rating and the number of supplierswith available rooms

The extant literature about revenuemanagement ismostlyfrom the perspective of the hotel itself However nowadaysthe competition among tourism enterprises turns to begradually and distinctly embodied in the competition amongtheir tourism supply chains In contrast to the above papersour model is more practical by considering pricing strategiesfrom the perspective of tourism dual-channel supply chain

This papermakes the following contributions Firstly thispaper introduces the tourism products into the dual-channelsupply chain framework while the aforementioned literatureignores this point Secondly the rooms in our research areclassified into economic and luxury type which can be betterto reflect the reality Thirdly this paper aims to illustrate thepricing decisions under several common cases which canprovide a valuable reference for hotels and OTAs

3 Model Setup and Notations

We consider a tourism supply chain model involving onehotel and one OTA (Figure 1) The hotel and OTA are both

Upstream(hotel)

Downstream(traveler)

Hotel alliance

Service agentseLong and Ctrip

wL wH pL

2 pH

2

pL

1 pH

1

Figure 1 Tourism dual-channel supply chain model diagram

risk neutral and completely rational The hotel is requiredto sign a cooperation agreement to join a HA HoweverHA charges the hotel trivial commissions Thus HA can betreated as a hotelrsquos direct sales platform and HArsquos price isdecided by the hotel directlyTherefore it is negligible to con-sider the contractual relationship between the hotel and HA

For the hotel customers are usually divided into twotypes business travelers and leisure travelers Leisure travel-ers aremore sensitive to roomprice than business ones so thatthey oftenmake a reservation before a long time Accordinglyhotels prefer to sell luxury rooms to business travelers Cor-respondingly the hotel rooms are usually classified accordingto different customersrsquo need such as luxury rooms economyrooms standard rooms and business roomsThrough settingdifferent rates for different rooms hotels are able to selldifferent types of rooms to specific target customers Basedon the above background in our model the hotel rooms areclassified into economic and luxury type In this paper hotelsells roommeans that hotel sells the right for guest to use theroom that is the hotel rents the room to guest for a periodof time The hotel sells the economy (luxury) rooms with theprice of 119901119871

1(1199011198671) to the customer directly and it sells rooms to

OTA with the wholesale prices of 119908119871(119908119867) respectively Pro-

viding combination of products and additional services OTAsells rooms to customers with the prices of 119901119871

2and 119901

119867

2

According to international practice in order to reducethe phenomenon of no-show customers must provide hotelreservation deposit with credit card or prepay the fee whenthey make reservation If customers cancel the booking orchoose no-show the hotel can deduct all or part of the roomcharge Take for example Ctripcom the orders can bedivided into two types orders that cannot be cancelled andtime-limited orders When customers choose the orders thatcannot be cancelled they cannot cancel the order after theyconform the booking if not the reservation deposit orprepaid fee will not be returnedThis kind of situation usuallyoccurs when guest room resources are intense The time-limited order means that customers can cancel the order forfree before the deadline (usually 1 to 3 days before check-in) Ifcustomers cancel the booking after the deadline or choose no-show Ctripcom will charge the customers for the first dayrsquosroom fee as a punishment This also means that when thecustomer reserves a room for more than one day he willreceive partial refund Such methods are also adopted byBookingcom and eLongcom Based on reality we assumethat customers must provide full guarantee with credit cardwhen they make reservation but if the customers cancel

4 Discrete Dynamics in Nature and Society

the booking or choose no-show finally the hotel would onlyreturn certain expense rate of 120572 (0 le 120572 le 1) If a customeris booking through OTA then OTA would return to thecustomer with the proportion of the retail prices At the sametime the hotel would return to OTA with the proportionof the wholesale prices We assume that the proportion thathotel returns to the customer the proportion that hotelreturns to OTA and the proportion that OTA returns to thecustomer are the same

We list the following notations where 119894 (119894 = 119871119867) insubscripts or superscripts are for economic (low price) andluxury (high price) rooms respectively

119876 the total number of rooms provided for renting toguests119876119894 the total number of economicluxury rooms

119863119894

1 the reservation amount of economicluxury room

booking through HA119863119894

2 the reservation amount of economicluxury room

booking through OTA119886119894 the market base demand of economicluxury

room119886 the total market base demand of rooms (119886 = 119886

119871+

119886119867)

119904 themarket share of HA in the tourism dual-channelsupply chain119901119894

1 HArsquos price of economicluxury rooms that is the

direct selling prices119901119894

2 OTArsquos price of economicluxury rooms that is the

retail prices119908119894 the wholesale price of economicluxury rooms

119887119894 the price sensitivity coefficient of 119894 price rooms

(119887119871gt 119887119867)

120579 the diffusion intensity which describes the shiftbetween two channels with regard to the price andvalue120582 the proportion of customer cancellations and no-show120572 the return expense proportion of customer cancel-lations and no-show (0 le 120572 le 1)120573 the services elasticity of demandV the value added by OTArsquos services120578 the coefficient of service cost119888(V) the function of service cost 119888(V) = 120578V221205871 the profit of the hotel

1205872 the profit of the OTA

In the model we do not consider the marginal sales costof the hotel since it is very low In reality OTA will firstlyintroduce to customers the hotelsrsquo facilities and quota andafterwards confirm the booking and finally book rooms fromthe hotel for customersTherefore the rooms sold by HA and

OTA are homogeneous In addition to providing hotel reser-vations OTA also provides other related services as wellsuch as offering plane ticket booking holiday booking andtravel information OTA aims to provide a full range of travelprogram for travelers In order to provide such services OTAneeds to pay for additional operating costs The customerswho want to get more tourist information and services willprefer to reserve rooms through OTA By contrast HA onlyprovides hotel room information for customers For instancecustomers cannot book the suitable hotel and air ticket at thesame time through the HA platform Consequently in orderto distinguish the influence of different information servicesto customerrsquos channel choice we suppose that OTA providesadditional service and the value added from the services is VFurther the cost for providing service is 119888(V) = 120578V22 wherethe parameter 120578measures the cost effectiveness of the serviceSuch cost function is commonly adopted in previous litera-ture and canwell describe the relationship between additionalservices and cost [28 29] When OTA does not provide theservice the cost should be zero

According to the process of demand function in Tsay andAgrawal [30] andChoi [31] the demands of economicluxuryrooms through each channel are expressed as follows

119863119894

1= (119904119886119894minus 119887119894119901119894

1) + 120579 (119901

119894

2minus V minus 119901

119894

1)

119863119894

2= [(1 minus 119904) 119886119894 minus 119887

119894119901119894

2] + 120573V + 120579 (119901

119894

1+ V minus 119901

119894

2)

(1)

Such linear demand functions are used because they canachieve approximate and satisfactory fit to certain types ofdemand and they are tractable and widely used in marketingand supply chain management literature [32] In our modelthe parameter 119887 represents the price sensitivity coefficientIt describes the marginal channel demand per respectivechannel price The own price elasticity is normally negative[33] And the parameter 120573measures the marginal demand ofOTA per service value added In addition the parameter 120579 isunderstood as the diffusion intensity (cross-price sensitivity)and describes the shift between two channels with regard tothe price and the value Suchmodelingmethod can guaranteethat the self-price sensitivity in absolute value is strongerthan the cross-price sensitivity which is proved by Hanssenset al [34] and used by Yao and Liu [28] Choi [31] and Kurataet al [35]

Now consider the situation without overbooking that is119863119871

1+ 119863119871

2le 119876119871and 119863

119867

1+ 119863119867

2le 119876119867 Thus the reservation

amount can be regarded as the final demandThe total profit for the hotel OTA and the whole supply

chain can be expressed as follows

1205871= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2) (2)

1205872= [(1 minus 120582120572) (119901

119871

2minus 119908119871) minus 119888 (V)]119863119871

2

+ [(1 minus 120582120572) (119901119867

2minus 119908119867) minus 119888 (V)]119863119867

2

(3)

120587 = 1205871+ 1205872 (4)

Discrete Dynamics in Nature and Society 5

4 Integrated System

As a benchmark we first consider an integrated systemwherethe common goal of supply chain upstream and downstreammembers is tomaximize the overall profit of the supply chainThis is an ideal model that the members in the supply chainoperate as an entirety In such an integratedmodel of tourismsupply chain the hotel and OTA cooperate to determine thepricing strategies

Proposition 1 In the integrated system the optimal pricingdecisions of HA and OTA are as follows

119901119894lowast

1=119886119894(119887119894119904 + 120579) + 120579V (120573 minus 119887

119894)

2 (119887119894)2+ 4119887119894120579

119901119894lowast

2=(119887119894+ 120579 minus 119887

119894119904) 119886119894+ 119887119894120573V + 120579V (120573 + 119887

119894)

2 (119887119894)2+ 4119887119894120579

+119888 (V)

2 (1 minus 120582120572)

119894 = 119871119867

(5)

From Proposition 1 the optimal prices shown above canexplain that in the integrated system the optimal prices of HAwill not be affected by the proportion of customer cancella-tions and no-show (120582) or the return expense proportion (120572)On the other hand with the increase of 120582 or 120572 the optimalprices for OTAwill increaseThis is reasonable because whenOTA faces unstable demand or it should return more tocustomersrsquo cancellation or no-show it would like to increasethe price to guarantee its profit

Corollary 2 119901119871lowast2

and 119901119867lowast2

are increasing in V Moreover

(1) if 120573 gt 119887119871gt 119887119867 then 120597119901

119871lowast

1120597V gt 0 120597119901119867lowast

1120597V gt 0

(2) if 119887119871gt 120573 gt 119887

119867 then 120597119901

119871lowast

1120597V lt 0 120597119901119867lowast

1120597V gt 0

(3) if 119887119871gt 119887119867gt 120573 then 120597119901

119871lowast

1120597V lt 0 120597119901119867lowast

1120597V lt 0

From Corollary 2 we can know that when OTA offersmore services OTArsquos optimal price will be increased accord-ingly It is reasonable that if V increases the cost of OTA willalso definitely increase So there is always a positive correla-tion between OTArsquos optimal prices and the added value

If 120573 gt 119887119871

gt 119887119867 the market of economy rooms and

that of luxury rooms are both service-oriented rather thanprice-oriented The implication is that the effective servicewill increase the optimal price of HAWhenOTA offersmoreeffective service its price will increase But some customerswant to enjoy the additional services so they are willingto make a booking through OTA despite spending moremoneyTherefore the demand inOTAwill increase while thedemand in HA will decrease

If 119887119871gt 120573 gt 119887

119867 the market of economy rooms is service-

oriented while the market of luxury rooms is price-orientedThe HArsquos optimal price of economy rooms will decrease withrespect to V Conversely the HArsquos optimal price of luxuryrooms will increase with respect to V For examples the

change of price has a great impact on leisure travelersrsquo deci-sions but for business travelers the price is not themost con-cern If the price ofOTA increasesOTArsquos demandof economyrooms will significantly reduce and the HArsquos demand willincrease thus the HArsquos optimal price will decline On theother hand for luxury rooms if OTA provides more effectiveservice the customer would be willing to pay higher pricesfor value-added service This will bring the increase in OTArsquosdemand and the reduction of HArsquos demand thus the optimalprice of HA will increase

If 119887119871gt 119887119867gt 120573 the market of economy rooms and that of

luxury rooms are both price-oriented than service-orientedThe HArsquos optimal price of both economy rooms and luxuryrooms will decrease with the increase of V When the marketis price-oriented the promotion of price in OTAwill lead to areduction in OTArsquos demandThereby the demand in HA willincrease and optimal price in HA will decline

5 Two Game Models

In the tourism dual-channel supply chain the relationshipbetween hotel and OTA is cooperative as well as competitiveIn the decentralized decision-making model they are morecompetitive than cooperative Their purposes are to maxi-mize their own profits In reality hotel can choose whether toinform the price ofHAor not forHA is competingwithOTAUninformed of the prices inHAOTAcan predict the range ofprice onHAby the star-rated and room type of the hotel but itcannot know the exact priceTherefore this section examinesthe pricing equilibrium between the hotel and OTA undertwo types of games namely the Bertrand and Stackelberggames For the Bertrand game both of the participantsregard price as a decision variable the hotel and OTA areuncooperative For the Stackelberg game the participantsare divided into two roles the leader and the follower Asa leader in tourism supply chain the hotel will provide thepolicy to maximize its interests As a follower OTA accepts ifprofitable By comparing the two models we can understandhow the behavior of hotel influences the pricing decisions

51 Bertrand Game In a Bertrand game the procedure isas follows keeping the wholesale price unchanged the hoteldetermines HArsquos prices 119901119871

1and 119901

119867

1 so as to maximize profit

1205871 Uninformed of the prices of HA OTA decides prices 119901119871

2

and 119901119867

2 so as to maximize his profit 120587

2 Let (119901119894

1)119861 (1199011198942)119861(119894 =

119871119867) denote HArsquos and OTArsquos prices under a Bertrand modelrespectively

In the following 119871119899(119899 = 1 2 5) 119904

0 and 119866

119898(119898 =

1 2) are the threshold values and are given in Appendix G

Proposition 3 There exist Bertrand equilibrium prices(119901119894

1)119861lowast (119901119894

2)119861lowast

(119894 = 119871119867) where

(119901119894

1)119861lowast

=(1 minus 120582120572) 1198711 + 119888120579 (119887

119894+ 120579)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

2)119861lowast

=(1 minus 120582120572) 1198712 + 2119888 (119887

119894+ 120579)2

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(6)

6 Discrete Dynamics in Nature and Society

From Proposition 3 in the Bertrand model the equilib-rium prices for hotel and OTA are both affected by 120572 and 120582With the increase of 120572 or 120582 both (119901

119894

1)119861lowast and (119901

119894

2)119861lowast will be

higher In otherwords with higher uncertainty of roomoccu-pancy the hotel and OTA tend to increase prices to protecttheir own profits

Denote 1198881= (1 minus 120582120572)(2119887

119871+ 120579 minus 120573)(119887

119871+ 120579) and 119888

2= (1 minus

120582120572)(2119887119867+ 120579 minus 120573)(119887

119867+ 120579) then 119888

1gt 1198882

Corollary 4 (1199011198712)119861lowast and (119901

119867

2)119861lowast are increasing in V (119901119871

1)119861lowast

and (119901119867

1)119861lowast have the following relationships with respect to

OTArsquos service

(1) if 1198881015840(V) gt 1198881 then 120597(119901

119871

1)119861lowast120597V gt 0 120597(119901119867

1)119861lowast120597V gt 0

(2) if 1198881gt 1198881015840(V) gt 119888

2 then 120597(119901

119871

1)119861lowast120597V lt 0 120597(119901119867

1)119861lowast120597V gt

0(3) if 1198881015840(V) lt 119888

2 then 120597(119901

119871

1)119861lowast120597V lt 0 120597(119901119867

1)119861lowast120597V lt 0

From Corollary 4 when OTA offers more effective ser-vices its optimal prices will increase due to the incrementin the cost Marginal cost measures the input costs and theoutput value per unit If the marginal cost is greater than1198881 then the costs of OTA to provide additional services are

higher So the equilibrium prices of HA will increase as thevalue added by OTArsquos services increases When the marginalcost is between 119888

1and 1198882 HArsquos equilibrium price of economy

rooms and the value added by OTArsquos service have a negativecorrelation but HArsquos equilibrium price of luxury roomswould increase with the increment of V In addition when themarginal cost is less than 119888

2 the costs of OTA to provide addi-

tional service are lower And the equilibriumprices ofHAwilldecrease when V increases

Corollary 5 There exist threshold unit wholesale prices 1199080119894

1199081

119894(119894 = 119871119867) such that

(1) (1199011198941)lowastlt (119901119894

1)119861lowast if 119908

119894gt 1199080

119894 (1199011198941)lowast= (119901119894

1)119861lowast if 119908

119894= 1199080

119894

(119901119894

1)lowastgt (119901119894

1)119861lowast if 119908

119894lt 1199080

119894

(2) (1199011198942)lowastlt (119901119894

2)119861lowast if 119908

119894gt 1199081

119894 (1199011198942)lowast= (119901119894

2)119861lowast if 119908

119894= 1199081

119894

(119901119894

2)lowastgt (119901119894

2)119861lowast if 119908

119894lt 1199081

119894

where

1199080

119894=

1198713

6119887119894(119887119894+ 120579) (119887

119894+ 2120579)

minus119888

3 (1 minus 120582120572)

1199081

119894=

120579 [(1 minus 120582120572) 1198714 minus 119888119887119894120579 (119887119894+ 2120579)]

2119887119894 (1 minus 120582120572) (119887119894 + 2120579) (31205792 + 21198872

119894+ 2119887119894120579)

(7)

FromProposition 1 it is easy to know that the equilibriumprices in the integrated system are not affected by the whole-sale prices However from Proposition 3 in the Bertrandmodel there is a positive correlation between the equilibriumprices and the wholesale prices Corollary 5 shows that theequilibrium price of HA in the Bertrand game is higherthan that in the integrated system if the wholesale price isgreater than a certain critical point (1199080

119894) Additionally if the

wholesale price is greater than1199081119894 then the equilibrium price

of OTA in Bertrand model will be higher than that in theintegrated model

Corollary 6 There exists a threshold unit wholesale price1199082

119894(119894 = 119871119867) such that if119908

119894gt 1199082

119894 then119863lowast

119894gt 119863119861lowast

119894(119894 = 119871119867)

where

1199082

119894=120579 [(1 minus 120582120572) (V120573 + 119886

119894) minus 119887119894119888]

2119887119894 (1 minus 120582120572) (119887119894 + 2120579)

(8)

Corollary 6 shows that when thewholesale price is greaterthan 119908

2

119894 the high price will lead to a lower demand in the

Bertrand game That is the reservation amount of Bertrandmodel is less than that in the integrated model The highersale price in OTA results from the higher wholesale priceThus the above result is reasonable because travelers are pricesensitive especially for leisure travelers the increase of pricewill bring the decline of reservation amount When the rela-tionship between the hotel and OTA is modeled as a Stackel-berg game the hotel canmotivate customers to reserve roomsthrough a reasonable wholesale price If the wholesale price isgreater than the threshold the sales volume in the centralizedcase is lower than that in the Bertrand case

52 Stackelberg Game In a Stackelberg game the procedureis as follows keeping thewholesale price unchanged the hotel(as the leader) announces HArsquos prices 119901119871

1and 119901119867

1of two types

of rooms respectively in order to maximize its profit 1205871 In

response to HArsquos prices OTA (as the follower) determinesprices 119901

119871

2and 119901

119867

2to maximize its profit 120587

2 Let (119901

119894

1)119878

(119901119894

2)119878(119894 = 119871119867) denote respectively HArsquos and OTArsquos prices

under a Stackelberg game

Proposition 7 The optimal prices are (119901119894

1)119878lowast (119901119894

2)119878lowast

(119894 =

119871119867) and there exists a threshold unit wholesale price 1199083119894(119894 =

119871119867) such that if 119908119894gt 1199083

119894 then (119901

119894

1)lowastlt (119901119894

1)119878lowast where

(119901119894

1)119878lowast

=(1 minus 120582120572) (1198711 minus 119908

1198941205792minus 119908119894119887119894120579) + 119888120579 (119887

119894+ 120579)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 21205792]

(119901119894

2)119878lowast

=120579 (119901119894

1)119878lowast

+ (1 minus 119904) 119886119894 + V (120579 + 120573) + 119908119894(119887119894+ 120579)

2 (119887119894+ 120579)

+119888

2 (1 minus 120582120572)

1199083

119894

=119887119894V120573 + 119886119887

119894+ 120579V119887119894+ 119886119894120579 + 120579V120573 minus 119886

119894119887119894119904

2119887119894(119887119894+ 2120579)

minus119888

2 (1 minus 120582120572)

(9)

Similar to the Bertrand competition the equilibriumprices in Stackelberg game will increase with the increase of

Discrete Dynamics in Nature and Society 7

the return expense proportion (120572) or the cancellations andno-show proportion (120582)

From Proposition 7 we can see that the Stackelbergmodel is similar to the Bertrand model that the equilibriumprices would increase with the increase of wholesale pricesFurthermore when thewholesale price is greater than1199083

119894 the

equilibrium price of HA in Stackelberg model will be higherthan that in the integrated model

In the Stackelberg game if OTA offers more effective ser-vices the equilibrium prices of OTA would increase accord-ingly The relationship between the Stackelberg equilibriumprices and V is similar to that in the Bertrand model

53 Contrastive Analysis of Bertrand and Stackelberg GamesBased on the equilibrium prices obtained in the previoussection we in this section compare the equilibriumprices andoptimal profit under Bertrand and Stackelberg games

Corollary 8 There exists a threshold unit wholesale price1199084

119894(119894 = 119871119867) such that

(1) (1199011198941)119861lowast

gt (119901119894

1)119878lowast and (119901119894

2)119861lowast

gt (119901119894

2)119878lowast if 119908

119894gt 1199084

119894

(2) (1199011198941)119861lowast

= (119901119894

1)119878lowast and (119901119894

2)119861lowast

= (119901119894

2)119878lowast if 119908

119894= 1199084

119894

(3) (1199011198941)119861lowast

lt (119901119894

1)119878lowast and (119901119894

2)119861lowast

lt (119901119894

2)119878lowast if 119908

119894lt 1199084

119894

where

1199084

119894=

120579 [(1 minus 120582120572) 1198715 + 119888120579 (119887119894+ 120579)]

4119887119894 (1 minus 120582120572) (119887119894 + 120579) (119887

119894+ 2120579)

(10)

Corollary 8 compares the equilibrium prices under theBertrand and Stackelberg game with respect to the wholesaleprice It shows that if the wholesale price is greater than1199084

119894 the pricing equilibrium under the Bertrand is higher

than that under the Stackelberg game Conversely the pricingequilibrium is lower if the wholesale price is less than 119908

4

119894

In the decentralized case both the manufacturer and theretailer want to maximize their profit A high wholesale pricecould be passed on to customersTherefore the above resultsexist In addition how to share the profit between the manu-facturer and the retailer depends on their bargaining powers

Corollary 9 If 119908119894

= 1199084

119894(119894 = 119871119867) then 120587

119878lowast

1gt 120587119861lowast

1 OTArsquos

profit has the following relationship with respect to 1199084119894

(1) 120587119861lowast2

gt 120587119878lowast

2if 119908119871gt 1199084

119871and 119908

119867gt 1199084

119867

(2) 120587119861lowast2

= 120587119878lowast

2if 119908119871= 1199084

119871and 119908

119867= 1199084

119867

(3) 120587119861lowast2

lt 120587119878lowast

2if 119908119871lt 1199084

119871and 119908

119867lt 1199084

119867

Thehotel is the leader in Stackelberg game and can alwaysbenefit from it except for the critical point1199084

119894 Comparedwith

the Bertrand game the hotel can get higher profits in Stackel-berg gamewhen the wholesale price is not equal to1199084

119894There-

fore in decentralized decision-making model the hotel willbe more inclined to be the price leader in order to ensure thatit can achieve higher profits

Corollary 9 indicates that the Stackelberg model is supe-rior to the Bertrand model when the wholesale price is less

than the critical point1199084119894 Not only the hotel but alsoOTA can

gain more profit from the Stackelberg game Though OTA isa follower in Stackelberg game the profit will not be reducedbecause the lower wholesale prices can compensate for theloss of profit caused by the opening of HA channel Conse-quently the hotel should play the role of the price leader inthe supply chain and develop reasonable wholesale prices toachieve optimization of the whole supply chain profit whileoptimizing its own profit

Corollary 10 Under either Bertrand or Stackelberg equi-librium channel prices there exists optimal wholesale price119908lowast

119894(119894 = 119871119867) that maximizes the total equilibrium channel

profit where 119908lowast119894= 11986611198662

According to Corollary 10 there exists optimal wholesaleprice 119908

lowast

119894(119894 = 119871119867) that maximizes the total equilibrium

channel profit under either Bertrand or Stackelberg gameThe optimal wholesale price will optimize the decentralizeddecision-making supply chainMeanwhile both the hotel andtheOTA can benefit from the optimal wholesale priceThere-fore the reasonable wholesale price can help promotemutualcooperation and communication between the supply chainmembers

54 Contrastive Analysis of Two Channels in the Supply Chain

Corollary 11 There exists a threshold unit market share of HAin the tourism dual-channel supply chain (119904

0) such that when

119904 gt 1199040 the hotelrsquos profit from HA is higher than that from OTA

Keeping the wholesale prices and sales prices unchangedwhen the market share of HA in the tourism dual-channelsupply chain exceeds a certain value 119904

0 the hotelrsquos profit from

HA is higher than that from OTA The result is suitable forthe integrated system Bertrand and Stackelberg games Fromthe perspective of hotelrsquos revenue the hotel should explorethe channel for direct selling actively Also the hotel canstrengthen the promotion of HA channel to improve thecustomerrsquos understanding and preference for theHA channelBut the premise is that the profit growth from the promotioncan compensate for the cost According to the statistical datafrom the hotel price competitiveness analysis report in thefirst half of 2012 we know that the booking cost from directselling channel is about 1 dollar per night but that fromOTAis about 10 dollars per night Booking cost can be reducedby 46 if the direct selling level is doubled Then improvingthe market share of direct selling will greatly reduce the costMore comparisons of different channelrsquos profits in eachmodelcan be found in part of numerical analysis

6 Overbooking

This section extends to consider the overbooking caseRegarding overbooking in the hospitality industry the com-mon practice is that the hotel upgrades the room type ortransfers customers to other hotels nearby that have the samelevel and same type In airline industry if customers aredenied boarding after arriving at the airport the airline will

8 Discrete Dynamics in Nature and Society

provide a free upgrade endorse the ticket or provide com-pensation for the customers according to specific situationCompared to the hotels the airlines cannot transfer cus-tomers to other companies The air ticket alteration will usu-ally disrupt customersrsquo traveling schedule Though the over-booking by airlines has been well studied in the literature ourresearch is new in the hospitality industry by considering theoverbooking withwithout room transfer with the hope thatcertain implications can be enlightened to the hotel man-agers

The hotel wants to increase the occupancy rates toincrease the profits through overbooking However over-booking will lead to the risk that the actual occupancyamount is greater than the number of hotel roomsThereforethe hotel has to provide compensation to travelers who can-not check in that is overbooking cost The greater the num-bers of overbooking the less the probability of room vacancybut at the same time travelers are more likely to be refusedby the hotel Therefore the hotel must balance between thevacancy lost and the overbooking costs We develop a modelto analyze the overbooking choice

In reality the OTA is always a crucial partner of hotelsfor it can attract a large number of customers for hotelsand improve their occupancy rates [36] Spontaneously theOTA plays an increasingly significant role in the distributionsystems of hotels [5 7] By contrast the HA mainly providesa platform for individual guest Compared with individualcustomers hotel pays more attention to the long-term coop-eration relationship with the OTA Therefore in our modelwe assume that when the market demand is greater than thesupply and the hotel does not carry out overbooking the hotelwould give priority to customers who are booking fromOTA

61 Without Room Transfer Here we consider the casewith no room transfer When the actual occupancy amountexceeds the total quantity of rooms the hotel does not arrangeother alternative accommodation for the customers who can-not check in But the hotel must pay the loss of goodwill costSuppose that the overbooking quantity of economy and lux-ury rooms isΔ119862

119871andΔ119862

119867and the overbooking cost is 119888

119871and

119888119867 respectivelyWe discuss economy roomsrsquo overbooking The actual

occupancy can be either of the following two cases (1) when119876119871

lt 119863119871

1+ 119863119871

2le 119876119871+ Δ119862

119871 the reservation amount of

rooms is 1198631198711+ 119863119871

2 so the actual occupancy amount is (119863119871

1+

119863119871

2)(1 minus 120582) (2) when119863

119871

1+ 119863119871

2gt 119876119871+ Δ119862

119871 the reservation

amount is 119876119871+ Δ119862119871 then the actual occupancy amount is

(119876119871+Δ119862119871)(1 minus 120582) Therefore if (119876

119871+Δ119862119871)(1 minus 120582) le 119876

119871 that

is Δ119862119871le 120582119876119871(1 minus 120582) the profit of hotel is

120587119871

11= (1 minus 120582120572) [119901

119871

1(119876119871+ Δ119862119871minus 119863119871

2) + 119908119871119863119871

2] (11)

If (119876119871+ Δ119862119871)(1 minus 120582) ge 119876

119871 that is Δ119862

119871ge 120582119876119871(1 minus 120582)

the economy roomsrsquo actual occupancy amount exceeds theeconomy roomsrsquo number in the hotel so the hotel must paythe overbooking cost then the profit of hotel is

120587119871

12= (1 minus 120582120572) [119901

119871

1(119876119871+ Δ119862119871minus 119863119871

2) + 119908119871119863119871

2]

minus (119901119871

1+ 119888119871) [(119876119871+ Δ119862119871) (1 minus 120582) minus 119876

119871]

(12)

Proposition 12 Without considering roomsrsquo transfer the opti-mal overbooking quantity of economy rooms and luxury roomsis

Δ119862lowast

119894=

120582

1 minus 120582119876119894 119894 = 119871119867 (13)

FromProposition 12 we know that the higher the propor-tion of customer cancellations and no-show is the larger theoptimal overbooking quantity of the hotel will be With theincrease of 120572 the penalty that customers need to pay for theircancellation or no-show decreases Two following extremesituations are considered When 120572 = 1 the hotel will returnall the guarantee fee in case of customersrsquo cancellation or no-showThat is the same as the hotel does not charge customersany guarantee fee when customers book the rooms Undersuch circumstances customers can book rooms for severaldays firstly after they identify a specific itinerary they cancancel the extra rooms for they do not suffer any loss It is nodoubt that such regulation will increase the cancellation andno-show rate On the other hand if 120572 = 1 all the guaranteefee will not be returned after cancellation or no-show In thiscase customers need to reserve a room cautiously If it is notnecessary customers will not choose cancellation or no-showbecause the penalty cost is too high Such policy will reducethe cancellation and no-show rate Spontaneously to someextent 120572 and 120582 are positive correlation When the hotelincreases proportion 120572 it would like to increase the over-booking quantity so as to increase the actual occupancy rateNowadays the time-limited orders are widely used amonghotels Such regulation cannot only reduce customersrsquo lossfor the change of schedule but also help the hotel confirmthe orders so as to handle the overbooking phenomenon inadvance

In addition the risk of overbooking the economy roomsis relatively lower than the luxury rooms Compared toeconomic rooms it is more difficult for the hotel to findalternative luxury rooms to satisfy the customers Naturallyoverbooking cost of luxury room is higher For instance ifeconomy rooms are overbooked the hotel can transfer thecustomers to luxury rooms and the customers are willingto accept By contrast if luxury rooms are overbooked cus-tomers are not willing to accept the adjustment from luxuryrooms to economic rooms This implies that the hotel has topay a higher default costTherefore the hotel should be morecareful to choose the overbooking quantity of luxury rooms

62 With Room Transfer The following discusses the casewith room transfer Firstly when the economy rooms areinsufficient and luxury rooms have a surplus customers cancheck in the hotelrsquos luxury rooms with the price of economyrooms Customers spend the same money and can enjoybetter service so they are willing to accept this adjustmentSecondly when the luxury roomsrsquo actual occupancy amountexceeds the number of luxury rooms in the hotel the hotelusually transfers customers to other hotels nearby that havethe same level and same type because the customers whobook luxury room have a high requirement Customers canenjoy the same service so they are willing to accept this trans-fer However the hotelrsquos credibility in customersrsquo mind will be

Discrete Dynamics in Nature and Society 9

damaged and it must pay the additional costsThirdly if boththe economy rooms and luxury rooms are unable to meetthe demand the hotel usually transfers the customers whocannot check in to other hotels Note that when119863119894

1+119863119894

2gt 119876119894

119894 = 119871119867 if the hotel does not overbook its profit is

120587111

= (1 minus 120582120572) [119901119871

1(119876119871minus 119863119871

2) + 119901119867

1(119876119867minus 119863119867

2)

+ 119908119871119863119871

2+ 119908119867119863119867

2]

(14)

Proposition 13 With room transfer there exists threshold unitoverbooking cost 119888

1198940 such that if 119888

119894lt 1198881198940 then overbooking is

profitable for the hotel where

1198881198940=(1 minus 120582120572) 119901

119894

1

1 minus 120582 119894 = 119871119867 (15)

From Propositions 12 and 13 we conclude that the hotelshould control the overbooking quantity in a certain rangeto prevent lacking of rooms If the overbooking proportionis too large then the hotel may face a loss Only when theoverbooking cost is low the hotel can obtain additional profitOtherwise if the overbooking cost exceeds a certain valuethe hotelrsquos profit would be lower when it carries out over-booking As the market demand increases the supply is closeto saturation and then the overbooking costs will be higherTherefore when the market demand is excessive the hotelshould strictly control the proportion of overbooking Inaddition if the number of hotels that have the same level andtype in the same region is little that is the possibility to trans-fer customer is small then the hotel should lower the propor-tion of overbooking

The proportion of overbooking depends on the propor-tion of customer cancellations andno-showaswell as the totalnumber of hotel rooms so the hotel can analyze the historicaldata to develop an appropriate overbooking proportion so asto maximize the hotelrsquos expected profit

Proposition 14 When the economy rooms and luxury roomsare both overbooked the optimal centralized prices are asfollows 119894 = 119871119867

119901119894lowast

14= 119901119894lowast

1+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

119901119894lowast

24= 119901119894lowast

2+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

(16)

Bertrand and Stackelberg prices are as follows

(119901119894

14)119861lowast

= (119901119894

1)119861lowast

+2119888119894

119906119887119894(119887119894+ 120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

24)119861lowast

= (119901119894

2)119861lowast

+120579119888119894

119906119887119894 (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

14)119878lowast

= (119901119894

1)119878lowast

+119888119894

119906119887119894(2119887119894+ 3120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 21205792]

(119901119894

24)119878lowast

=120579 (119901119894

14)119878lowast

+ (1 minus 119904) 119886119894 + V (120579 + 120573) + 119908119894(119887119894+ 120579)

2 (119887119894+ 120579)

+119888

2 (1 minus 120582120572)

(17)

For the hotel the premise to overbook rooms is that themarket demand is greater than the supply When the hotelfaces the risk of overbooking the equilibrium prices in bothcentralized and decentralized decision-making supply chainwill improve In the busy season in order to reduce the riskof overbooking the hotel would increase the prices and theincrement will increase as the transfer cost increases From(16) and (17) we can know that the increment in centralizeddecision-making model is the greatest and that in Bertrandgame is the smallest

7 Numerical Analysis

In this section we do some numerical experiment to gainmore insights According to the China Hotel Sales Chan-nel Report by I-Research (httpreportiresearchcnreport2013031892shtml) there are 381 of the hotels that aresuitable for high-end travelers and 619 of the hotels thatare suitable for low-end travelersTherefore this part assumesthat the proportion of the economical rooms and the luxuryrooms is 4 6 that is 119886

119871= 06119886 119886

119867= 04119886 Other parameter

settings are made as follows 119886 = 600 119904 = 05 and 119887119871= 06

119887119867= 02 120573 = 120579 = 05 120578 = 004 120572 = 08 120582 = 01 119908

119894= 05119901

119894

1

(119894 = 119871119867) In the following we investigate the impact of V onthe optimal prices and profits

When V = 0 that is the OTA does not offer any servicethen the optimal prices of HA are equal to the prices ofOTA Since 119887

119871gt 120573 gt 119887

119867 then the market of economy

rooms is service-oriented while the market of luxury roomsis price-oriented FromFigure 2 we can know that whenOTAoffers more services OTArsquos optimal price will be increasedaccordingly It is reasonable that if V increases the cost ofOTAwill also definitely increase With the increase of V 119901119871lowast

1will

decline slowly while 119901119867lowast1

will increaseThe OTArsquos profit status becomes better with the improve-

ment of its price But as the V increases the cost of OTA willalso definitely increase When V is equal to 27 then the profitof OTA is the highest If V is larger then the high costs willreduce the profits of OTAWhen V is equal to 34 the profit ofthewhole supply chain is the highest So from the perspectiveof the supply chain V is expected to be 34 rather than 27Similarly for the integrated system the profit of the OTAalso rises first and then declines with the increase of V Aftercalculationwe can get thatwhen V = 27 both120587119861lowast

2and120587119878lowast2will

be the highest From Figures 3 and 4 we know that the OTAwould tend to offer service that valued 27 so as to maximizeits own profit

After calculation we can conclude that when V = 34 then120587119861lowast is highest when V = 35 then 120587

119878lowast is highest (Figure 5)

10 Discrete Dynamics in Nature and Society

0 10 20 30 40 50 60 70 80100

150

200

250

300

350

400

450

Pric

e

pLlowast

1

pLlowast

2

pHlowast

1

pHlowast

2

Value added by OTArsquos services ()

Figure 2 Equilibrium prices in the integrated system

0 10 20 30 40 50 60 70 800

1

2

3

4

5

6

7

Profi

t

times104

120587lowast

1

120587lowast

2

120587lowast

Value added by OTArsquos services ()

Figure 3 Profits in the integrated system

From the perspective of the supply chain theOTA is expectedto offer more services Despite the rising cost of OTA willlower its profit the hotel can lower the wholesale prices tocoordinate the distribution of profits so as to achieve a win-win situation

In the following we focus on the comparison of differentchannelrsquos profit in each model Figure 6 depicts the curves ofthe total profits of the HAOTA channels in the integratedsystem with respect to V Figure 7 draws the curves of the dif-ferent channelsrsquo profits under both Bertrand and Stackelberggame The profit of the HA channel refers to the profit thatthe hotel derived from the HA channelThe profit of the OTA

0 10 20 30 40 50 60125

13

135

14

145

15

155

16

165

Profi

t

times104

120587Blowast

2

120587Slowast

2

Value added by OTArsquos services ()

Figure 4 OTArsquos profits under two games

0 10 20 30 40 50 60 70 8052

53

54

55

56

57

58

59

6

61

62

Profi

t

times104

120587Blowast

2

120587Slowast

2120587lowast

Value added by OTArsquos services ()

Figure 5 The profit comparison

channel involves the OTArsquos profit and the hotelrsquos profit gainedfrom the OTA channel

As shown in Figures 6 and 7 with the increase of V theprofit of the OTA channel will increase first and will thendecrease This indicates that a high level of service by OTAwill be detrimental to the channel profit That is because ahigh level of service will bring a high cost undoubtedly Forthe integrated model and Bertrand game model this disad-vantage is more evident The OTArsquos service can motivate theactual purchase behavior of customers in the OTA channelWhen V is relatively lower the additional profits from OTArsquos

Discrete Dynamics in Nature and Society 11

0 10 20 30 40 50 60 70 8018

2

22

24

26

28

3

32

34

36

38

4

Profi

t

HA channelOTA channel

times104

Value added by OTArsquos services ()

Figure 6 Channel profits in the integrated system

0 10 20 30 40 50 60 70 8005

1

15

2

25

3

35

4

45

Profi

t

HA channel in Bertrand gameOTA channel in Bertrand gameHA channel in Stackelberg gameOTA channel in Stackelberg game

times104

Value added by OTArsquos services ()

Figure 7 Channel profits in two games

service are enough to compensate for the cost In this casethe hotel and the OTA can get more profit from providing theservice However when V is high the additional profits fromOTArsquos service cannot make up for the high cost In such phe-nomenon the OTA should not increase investment in ser-vice

For both integrated model and Bertrand game modelwith the increase of V the profit of the HA channel willdecrease first and will then increase while in the Stackelberggamemodel the profit of theHA channel will always increase

with V With Figure 2 we can know that when OTA providesmore additional services it tends to increase its price Someof the customers will turn to reserve rooms from the HAbecause of the excessively high price in OTA As a result thehotel can gain more profits from the HA channel

8 Conclusion

With the development of e-commerce the providers oftourism products are more inclined to build dual-channelsIn this paper we consider the direct selling channel of HAand the traditional retail channel ofOTA from the perspectiveof tourism supply chain We develop a two-echelon tourismsupply chain model involving one hotel and one OTA wheretheOTAprovides related service Customers will be refundedpartially in case of cancelation or no-show We investigatethe optimal pricing strategies under several common casesThe integrated operation and the decentralized operationbased on Bertrand and Stackelberg games are studied andcorresponding equilibrium pricing policies are obtained

Our findings demonstrate that the hotel plays a crucialrole in optimizing the benefits of supply chain Consideringthe overall profit of the supply chain the hotel should act as aleader in dual-channel supply chain and formulate reasonablewholesale prices to improve the cooperative enthusiasm ofOTA so as to achieve optimization of the whole supplychain A lower wholesale price can help reduce OTArsquos loss ofprofit because of the opening of HA channel In addition weconsider the overbooking of the hotel and obtain the optimaloverbooking quantity We conclude that the hotel can alwaysobtain higher profits when the overbooking proportion iscontrolledwithin a certain range Otherwise if the overbook-ing proportion is too high the hotel can get extra profits onlywhen the overbooking cost is lower than a certain value

The contribution of this paper is that we extend tourismsupply chain to the dual-channel structure in which the hotelopens its direct channel to sell tourism products And theextant literature only refers to the single channel In additionwe realize that customer cancellations andno-showoccur fre-quently in hotel industry Thus we develop the game modelsbased on such phenomenon At last we derive the conditionsunder which the hotel dominant case is profitable for boththe supply chain members Our results can provide hotelsand OTAs with some new managerial insights under thedual-channel environment

This research can be extended in several directions infuture work For example in this paper we assume that allinformation is known to the hotel and OTA However someinformation could be asymmetric (eg see Chen [37]) Thuswe can explore the Bayesian equilibrium under asymmetricinformation settings Secondly the assumption of lineardemand is a limitation of this paperWe can further study thedynamic pricing in tourism dual-channel supply chain

Appendix

A Proof of Corollary 8

First we set (1199011198711)119861lowast

gt (119901119871

1)119878lowast which can be expressed as

12 Discrete Dynamics in Nature and Society

(1 minus 120582120572) (120579119886119871 + 120579119904119886119871+ 2119887119871119904119886119871+ 120579V120573 + 3119908

1198711205792+ 3119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

gt(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(A1)

The above equation can be simplified as

119908119871gt120579 [(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)]

4119887119871 (1 minus 120582120572) (119887119871 + 120579) (119887

119871+ 2120579)

(A2)

So we can get Corollary 8 B Proof of Corollary 9

If (1199011198941)119878lowast

gt (119901119894

1)119861lowast then

(1 minus 120582120572) (120579119886119894 + 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 2119908

1198941205792+ 2119908119894119887119894120579 minus 1205792V minus 2120579119887

119894V) + 119888120579 (119887

119894+ 120579)

minus (1 minus 120582120572) ((119901119894

1)119878lowast

+ (119901119894

1)119861lowast

) [2 (119887119894+ 120579)2minus 1205792] gt 0

120587119878lowast

1minus 120587119861lowast

1=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

2 (119887119871+ 120579)

((119901119871

1)119878lowast

minus (119901119871

1)119861lowast

)

+(1 minus 120582120572) (120579119886119867 + 120579119904119886

119867+ 2119887119867119904119886119867+ 120579V120573 + 2119908

1198671205792+ 2119908119867119887119867120579 minus 1205792V minus 2120579119887

119867V) + 119888120579 (119887

119867+ 120579)

2 (119887119867+ 120579)

((119901119867

1)119878lowast

minus (119901119867

1)119861lowast

)

minus (1 minus 120582120572)2 (119887119871+ 120579)2minus 1205792

2 (119887119871+ 120579)

[((119901119871

1)119878lowast

)2

minus ((119901119871

1)119861lowast

)2

] minus (1 minus 120582120572)2 (119887119867+ 120579)2minus 1205792

2 (119887119867+ 120579)

[((119901119867

1)119878lowast

)2

minus ((119901119867

1)119861lowast

)2

] gt 0

(B1)

If (1199011198711)119878lowast

lt (119901119871

1)119861lowast and (119901

119867

1)119878lowast

lt (119901119867

1)119861lowast we can prove

120587119878lowast

1gt 120587119861lowast

1similarly

From Propositions 3 and 7 with (3) we obtain that

120587119861lowast

2minus 120587119878lowast

2=

120579

4 (119887119871+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119871 + V (120573 + 120579) minus 119908119871(119887119871+ 120579)]

minus 2119888 (119887119871+ 120579) + 120579 (1 minus 120582120572) ((119901

119871

1)119861lowast

+ (119901119871

1)119878lowast

)

sdot ((119901119871

1)119861lowast

minus (119901119871

1)119878lowast

) +120579

4 (119887119867+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119867 + V (120573 + 120579) minus 119908 (119887119867+ 120579)]

minus 2119888 (119887119867+ 120579) + 120579 (1 minus 120582120572) ((119901

119867

1)119861lowast

+ (119901119867

1)119878lowast

)

sdot ((119901119867

1)119861lowast

minus (119901119867

1)119878lowast

)

(B2)

Note that

119863119894

2= [(1 minus 119904) 119886119894 minus 119887

119894119901119894

2] + 120573V + 120579 (119901

119894

1+ V minus 119901

119894

2) gt 0 (B3)

so we show that

2 (1 minus 120582120572) [(1 minus 119904) 119886119894 + V (120573 + 120579) minus 119908119894(119887119894+ 120579)]

minus 2119888 (119887119894+ 120579) + 120579 (1 minus 120582120572) ((119901

119894

1)119861lowast

+ (119901119894

1)119878lowast

)

gt 0

(B4)

Thus we have the following

(1) 120587119861lowast2

gt 120587119878lowast

2 if (1199011198711)119861lowast

gt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

gt (119901119867

1)119878lowast

(2) 120587119861lowast2

= 120587119878lowast

2 if (1199011198711)119861lowast

= (119901119871

1)119878lowast and (119901

119867

1)119861lowast

= (119901119867

1)119878lowast

(3) 120587119861lowast2

lt 120587119878lowast

2 if (1199011198711)119861lowast

lt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

lt (119901119867

1)119878lowast

Combined with Corollary 8 the proposition is proved

Discrete Dynamics in Nature and Society 13

C Proof of Corollary 10

The profit of hotel from the economy rooms is as follows

120587119871

= [(1 minus 120582120572) (119904119886119871 minus 120579V) minus 119888120579] 119901119871

1

+ [(1 minus 120582120572) (119886119871 minus 119904119886119871+ 120573V + 120579V) + 119888 (119887

119871+ 120579)] 119901

119871

2

+ 2120579 (1 minus 120582120572) 119901119871

1119901119871

2minus (1 minus 120582120572) (119887119871 + 120579) (119901

119871

1)2

minus (1 minus 120582120572) (119887119871 + 120579) (119901119871

2)2

minus (119886119871minus 119904119886119871+ 120573V + 120579V) 119888

(C1)

Define (119901119871

1)119861(119878)

= (119860119871

1)119861(119878)

+ (119861119871

1)119861(119878)

119908119871 (1199011198712)119861(119878)

=

(119860119871

2)119861(119878)

+ (119861119871

2)119861(119878)

119908119871 where

(119861119871

1)119861

=3120579 (119887119871+ 120579)

4 (119887119871+ 120579)2minus 1205792

(119861119871

1)119878

=120579 (119887119871+ 120579)

2 (119887119871+ 120579)2minus 1205792

(119861119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119861119871

1)119861(119878)

+1

2

(119860119871

1)119861

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

(119860119871

1)119878

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(119860119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119860119871

1)119861(119878)

+(1 minus 120582120572) [(1 minus 119904) 119886119871 + V (120579 + 120573)] + 119888 (119887

119871+ 120579)

2 (1 minus 120582120572) (119887119871 + 120579)

(C2)

Let 120597120587119871120597119908 = 0 then we get119908lowast

119871 Similarly we can get119908lowast

119867

D Proof of Proposition 12

Let 120587119889minus 120587119903gt 0 then we can get 119904

0 where the profits of hotel

from HA and OTA are as follows

120587119889= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1)

120587119903= (1 minus 120582120572) (119908119871119863

119871

2+ 119908119867119863119867

2)

(D1)

E Proof of Corollary 11

If Δ119862119871le 120582(1 minus 120582)119876

119871 then the profit of hotel is 120587119871

11 The

derivative of 12058711987111(Δ119862119871) is 120597120587119871

11120597Δ119862119871= (1 minus 120582120572)119901

119871

1gt 0 So

with the increase of Δ119862119871 12058711987111

will increase When Δ119862119871

=

120582(1 minus 120582)119876119871 12058711987111

is maximized If Δ119862119871

ge 120582(1 minus 120582)119876119871

then the profit of hotel is 12058711987112 The derivative of 120587119871

12(Δ119862119871) is

120597120587119871

12120597Δ119862119871= (1 minus 120582120572)119901

119871

1minus (1 minus 120582)(119901

119871

1+ 119888119871) lt 0 So with the

increase of Δ119862119871 12058711987111will decline When Δ119862

119871= 120582(1 minus 120582)119876

119871

120587119871

11is maximizedSimilarly we can get Δ119862lowast

119867

F Proof of Proposition 13

Assume that the overbooking proportion is 120574119871and 120574119867

(1) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) le 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

That is

120574119867lt

120582

1 minus 120582lt 120574119871

le120582119876119871+ 119876119867[1 minus (1 minus 120582) (1 + 120574

119867)]

(1 minus 120582)119876119871

(F1)

Thus the hotel would like to overbook to get more profitrather than room vacancy

(2) Consider (1198631198711+119863119871

2)(1minus120582) lt 119876

119871and (119863119867

1+119863119867

2)(1minus120582) gt

119876119867That is 120574

119871lt 120582(1 minus 120582) lt 120574

119867 Then the profit of hotel is

120587112

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F2)

Thenwhen 119888119867119906

lt (1minus120582120572)119901119867

1(1minus120582) that is120587

112minus120587111

gt 0the hotel would carry out overbooking

(3) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

14 Discrete Dynamics in Nature and Society

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867lt 120582(1 minus 120582) Then the profit of hotel is

120587113

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2+ 119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876]

(F3)

Then when 119888119871

119906lt (1 minus 120582120572)119901

119871

1(1 minus 120582) 120587

113minus120587111

gt 0 thusthe hotel would carry out overbooking

(4) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) gt 119876

119867

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867gt (120582119876

119867+ 119876119871[1 minus (1 minus 120582)(1 + 120574

119871)])(1 minus 120582)119876

119867

Then the profit of hotel is as follows

120587114

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2) (1 minus 120582) minus 119876

119871]

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F4)

Then when 119888119871119906lt (1minus120582120572)119901

119871

1(1minus120582) and 119888119867

119906lt (1minus120582120572)119901

119867

1

(1 minus 120582) 120587114

minus 120587111

gt 0 overbooking is preferred

G Threshold Values

Threshold values are as follows

1198711= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 3119908

1198941205792+ 3119908119894119887119894120579

minus 1205792V minus 2120579119887

119894V

1198712= 2119886119894(119887119894+ 120579) minus 119904119886

119894(2119887119894+ 120579) + 120579

2119908119894+ 2 (120579 + 120573) (119887

119894

+ 120579) V + 2119908119894(119887119894+ 120579)2minus 1205792V

1198713= 4120579V119887

119894120573 minus 120579119904119886

119894119887119894+ 2V1205731198872

119894+ 31198861198941205792+ 4119886119894119887119894120579

minus 21198861198941198872

119894119904 + 3120579

2V120573 + 1205792V119887119894+ 2120579V1198872

119894+ 21198861198941198872

119894

1198714= 3119886119894119887119894120579 + 3120579

2V120573 minus 2120579V1198872119894minus 1205792V119887119894+ 31198861198941205792

+ 21198861198941198872

119894119904 + 119886119887

119894119904120579 + 3119887

119894120573V120579

1198715= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 minus 120579

2V minus 2120579119887119894V

1198661= [(1 minus 120582120572) (119904119886119894 minus 120579V) minus 119888120579] (119861

119894

1)119861(119878)

+ [(1 minus 120582120572) (119886119894 minus 119904119886119894+ 120573V + 120579V) + 119888 (119887

119894+ 120579)]

sdot (119861119894

1)119861(119878)

+ 2120579 (1 minus 120582120572) [(119860119894

1)119861(119878)

(119861119894

2)119861(119878)

+ (119861119894

1)119861(119878)

(119860119894

2)119861(119878)

] minus 2 (1 minus 120582120572) (119887119894 + 120579)

sdot [(119860119894

1)119861(119878)

(119861119894

1)119861(119878)

+ (119860119894

2)119861(119878)

(119861119894

2)119861(119878)

]

1198662= 2 (1 minus 120582120572)

sdot (119887119894+ 120579) [((119861

119894

1)119861(119878)

)

2

+ ((119861119894

2)119861(119878)

)

2

]

minus 2120579 (119861119894

1)119861(119878)

(119861119894

2)119861(119878)

1199040= ((119887119871+ 120579) (119901

119871

1)2

+ (119887119867+ 120579) (119901

119867

1)2

+ 120579119908119871(119901119871

1minus 119901119871

2) + 120579119908

119867(119901119867

1minus 119901119867

2)

+ 120579V (1199011198711+ 119901119867

1) + (119908

119871+ 119908119867) (120573 + 120579) V

+ 119908119871(119886119871minus 119887119871119901119871

2) + 119908119867(119886119867minus 119887119867119901119867

2)

minus 120579 (119901119871

1119901119871

2+ 119901119867

1119901119867

2)) (119886119871(119901119871

1+ 119908119871)

+ 119886119867(119901119867

1+ 119908119867))minus1

(G1)

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The authors thank associate editor and anonymous refereesfor their numerous constructive comments and encourage-ment that have improved their paper greatly The work waspartly supported by (i) the National Natural Science Founda-tion ofChina (71201083 71572058 and 71571100) (ii) the Fun-damental Research Funds for the Central Universities SCUT(2015ZZ057) (iii) Jiangsu Province Science Foundation forYouths (BK2012379) and (iv) the Fundamental ResearchFunds for the Central Universities (NS2015076)

References

[1] J Li W N Zhang H Xu and J Jiang ldquoDynamic competitionand cooperation of road infrastructure investment of multipletourism destinations a case Study of Xidi and Hongcun WorldCulturalHeritagerdquoDiscreteDynamics inNature and Society vol2015 Article ID 962028 10 pages 2015

[2] T Paksoy EOzceylan andG-WWeber ldquoProfit oriented supplychain network optimizationrdquoCentral European Journal of Oper-ations Research vol 21 no 2 pp 455ndash478 2013

[3] X Zhang H Song and G Q Huang ldquoTourism supply chainmanagement a new research agendardquo Tourism Managementvol 30 no 3 pp 345ndash358 2009

[4] Z Yang and J Cai ldquoDo regional factors matter Determinantsof hotel industry performance in Chinardquo TourismManagementvol 52 pp 242ndash253 2016

[5] B Pan L Zhang and R Law ldquoThe complex matter of onlinehotel choicerdquoCornell Hospitality Quarterly vol 54 no 1 pp 74ndash83 2013

[6] L Ling X Guo and C Yang ldquoOpening the online marketplacean examination of hotel pricing and travel agency on-line

Discrete Dynamics in Nature and Society 15

distribution of roomsrdquo Tourism Management vol 45 pp 234ndash243 2014

[7] L Ling Y Dong X Guo and L Liang ldquoAvailability man-agement of hotel rooms under cooperation with online travelagenciesrdquo International Journal of Hospitality Management vol50 pp 145ndash152 2015

[8] J N K Liu andE Y Zhang ldquoAn investigation of factors affectingcustomer selection of online hotel booking channelsrdquo Interna-tional Journal of Hospitality Management vol 39 pp 71ndash832014

[9] L Fox ldquoFour Seasons Unveils $18 Million Website as LuxuryTravel Growsrdquo 2012 httpwwwtnoozcomarticlefour-sea-sons-unveils-18-million-dollar-website-as-luxury-travel-grows

[10] C-M Chen and Y-C Lin ldquoThe influence of uncertain demandon hotel capacityrdquo International Journal of Hospitality Manage-ment vol 34 no 1 pp 462ndash465 2013

[11] S Yang G Q Huang H Song and L Liang ldquoGame-theoreticapproach to competition dynamics in tourism supply chainsrdquoJournal of Travel Research vol 47 no 4 pp 425ndash439 2009

[12] G Q Huang H Song and X Zhang ldquoA comparative analysis ofquantity and price competitions in tourism supply chain net-works for package holidaysrdquo Service Industries Journal vol 30no 10 pp 1593ndash1606 2010

[13] Y Huang H Song G Q Huang and J Lou ldquoA comparativestudy of tourism supply chains with quantity competitionrdquoJournal of Travel Research vol 51 no 6 pp 717ndash729 2012

[14] H K Lee and Y Fernando ldquoThe antecedents and outcomes ofthe medical tourism supply chainrdquo Tourism Management vol46 pp 148ndash157 2015

[15] W-Y K Chiang D Chhajed and J D Hess ldquoDirect marketingindirect profits a strategic analysis of dual-channel supply-chain designrdquoManagement Science vol 49 no 1 pp 1ndash20 2003

[16] A A Tsay and N Agrawal ldquoChannel conflict and coordinationin the E-commerce agerdquo Production and Operations Manage-ment vol 13 no 1 pp 93ndash110 2004

[17] Q-H Li and B Li ldquoDual-channel supply chain equilibriumproblems regarding retail services and fairness concernsrdquoApplied Mathematical Modelling 2016

[18] S Panda N M Modak S S Sana and M Basu ldquoPricingand replenishment policies in dual-channel supply chain undercontinuous unit cost decreaserdquo Applied Mathematics and Com-putation vol 256 pp 913ndash929 2015

[19] Y Liu C Ding C Fan and X Chen ldquoPricing decision underdual-channel structure considering fairness and free-ridingbehaviorrdquo Discrete Dynamics in Nature and Society vol 2014Article ID 536576 10 pages 2014

[20] J Chen H Zhang and Y Sun ldquoImplementing coordinationcontracts in a manufacturer Stackelberg dual-channel supplychainrdquo Omega vol 40 no 5 pp 571ndash583 2012

[21] Q Ding C Dong and Z Pan ldquoA hierarchical pricing decisionprocess on a dual-channel problem with one manufacturer andone retailerrdquo International Journal of Production Economics vol175 pp 197ndash212 2016

[22] B Rodriguez and G Aydin ldquoPricing and assortment decisionsfor a manufacturer selling through dual channelsrdquo EuropeanJournal of Operational Research vol 242 no 3 pp 901ndash9092015

[23] T Lockyer ldquoThe perceived importance of price as one hotelselection dimensionrdquo Tourism Management vol 26 no 4 pp529ndash537 2005

[24] C-M Chen H-W Yang E Y Li and C-C Liu ldquoHow doeshotel pricing influence guest satisfaction by the moderatinginfluence of room occupancyrdquo International Journal of Hospi-tality Management vol 49 pp 136ndash138 2015

[25] J-M Espinet M Fluvia R Rigall-I-Torrent and A Salo ldquoHotelcharacteristics and seasonality in prices an analysis usingSpanish tour operatorsrsquo brochuresrdquo Tourism Economics vol 18no 4 pp 749ndash767 2012

[26] C Juaneda J M Raya and F Sastre ldquoPricing the time and loca-tion of a stay at a hotel or apartmentrdquo Tourism Economics vol17 no 2 pp 321ndash338 2011

[27] G Abrate G Fraquelli and G Viglia ldquoDynamic pricing strate-gies evidence from European hotelsrdquo International Journal ofHospitality Management vol 31 no 1 pp 160ndash168 2012

[28] D Q Yao and J J Liu ldquoCompetitive pricing of mixed retail ande-tail distribution channelsrdquo Omega vol 33 no 3 pp 235ndash2472005

[29] J Zhao and L Wang ldquoPricing and retail service decisionsin fuzzy uncertainty environmentsrdquo Applied Mathematics andComputation vol 250 pp 580ndash592 2015

[30] A A Tsay and N Agrawal ldquoChannel dynamics under priceand service competitionrdquo Manufacturing amp Service OperationsManagement vol 2 no 4 pp 372ndash391 2000

[31] S C Choi ldquoPrice competition in a duopoly common retailerchannelrdquo Journal of Retailing vol 72 no 2 pp 117ndash134 1996

[32] Y Bakos andE Brynjolfsson ldquoBundling and competition on theinternetrdquoMarketing Science vol 19 no 1 pp 63ndash82 2000

[33] H Song J H Kim and S Yang ldquoConfidence intervals fortourism demand elasticityrdquo Annals of Tourism Research vol 37no 2 pp 377ndash396 2010

[34] DMHanssens L J Parsons andR L SchultzMarket ResponseModels Econometric and Time Series Analysis Kluwer Aca-demic Publishers Boston Mass USA 2nd edition 2001

[35] H Kurata D-Q Yao and J J Liu ldquoPricing policies under directvs indirect channel competition and national vs store brandcompetitionrdquo European Journal of Operational Research vol180 no 1 pp 262ndash281 2007

[36] R Law and C Cheung ldquoA study of the perceived importance ofthe overall website quality of different classes of hotelsrdquo Inter-national Journal of Hospitality Management vol 25 no 3 pp525ndash531 2006

[37] K B Chen ldquoProcurement strategies and coordination mecha-nism of the supply chain with one manufacturer and multiplesuppliersrdquo International Journal of Production Economics vol138 no 1 pp 125ndash135 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Differential EquationsInternational Journal of

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Complex AnalysisJournal of

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Journal of

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Discrete Dynamics in Nature and Society

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Discrete Dynamics in Nature and Society

Ctripcom eLongcom andMangocitycomHowever a com-mon phenomenon is that hotels must pay high commissionfor each sold room [6 7] In order to reduce commissionfees and sell rooms to customers directly hotels join a HAwhere the HA can be regarded as a direct sales platform Forinstance WeChat public platform and alitripcom offer thedirect selling platforms for hotels Comparedwith developingofficial websites joining HA can help the hotels reducecost Hotels have not been benefited much from websitedevelopment investment [8] Take for example Four Seasonshotel it has invested 18 million for its new website whileonline revenue only increases by 2 in five years [9] On thecontrary hotels can pay 0 to 15000 yuan per year to join thealitripcom so as to deal with orders through this websitedirectly Generally speaking the reservation price throughthe alliance is up to 20 to 70 of the rack rate In the light ofthe uncertain factors such as time city room type and roomquantity the discount is not fixed In most cases the priceof HA is 10 to 30 lower than OTA except for a plan ofpromotion with the extent to which the price will be equalto that of OTA Pricing competition exists between the twochannels Therefore how to determine the pricing decisionshas much practical significance for hotels

Customer cancellations and no-show occur frequentlyin the yield management of hotel reservations [10] Oncecustomers cancel the reservation or fail to show up thehotel will suffer loss for the rooms That is because roomsare perishable products In order to deal with this case thehotel usually permits overbooking However overbookingwill bring a risk that the actual booking quantity is greaterthan the number of hotel rooms As a result the overbookingcosts must be paid A question therefore arises as to how ahotel determines the overbooking quantity so as to keep abalance between the vacancy lost and the overbooking costs

Since more and more hotels employ dual-channel struc-ture we develop a two-echelon tourism supply chain modelinvolving one hotel and one OTA to study hotel room pricingstrategies with whichOTAprovides related service Bertrandand Stackelberg game models are both analyzed Further-more this paper considers customersrsquo no-show phenomenonin a dual-channel setting under tourism supply chain Theresults of the study will assist hotels to manage and optimizetheir pricing decisions

The remainder of this paper is organized as followsSection 2 provides a literature review and Section 3 presentsnotations Section 4 analyzes the integrated tourism supplychain Section 5 shows the Bertrand and Stackelberg gamemodels respectively The overbooking situation is illustratedin Section 6 Section 7 conducts numerical experiments toprovide more insights Conclusions and outlooks are finallypresented in Section 8 To make the paper more readable allproofs are presented in Appendix

2 Literature Review

This research is closely related to tourism supply chainpricing strategies in dual-channel supply chain and revenuemanagement To highlight our contributions we review only

the literature that is representative and particularly relevantto our study

21 Tourism Supply Chain Management Tourism supplychain management has been studied since the 1990s Forexample Yang et al [11] utilized game theory to investigate thecooperation and competition between two tourism supplychains which consist of service providers a theme parkoperator and accommodation providers They concludedthat in order to optimize performance the decision makersof the two tourism supply chains are expected to adoptappropriate product differentiation strategies Differentlywe highlight the comparison between the Bertrand andStackelberg game in a two-echelon tourism supply chainHuang et al [12] did research on competition strategies ina tourism supply chain network consisting of theme parksaccommodation providers and tour operators which areinvolved in producing and providing package holidays Theyanalyzed the differences between the impacts of quantity andprice competitions Huang et al [13] studied the impact of theinvolvement of tour operators in a tourism supply chain withmultiple hotels and travel agencies and showed that when themarket size of travel agencies is lower than a certain levelboth travel agencies and the hotel can benefit more fromthe presence of a tour operator in a tourism supply chainSimilarly we focus on the supply chain involving hotels andtour operators However our contributions are directed toformulating a dual-channel environment by considering theno-show phenomenon Furthermore Lee and Fernando [14]developed a model for the medical tourism supply chain andshowed that supply chain coordination and information shar-ing have a direct effect on organizational performance Weaim to contribute to this stream of literature by consideringhotelsrsquo pricing decisions under dual-channel structure

22 Pricing Strategies in Dual-Channel Supply Chain Theresearch on dual-channel supply chain management hasgained much attention among the marketing and supplychain management In particular the studies focusing onpricing strategies are closely related to our study In thisaspect Chiang et al [15] make a great contribution Theyconstructed a price-setting game between a manufacturerand its independent retailer They pointed out that thedirect sales channel can help the manufacturer improveoverall profitability by reducing the degree of inefficientprice double marginalization Tsay and Agrawal [16] foundthat the manufacturer can coordinate the supply chain andachieve a win-win situation through adjusting the directprice Q-H Li and B Li [17] studied a dual-channel supplychain in which the retailer provides value-added servicesto products Their results indicate that the entire supplychain cannot be coordinated with a constant wholesale pricewhen the retailer provides value-added services and hasfairness concerns Similarly we also assume that the OTAadds additional value to the tourism product Panda et al[18] explored pricing and replenishment policies for a high-tech product in a dual-channel supply chain that consistsof a brick-and-mortar channel and an internet channel

Discrete Dynamics in Nature and Society 3

Liu et al [19] investigated the pricing decisions under dual-channel structure In their model fairness and free-ridingbehavior are considered They detected that manufacturerrsquosequilibrium price based on channel fairness is below its equi-librium price ignoring fairness More related articles on thisissue have been presented by Chen et al [20] Ding et al [21]and Rodriguez and Aydin [22]

23 RevenueManagement Revenuemanagement whichwasoriginated in the airline industry is also widely used in thehotel industry That is because airline and hotel have similarcharacteristics (eg perishable service or product fixedcapacity distinct customer segmentation and price differen-tiation) In this aspect the room pricing decision has beenstudied extensively since price has an important influence oncustomerrsquos accommodation selection decisions [23] It is alsorelevant to our study

Chen et al [24] examined the impact of hotel pricing onguest satisfaction Their results imply that at the low pricelevel room price and food and beverage price lead to anincrease in guest satisfaction whereas the high price levelcould have just the opposite effect Ling et al [6] consid-ered the case that customers can make reservations directlythrough the distribution channel of the hotel or indirectlythrough the OTA Although the background of the studyis similar to that in our model they aim to find a methodfor hotels to manage their room availability for cooperativeOTAs Espinet et al [25] analyzed how hotel characteristicsaffect seasonality in prices and find that more hotel servicesand higher star ratings are associated with fewer seasonalvariations in hotel prices Juaneda et al [26] investigated theprice component of physical characteristics and the locationof apartments and hotels and compare their effect on thefinal price of both types of accommodation Abrate et al [27]collected data from almost 1000 hotels in Europe to analyzethe dynamic pricing strategies of hotels they showed thatthe intertemporal pricing structure primarily depends on thetype of customer the star rating and the number of supplierswith available rooms

The extant literature about revenuemanagement ismostlyfrom the perspective of the hotel itself However nowadaysthe competition among tourism enterprises turns to begradually and distinctly embodied in the competition amongtheir tourism supply chains In contrast to the above papersour model is more practical by considering pricing strategiesfrom the perspective of tourism dual-channel supply chain

This papermakes the following contributions Firstly thispaper introduces the tourism products into the dual-channelsupply chain framework while the aforementioned literatureignores this point Secondly the rooms in our research areclassified into economic and luxury type which can be betterto reflect the reality Thirdly this paper aims to illustrate thepricing decisions under several common cases which canprovide a valuable reference for hotels and OTAs

3 Model Setup and Notations

We consider a tourism supply chain model involving onehotel and one OTA (Figure 1) The hotel and OTA are both

Upstream(hotel)

Downstream(traveler)

Hotel alliance

Service agentseLong and Ctrip

wL wH pL

2 pH

2

pL

1 pH

1

Figure 1 Tourism dual-channel supply chain model diagram

risk neutral and completely rational The hotel is requiredto sign a cooperation agreement to join a HA HoweverHA charges the hotel trivial commissions Thus HA can betreated as a hotelrsquos direct sales platform and HArsquos price isdecided by the hotel directlyTherefore it is negligible to con-sider the contractual relationship between the hotel and HA

For the hotel customers are usually divided into twotypes business travelers and leisure travelers Leisure travel-ers aremore sensitive to roomprice than business ones so thatthey oftenmake a reservation before a long time Accordinglyhotels prefer to sell luxury rooms to business travelers Cor-respondingly the hotel rooms are usually classified accordingto different customersrsquo need such as luxury rooms economyrooms standard rooms and business roomsThrough settingdifferent rates for different rooms hotels are able to selldifferent types of rooms to specific target customers Basedon the above background in our model the hotel rooms areclassified into economic and luxury type In this paper hotelsells roommeans that hotel sells the right for guest to use theroom that is the hotel rents the room to guest for a periodof time The hotel sells the economy (luxury) rooms with theprice of 119901119871

1(1199011198671) to the customer directly and it sells rooms to

OTA with the wholesale prices of 119908119871(119908119867) respectively Pro-

viding combination of products and additional services OTAsells rooms to customers with the prices of 119901119871

2and 119901

119867

2

According to international practice in order to reducethe phenomenon of no-show customers must provide hotelreservation deposit with credit card or prepay the fee whenthey make reservation If customers cancel the booking orchoose no-show the hotel can deduct all or part of the roomcharge Take for example Ctripcom the orders can bedivided into two types orders that cannot be cancelled andtime-limited orders When customers choose the orders thatcannot be cancelled they cannot cancel the order after theyconform the booking if not the reservation deposit orprepaid fee will not be returnedThis kind of situation usuallyoccurs when guest room resources are intense The time-limited order means that customers can cancel the order forfree before the deadline (usually 1 to 3 days before check-in) Ifcustomers cancel the booking after the deadline or choose no-show Ctripcom will charge the customers for the first dayrsquosroom fee as a punishment This also means that when thecustomer reserves a room for more than one day he willreceive partial refund Such methods are also adopted byBookingcom and eLongcom Based on reality we assumethat customers must provide full guarantee with credit cardwhen they make reservation but if the customers cancel

4 Discrete Dynamics in Nature and Society

the booking or choose no-show finally the hotel would onlyreturn certain expense rate of 120572 (0 le 120572 le 1) If a customeris booking through OTA then OTA would return to thecustomer with the proportion of the retail prices At the sametime the hotel would return to OTA with the proportionof the wholesale prices We assume that the proportion thathotel returns to the customer the proportion that hotelreturns to OTA and the proportion that OTA returns to thecustomer are the same

We list the following notations where 119894 (119894 = 119871119867) insubscripts or superscripts are for economic (low price) andluxury (high price) rooms respectively

119876 the total number of rooms provided for renting toguests119876119894 the total number of economicluxury rooms

119863119894

1 the reservation amount of economicluxury room

booking through HA119863119894

2 the reservation amount of economicluxury room

booking through OTA119886119894 the market base demand of economicluxury

room119886 the total market base demand of rooms (119886 = 119886

119871+

119886119867)

119904 themarket share of HA in the tourism dual-channelsupply chain119901119894

1 HArsquos price of economicluxury rooms that is the

direct selling prices119901119894

2 OTArsquos price of economicluxury rooms that is the

retail prices119908119894 the wholesale price of economicluxury rooms

119887119894 the price sensitivity coefficient of 119894 price rooms

(119887119871gt 119887119867)

120579 the diffusion intensity which describes the shiftbetween two channels with regard to the price andvalue120582 the proportion of customer cancellations and no-show120572 the return expense proportion of customer cancel-lations and no-show (0 le 120572 le 1)120573 the services elasticity of demandV the value added by OTArsquos services120578 the coefficient of service cost119888(V) the function of service cost 119888(V) = 120578V221205871 the profit of the hotel

1205872 the profit of the OTA

In the model we do not consider the marginal sales costof the hotel since it is very low In reality OTA will firstlyintroduce to customers the hotelsrsquo facilities and quota andafterwards confirm the booking and finally book rooms fromthe hotel for customersTherefore the rooms sold by HA and

OTA are homogeneous In addition to providing hotel reser-vations OTA also provides other related services as wellsuch as offering plane ticket booking holiday booking andtravel information OTA aims to provide a full range of travelprogram for travelers In order to provide such services OTAneeds to pay for additional operating costs The customerswho want to get more tourist information and services willprefer to reserve rooms through OTA By contrast HA onlyprovides hotel room information for customers For instancecustomers cannot book the suitable hotel and air ticket at thesame time through the HA platform Consequently in orderto distinguish the influence of different information servicesto customerrsquos channel choice we suppose that OTA providesadditional service and the value added from the services is VFurther the cost for providing service is 119888(V) = 120578V22 wherethe parameter 120578measures the cost effectiveness of the serviceSuch cost function is commonly adopted in previous litera-ture and canwell describe the relationship between additionalservices and cost [28 29] When OTA does not provide theservice the cost should be zero

According to the process of demand function in Tsay andAgrawal [30] andChoi [31] the demands of economicluxuryrooms through each channel are expressed as follows

119863119894

1= (119904119886119894minus 119887119894119901119894

1) + 120579 (119901

119894

2minus V minus 119901

119894

1)

119863119894

2= [(1 minus 119904) 119886119894 minus 119887

119894119901119894

2] + 120573V + 120579 (119901

119894

1+ V minus 119901

119894

2)

(1)

Such linear demand functions are used because they canachieve approximate and satisfactory fit to certain types ofdemand and they are tractable and widely used in marketingand supply chain management literature [32] In our modelthe parameter 119887 represents the price sensitivity coefficientIt describes the marginal channel demand per respectivechannel price The own price elasticity is normally negative[33] And the parameter 120573measures the marginal demand ofOTA per service value added In addition the parameter 120579 isunderstood as the diffusion intensity (cross-price sensitivity)and describes the shift between two channels with regard tothe price and the value Suchmodelingmethod can guaranteethat the self-price sensitivity in absolute value is strongerthan the cross-price sensitivity which is proved by Hanssenset al [34] and used by Yao and Liu [28] Choi [31] and Kurataet al [35]

Now consider the situation without overbooking that is119863119871

1+ 119863119871

2le 119876119871and 119863

119867

1+ 119863119867

2le 119876119867 Thus the reservation

amount can be regarded as the final demandThe total profit for the hotel OTA and the whole supply

chain can be expressed as follows

1205871= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2) (2)

1205872= [(1 minus 120582120572) (119901

119871

2minus 119908119871) minus 119888 (V)]119863119871

2

+ [(1 minus 120582120572) (119901119867

2minus 119908119867) minus 119888 (V)]119863119867

2

(3)

120587 = 1205871+ 1205872 (4)

Discrete Dynamics in Nature and Society 5

4 Integrated System

As a benchmark we first consider an integrated systemwherethe common goal of supply chain upstream and downstreammembers is tomaximize the overall profit of the supply chainThis is an ideal model that the members in the supply chainoperate as an entirety In such an integratedmodel of tourismsupply chain the hotel and OTA cooperate to determine thepricing strategies

Proposition 1 In the integrated system the optimal pricingdecisions of HA and OTA are as follows

119901119894lowast

1=119886119894(119887119894119904 + 120579) + 120579V (120573 minus 119887

119894)

2 (119887119894)2+ 4119887119894120579

119901119894lowast

2=(119887119894+ 120579 minus 119887

119894119904) 119886119894+ 119887119894120573V + 120579V (120573 + 119887

119894)

2 (119887119894)2+ 4119887119894120579

+119888 (V)

2 (1 minus 120582120572)

119894 = 119871119867

(5)

From Proposition 1 the optimal prices shown above canexplain that in the integrated system the optimal prices of HAwill not be affected by the proportion of customer cancella-tions and no-show (120582) or the return expense proportion (120572)On the other hand with the increase of 120582 or 120572 the optimalprices for OTAwill increaseThis is reasonable because whenOTA faces unstable demand or it should return more tocustomersrsquo cancellation or no-show it would like to increasethe price to guarantee its profit

Corollary 2 119901119871lowast2

and 119901119867lowast2

are increasing in V Moreover

(1) if 120573 gt 119887119871gt 119887119867 then 120597119901

119871lowast

1120597V gt 0 120597119901119867lowast

1120597V gt 0

(2) if 119887119871gt 120573 gt 119887

119867 then 120597119901

119871lowast

1120597V lt 0 120597119901119867lowast

1120597V gt 0

(3) if 119887119871gt 119887119867gt 120573 then 120597119901

119871lowast

1120597V lt 0 120597119901119867lowast

1120597V lt 0

From Corollary 2 we can know that when OTA offersmore services OTArsquos optimal price will be increased accord-ingly It is reasonable that if V increases the cost of OTA willalso definitely increase So there is always a positive correla-tion between OTArsquos optimal prices and the added value

If 120573 gt 119887119871

gt 119887119867 the market of economy rooms and

that of luxury rooms are both service-oriented rather thanprice-oriented The implication is that the effective servicewill increase the optimal price of HAWhenOTA offersmoreeffective service its price will increase But some customerswant to enjoy the additional services so they are willingto make a booking through OTA despite spending moremoneyTherefore the demand inOTAwill increase while thedemand in HA will decrease

If 119887119871gt 120573 gt 119887

119867 the market of economy rooms is service-

oriented while the market of luxury rooms is price-orientedThe HArsquos optimal price of economy rooms will decrease withrespect to V Conversely the HArsquos optimal price of luxuryrooms will increase with respect to V For examples the

change of price has a great impact on leisure travelersrsquo deci-sions but for business travelers the price is not themost con-cern If the price ofOTA increasesOTArsquos demandof economyrooms will significantly reduce and the HArsquos demand willincrease thus the HArsquos optimal price will decline On theother hand for luxury rooms if OTA provides more effectiveservice the customer would be willing to pay higher pricesfor value-added service This will bring the increase in OTArsquosdemand and the reduction of HArsquos demand thus the optimalprice of HA will increase

If 119887119871gt 119887119867gt 120573 the market of economy rooms and that of

luxury rooms are both price-oriented than service-orientedThe HArsquos optimal price of both economy rooms and luxuryrooms will decrease with the increase of V When the marketis price-oriented the promotion of price in OTAwill lead to areduction in OTArsquos demandThereby the demand in HA willincrease and optimal price in HA will decline

5 Two Game Models

In the tourism dual-channel supply chain the relationshipbetween hotel and OTA is cooperative as well as competitiveIn the decentralized decision-making model they are morecompetitive than cooperative Their purposes are to maxi-mize their own profits In reality hotel can choose whether toinform the price ofHAor not forHA is competingwithOTAUninformed of the prices inHAOTAcan predict the range ofprice onHAby the star-rated and room type of the hotel but itcannot know the exact priceTherefore this section examinesthe pricing equilibrium between the hotel and OTA undertwo types of games namely the Bertrand and Stackelberggames For the Bertrand game both of the participantsregard price as a decision variable the hotel and OTA areuncooperative For the Stackelberg game the participantsare divided into two roles the leader and the follower Asa leader in tourism supply chain the hotel will provide thepolicy to maximize its interests As a follower OTA accepts ifprofitable By comparing the two models we can understandhow the behavior of hotel influences the pricing decisions

51 Bertrand Game In a Bertrand game the procedure isas follows keeping the wholesale price unchanged the hoteldetermines HArsquos prices 119901119871

1and 119901

119867

1 so as to maximize profit

1205871 Uninformed of the prices of HA OTA decides prices 119901119871

2

and 119901119867

2 so as to maximize his profit 120587

2 Let (119901119894

1)119861 (1199011198942)119861(119894 =

119871119867) denote HArsquos and OTArsquos prices under a Bertrand modelrespectively

In the following 119871119899(119899 = 1 2 5) 119904

0 and 119866

119898(119898 =

1 2) are the threshold values and are given in Appendix G

Proposition 3 There exist Bertrand equilibrium prices(119901119894

1)119861lowast (119901119894

2)119861lowast

(119894 = 119871119867) where

(119901119894

1)119861lowast

=(1 minus 120582120572) 1198711 + 119888120579 (119887

119894+ 120579)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

2)119861lowast

=(1 minus 120582120572) 1198712 + 2119888 (119887

119894+ 120579)2

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(6)

6 Discrete Dynamics in Nature and Society

From Proposition 3 in the Bertrand model the equilib-rium prices for hotel and OTA are both affected by 120572 and 120582With the increase of 120572 or 120582 both (119901

119894

1)119861lowast and (119901

119894

2)119861lowast will be

higher In otherwords with higher uncertainty of roomoccu-pancy the hotel and OTA tend to increase prices to protecttheir own profits

Denote 1198881= (1 minus 120582120572)(2119887

119871+ 120579 minus 120573)(119887

119871+ 120579) and 119888

2= (1 minus

120582120572)(2119887119867+ 120579 minus 120573)(119887

119867+ 120579) then 119888

1gt 1198882

Corollary 4 (1199011198712)119861lowast and (119901

119867

2)119861lowast are increasing in V (119901119871

1)119861lowast

and (119901119867

1)119861lowast have the following relationships with respect to

OTArsquos service

(1) if 1198881015840(V) gt 1198881 then 120597(119901

119871

1)119861lowast120597V gt 0 120597(119901119867

1)119861lowast120597V gt 0

(2) if 1198881gt 1198881015840(V) gt 119888

2 then 120597(119901

119871

1)119861lowast120597V lt 0 120597(119901119867

1)119861lowast120597V gt

0(3) if 1198881015840(V) lt 119888

2 then 120597(119901

119871

1)119861lowast120597V lt 0 120597(119901119867

1)119861lowast120597V lt 0

From Corollary 4 when OTA offers more effective ser-vices its optimal prices will increase due to the incrementin the cost Marginal cost measures the input costs and theoutput value per unit If the marginal cost is greater than1198881 then the costs of OTA to provide additional services are

higher So the equilibrium prices of HA will increase as thevalue added by OTArsquos services increases When the marginalcost is between 119888

1and 1198882 HArsquos equilibrium price of economy

rooms and the value added by OTArsquos service have a negativecorrelation but HArsquos equilibrium price of luxury roomswould increase with the increment of V In addition when themarginal cost is less than 119888

2 the costs of OTA to provide addi-

tional service are lower And the equilibriumprices ofHAwilldecrease when V increases

Corollary 5 There exist threshold unit wholesale prices 1199080119894

1199081

119894(119894 = 119871119867) such that

(1) (1199011198941)lowastlt (119901119894

1)119861lowast if 119908

119894gt 1199080

119894 (1199011198941)lowast= (119901119894

1)119861lowast if 119908

119894= 1199080

119894

(119901119894

1)lowastgt (119901119894

1)119861lowast if 119908

119894lt 1199080

119894

(2) (1199011198942)lowastlt (119901119894

2)119861lowast if 119908

119894gt 1199081

119894 (1199011198942)lowast= (119901119894

2)119861lowast if 119908

119894= 1199081

119894

(119901119894

2)lowastgt (119901119894

2)119861lowast if 119908

119894lt 1199081

119894

where

1199080

119894=

1198713

6119887119894(119887119894+ 120579) (119887

119894+ 2120579)

minus119888

3 (1 minus 120582120572)

1199081

119894=

120579 [(1 minus 120582120572) 1198714 minus 119888119887119894120579 (119887119894+ 2120579)]

2119887119894 (1 minus 120582120572) (119887119894 + 2120579) (31205792 + 21198872

119894+ 2119887119894120579)

(7)

FromProposition 1 it is easy to know that the equilibriumprices in the integrated system are not affected by the whole-sale prices However from Proposition 3 in the Bertrandmodel there is a positive correlation between the equilibriumprices and the wholesale prices Corollary 5 shows that theequilibrium price of HA in the Bertrand game is higherthan that in the integrated system if the wholesale price isgreater than a certain critical point (1199080

119894) Additionally if the

wholesale price is greater than1199081119894 then the equilibrium price

of OTA in Bertrand model will be higher than that in theintegrated model

Corollary 6 There exists a threshold unit wholesale price1199082

119894(119894 = 119871119867) such that if119908

119894gt 1199082

119894 then119863lowast

119894gt 119863119861lowast

119894(119894 = 119871119867)

where

1199082

119894=120579 [(1 minus 120582120572) (V120573 + 119886

119894) minus 119887119894119888]

2119887119894 (1 minus 120582120572) (119887119894 + 2120579)

(8)

Corollary 6 shows that when thewholesale price is greaterthan 119908

2

119894 the high price will lead to a lower demand in the

Bertrand game That is the reservation amount of Bertrandmodel is less than that in the integrated model The highersale price in OTA results from the higher wholesale priceThus the above result is reasonable because travelers are pricesensitive especially for leisure travelers the increase of pricewill bring the decline of reservation amount When the rela-tionship between the hotel and OTA is modeled as a Stackel-berg game the hotel canmotivate customers to reserve roomsthrough a reasonable wholesale price If the wholesale price isgreater than the threshold the sales volume in the centralizedcase is lower than that in the Bertrand case

52 Stackelberg Game In a Stackelberg game the procedureis as follows keeping thewholesale price unchanged the hotel(as the leader) announces HArsquos prices 119901119871

1and 119901119867

1of two types

of rooms respectively in order to maximize its profit 1205871 In

response to HArsquos prices OTA (as the follower) determinesprices 119901

119871

2and 119901

119867

2to maximize its profit 120587

2 Let (119901

119894

1)119878

(119901119894

2)119878(119894 = 119871119867) denote respectively HArsquos and OTArsquos prices

under a Stackelberg game

Proposition 7 The optimal prices are (119901119894

1)119878lowast (119901119894

2)119878lowast

(119894 =

119871119867) and there exists a threshold unit wholesale price 1199083119894(119894 =

119871119867) such that if 119908119894gt 1199083

119894 then (119901

119894

1)lowastlt (119901119894

1)119878lowast where

(119901119894

1)119878lowast

=(1 minus 120582120572) (1198711 minus 119908

1198941205792minus 119908119894119887119894120579) + 119888120579 (119887

119894+ 120579)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 21205792]

(119901119894

2)119878lowast

=120579 (119901119894

1)119878lowast

+ (1 minus 119904) 119886119894 + V (120579 + 120573) + 119908119894(119887119894+ 120579)

2 (119887119894+ 120579)

+119888

2 (1 minus 120582120572)

1199083

119894

=119887119894V120573 + 119886119887

119894+ 120579V119887119894+ 119886119894120579 + 120579V120573 minus 119886

119894119887119894119904

2119887119894(119887119894+ 2120579)

minus119888

2 (1 minus 120582120572)

(9)

Similar to the Bertrand competition the equilibriumprices in Stackelberg game will increase with the increase of

Discrete Dynamics in Nature and Society 7

the return expense proportion (120572) or the cancellations andno-show proportion (120582)

From Proposition 7 we can see that the Stackelbergmodel is similar to the Bertrand model that the equilibriumprices would increase with the increase of wholesale pricesFurthermore when thewholesale price is greater than1199083

119894 the

equilibrium price of HA in Stackelberg model will be higherthan that in the integrated model

In the Stackelberg game if OTA offers more effective ser-vices the equilibrium prices of OTA would increase accord-ingly The relationship between the Stackelberg equilibriumprices and V is similar to that in the Bertrand model

53 Contrastive Analysis of Bertrand and Stackelberg GamesBased on the equilibrium prices obtained in the previoussection we in this section compare the equilibriumprices andoptimal profit under Bertrand and Stackelberg games

Corollary 8 There exists a threshold unit wholesale price1199084

119894(119894 = 119871119867) such that

(1) (1199011198941)119861lowast

gt (119901119894

1)119878lowast and (119901119894

2)119861lowast

gt (119901119894

2)119878lowast if 119908

119894gt 1199084

119894

(2) (1199011198941)119861lowast

= (119901119894

1)119878lowast and (119901119894

2)119861lowast

= (119901119894

2)119878lowast if 119908

119894= 1199084

119894

(3) (1199011198941)119861lowast

lt (119901119894

1)119878lowast and (119901119894

2)119861lowast

lt (119901119894

2)119878lowast if 119908

119894lt 1199084

119894

where

1199084

119894=

120579 [(1 minus 120582120572) 1198715 + 119888120579 (119887119894+ 120579)]

4119887119894 (1 minus 120582120572) (119887119894 + 120579) (119887

119894+ 2120579)

(10)

Corollary 8 compares the equilibrium prices under theBertrand and Stackelberg game with respect to the wholesaleprice It shows that if the wholesale price is greater than1199084

119894 the pricing equilibrium under the Bertrand is higher

than that under the Stackelberg game Conversely the pricingequilibrium is lower if the wholesale price is less than 119908

4

119894

In the decentralized case both the manufacturer and theretailer want to maximize their profit A high wholesale pricecould be passed on to customersTherefore the above resultsexist In addition how to share the profit between the manu-facturer and the retailer depends on their bargaining powers

Corollary 9 If 119908119894

= 1199084

119894(119894 = 119871119867) then 120587

119878lowast

1gt 120587119861lowast

1 OTArsquos

profit has the following relationship with respect to 1199084119894

(1) 120587119861lowast2

gt 120587119878lowast

2if 119908119871gt 1199084

119871and 119908

119867gt 1199084

119867

(2) 120587119861lowast2

= 120587119878lowast

2if 119908119871= 1199084

119871and 119908

119867= 1199084

119867

(3) 120587119861lowast2

lt 120587119878lowast

2if 119908119871lt 1199084

119871and 119908

119867lt 1199084

119867

Thehotel is the leader in Stackelberg game and can alwaysbenefit from it except for the critical point1199084

119894 Comparedwith

the Bertrand game the hotel can get higher profits in Stackel-berg gamewhen the wholesale price is not equal to1199084

119894There-

fore in decentralized decision-making model the hotel willbe more inclined to be the price leader in order to ensure thatit can achieve higher profits

Corollary 9 indicates that the Stackelberg model is supe-rior to the Bertrand model when the wholesale price is less

than the critical point1199084119894 Not only the hotel but alsoOTA can

gain more profit from the Stackelberg game Though OTA isa follower in Stackelberg game the profit will not be reducedbecause the lower wholesale prices can compensate for theloss of profit caused by the opening of HA channel Conse-quently the hotel should play the role of the price leader inthe supply chain and develop reasonable wholesale prices toachieve optimization of the whole supply chain profit whileoptimizing its own profit

Corollary 10 Under either Bertrand or Stackelberg equi-librium channel prices there exists optimal wholesale price119908lowast

119894(119894 = 119871119867) that maximizes the total equilibrium channel

profit where 119908lowast119894= 11986611198662

According to Corollary 10 there exists optimal wholesaleprice 119908

lowast

119894(119894 = 119871119867) that maximizes the total equilibrium

channel profit under either Bertrand or Stackelberg gameThe optimal wholesale price will optimize the decentralizeddecision-making supply chainMeanwhile both the hotel andtheOTA can benefit from the optimal wholesale priceThere-fore the reasonable wholesale price can help promotemutualcooperation and communication between the supply chainmembers

54 Contrastive Analysis of Two Channels in the Supply Chain

Corollary 11 There exists a threshold unit market share of HAin the tourism dual-channel supply chain (119904

0) such that when

119904 gt 1199040 the hotelrsquos profit from HA is higher than that from OTA

Keeping the wholesale prices and sales prices unchangedwhen the market share of HA in the tourism dual-channelsupply chain exceeds a certain value 119904

0 the hotelrsquos profit from

HA is higher than that from OTA The result is suitable forthe integrated system Bertrand and Stackelberg games Fromthe perspective of hotelrsquos revenue the hotel should explorethe channel for direct selling actively Also the hotel canstrengthen the promotion of HA channel to improve thecustomerrsquos understanding and preference for theHA channelBut the premise is that the profit growth from the promotioncan compensate for the cost According to the statistical datafrom the hotel price competitiveness analysis report in thefirst half of 2012 we know that the booking cost from directselling channel is about 1 dollar per night but that fromOTAis about 10 dollars per night Booking cost can be reducedby 46 if the direct selling level is doubled Then improvingthe market share of direct selling will greatly reduce the costMore comparisons of different channelrsquos profits in eachmodelcan be found in part of numerical analysis

6 Overbooking

This section extends to consider the overbooking caseRegarding overbooking in the hospitality industry the com-mon practice is that the hotel upgrades the room type ortransfers customers to other hotels nearby that have the samelevel and same type In airline industry if customers aredenied boarding after arriving at the airport the airline will

8 Discrete Dynamics in Nature and Society

provide a free upgrade endorse the ticket or provide com-pensation for the customers according to specific situationCompared to the hotels the airlines cannot transfer cus-tomers to other companies The air ticket alteration will usu-ally disrupt customersrsquo traveling schedule Though the over-booking by airlines has been well studied in the literature ourresearch is new in the hospitality industry by considering theoverbooking withwithout room transfer with the hope thatcertain implications can be enlightened to the hotel man-agers

The hotel wants to increase the occupancy rates toincrease the profits through overbooking However over-booking will lead to the risk that the actual occupancyamount is greater than the number of hotel roomsThereforethe hotel has to provide compensation to travelers who can-not check in that is overbooking cost The greater the num-bers of overbooking the less the probability of room vacancybut at the same time travelers are more likely to be refusedby the hotel Therefore the hotel must balance between thevacancy lost and the overbooking costs We develop a modelto analyze the overbooking choice

In reality the OTA is always a crucial partner of hotelsfor it can attract a large number of customers for hotelsand improve their occupancy rates [36] Spontaneously theOTA plays an increasingly significant role in the distributionsystems of hotels [5 7] By contrast the HA mainly providesa platform for individual guest Compared with individualcustomers hotel pays more attention to the long-term coop-eration relationship with the OTA Therefore in our modelwe assume that when the market demand is greater than thesupply and the hotel does not carry out overbooking the hotelwould give priority to customers who are booking fromOTA

61 Without Room Transfer Here we consider the casewith no room transfer When the actual occupancy amountexceeds the total quantity of rooms the hotel does not arrangeother alternative accommodation for the customers who can-not check in But the hotel must pay the loss of goodwill costSuppose that the overbooking quantity of economy and lux-ury rooms isΔ119862

119871andΔ119862

119867and the overbooking cost is 119888

119871and

119888119867 respectivelyWe discuss economy roomsrsquo overbooking The actual

occupancy can be either of the following two cases (1) when119876119871

lt 119863119871

1+ 119863119871

2le 119876119871+ Δ119862

119871 the reservation amount of

rooms is 1198631198711+ 119863119871

2 so the actual occupancy amount is (119863119871

1+

119863119871

2)(1 minus 120582) (2) when119863

119871

1+ 119863119871

2gt 119876119871+ Δ119862

119871 the reservation

amount is 119876119871+ Δ119862119871 then the actual occupancy amount is

(119876119871+Δ119862119871)(1 minus 120582) Therefore if (119876

119871+Δ119862119871)(1 minus 120582) le 119876

119871 that

is Δ119862119871le 120582119876119871(1 minus 120582) the profit of hotel is

120587119871

11= (1 minus 120582120572) [119901

119871

1(119876119871+ Δ119862119871minus 119863119871

2) + 119908119871119863119871

2] (11)

If (119876119871+ Δ119862119871)(1 minus 120582) ge 119876

119871 that is Δ119862

119871ge 120582119876119871(1 minus 120582)

the economy roomsrsquo actual occupancy amount exceeds theeconomy roomsrsquo number in the hotel so the hotel must paythe overbooking cost then the profit of hotel is

120587119871

12= (1 minus 120582120572) [119901

119871

1(119876119871+ Δ119862119871minus 119863119871

2) + 119908119871119863119871

2]

minus (119901119871

1+ 119888119871) [(119876119871+ Δ119862119871) (1 minus 120582) minus 119876

119871]

(12)

Proposition 12 Without considering roomsrsquo transfer the opti-mal overbooking quantity of economy rooms and luxury roomsis

Δ119862lowast

119894=

120582

1 minus 120582119876119894 119894 = 119871119867 (13)

FromProposition 12 we know that the higher the propor-tion of customer cancellations and no-show is the larger theoptimal overbooking quantity of the hotel will be With theincrease of 120572 the penalty that customers need to pay for theircancellation or no-show decreases Two following extremesituations are considered When 120572 = 1 the hotel will returnall the guarantee fee in case of customersrsquo cancellation or no-showThat is the same as the hotel does not charge customersany guarantee fee when customers book the rooms Undersuch circumstances customers can book rooms for severaldays firstly after they identify a specific itinerary they cancancel the extra rooms for they do not suffer any loss It is nodoubt that such regulation will increase the cancellation andno-show rate On the other hand if 120572 = 1 all the guaranteefee will not be returned after cancellation or no-show In thiscase customers need to reserve a room cautiously If it is notnecessary customers will not choose cancellation or no-showbecause the penalty cost is too high Such policy will reducethe cancellation and no-show rate Spontaneously to someextent 120572 and 120582 are positive correlation When the hotelincreases proportion 120572 it would like to increase the over-booking quantity so as to increase the actual occupancy rateNowadays the time-limited orders are widely used amonghotels Such regulation cannot only reduce customersrsquo lossfor the change of schedule but also help the hotel confirmthe orders so as to handle the overbooking phenomenon inadvance

In addition the risk of overbooking the economy roomsis relatively lower than the luxury rooms Compared toeconomic rooms it is more difficult for the hotel to findalternative luxury rooms to satisfy the customers Naturallyoverbooking cost of luxury room is higher For instance ifeconomy rooms are overbooked the hotel can transfer thecustomers to luxury rooms and the customers are willingto accept By contrast if luxury rooms are overbooked cus-tomers are not willing to accept the adjustment from luxuryrooms to economic rooms This implies that the hotel has topay a higher default costTherefore the hotel should be morecareful to choose the overbooking quantity of luxury rooms

62 With Room Transfer The following discusses the casewith room transfer Firstly when the economy rooms areinsufficient and luxury rooms have a surplus customers cancheck in the hotelrsquos luxury rooms with the price of economyrooms Customers spend the same money and can enjoybetter service so they are willing to accept this adjustmentSecondly when the luxury roomsrsquo actual occupancy amountexceeds the number of luxury rooms in the hotel the hotelusually transfers customers to other hotels nearby that havethe same level and same type because the customers whobook luxury room have a high requirement Customers canenjoy the same service so they are willing to accept this trans-fer However the hotelrsquos credibility in customersrsquo mind will be

Discrete Dynamics in Nature and Society 9

damaged and it must pay the additional costsThirdly if boththe economy rooms and luxury rooms are unable to meetthe demand the hotel usually transfers the customers whocannot check in to other hotels Note that when119863119894

1+119863119894

2gt 119876119894

119894 = 119871119867 if the hotel does not overbook its profit is

120587111

= (1 minus 120582120572) [119901119871

1(119876119871minus 119863119871

2) + 119901119867

1(119876119867minus 119863119867

2)

+ 119908119871119863119871

2+ 119908119867119863119867

2]

(14)

Proposition 13 With room transfer there exists threshold unitoverbooking cost 119888

1198940 such that if 119888

119894lt 1198881198940 then overbooking is

profitable for the hotel where

1198881198940=(1 minus 120582120572) 119901

119894

1

1 minus 120582 119894 = 119871119867 (15)

From Propositions 12 and 13 we conclude that the hotelshould control the overbooking quantity in a certain rangeto prevent lacking of rooms If the overbooking proportionis too large then the hotel may face a loss Only when theoverbooking cost is low the hotel can obtain additional profitOtherwise if the overbooking cost exceeds a certain valuethe hotelrsquos profit would be lower when it carries out over-booking As the market demand increases the supply is closeto saturation and then the overbooking costs will be higherTherefore when the market demand is excessive the hotelshould strictly control the proportion of overbooking Inaddition if the number of hotels that have the same level andtype in the same region is little that is the possibility to trans-fer customer is small then the hotel should lower the propor-tion of overbooking

The proportion of overbooking depends on the propor-tion of customer cancellations andno-showaswell as the totalnumber of hotel rooms so the hotel can analyze the historicaldata to develop an appropriate overbooking proportion so asto maximize the hotelrsquos expected profit

Proposition 14 When the economy rooms and luxury roomsare both overbooked the optimal centralized prices are asfollows 119894 = 119871119867

119901119894lowast

14= 119901119894lowast

1+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

119901119894lowast

24= 119901119894lowast

2+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

(16)

Bertrand and Stackelberg prices are as follows

(119901119894

14)119861lowast

= (119901119894

1)119861lowast

+2119888119894

119906119887119894(119887119894+ 120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

24)119861lowast

= (119901119894

2)119861lowast

+120579119888119894

119906119887119894 (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

14)119878lowast

= (119901119894

1)119878lowast

+119888119894

119906119887119894(2119887119894+ 3120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 21205792]

(119901119894

24)119878lowast

=120579 (119901119894

14)119878lowast

+ (1 minus 119904) 119886119894 + V (120579 + 120573) + 119908119894(119887119894+ 120579)

2 (119887119894+ 120579)

+119888

2 (1 minus 120582120572)

(17)

For the hotel the premise to overbook rooms is that themarket demand is greater than the supply When the hotelfaces the risk of overbooking the equilibrium prices in bothcentralized and decentralized decision-making supply chainwill improve In the busy season in order to reduce the riskof overbooking the hotel would increase the prices and theincrement will increase as the transfer cost increases From(16) and (17) we can know that the increment in centralizeddecision-making model is the greatest and that in Bertrandgame is the smallest

7 Numerical Analysis

In this section we do some numerical experiment to gainmore insights According to the China Hotel Sales Chan-nel Report by I-Research (httpreportiresearchcnreport2013031892shtml) there are 381 of the hotels that aresuitable for high-end travelers and 619 of the hotels thatare suitable for low-end travelersTherefore this part assumesthat the proportion of the economical rooms and the luxuryrooms is 4 6 that is 119886

119871= 06119886 119886

119867= 04119886 Other parameter

settings are made as follows 119886 = 600 119904 = 05 and 119887119871= 06

119887119867= 02 120573 = 120579 = 05 120578 = 004 120572 = 08 120582 = 01 119908

119894= 05119901

119894

1

(119894 = 119871119867) In the following we investigate the impact of V onthe optimal prices and profits

When V = 0 that is the OTA does not offer any servicethen the optimal prices of HA are equal to the prices ofOTA Since 119887

119871gt 120573 gt 119887

119867 then the market of economy

rooms is service-oriented while the market of luxury roomsis price-oriented FromFigure 2 we can know that whenOTAoffers more services OTArsquos optimal price will be increasedaccordingly It is reasonable that if V increases the cost ofOTAwill also definitely increase With the increase of V 119901119871lowast

1will

decline slowly while 119901119867lowast1

will increaseThe OTArsquos profit status becomes better with the improve-

ment of its price But as the V increases the cost of OTA willalso definitely increase When V is equal to 27 then the profitof OTA is the highest If V is larger then the high costs willreduce the profits of OTAWhen V is equal to 34 the profit ofthewhole supply chain is the highest So from the perspectiveof the supply chain V is expected to be 34 rather than 27Similarly for the integrated system the profit of the OTAalso rises first and then declines with the increase of V Aftercalculationwe can get thatwhen V = 27 both120587119861lowast

2and120587119878lowast2will

be the highest From Figures 3 and 4 we know that the OTAwould tend to offer service that valued 27 so as to maximizeits own profit

After calculation we can conclude that when V = 34 then120587119861lowast is highest when V = 35 then 120587

119878lowast is highest (Figure 5)

10 Discrete Dynamics in Nature and Society

0 10 20 30 40 50 60 70 80100

150

200

250

300

350

400

450

Pric

e

pLlowast

1

pLlowast

2

pHlowast

1

pHlowast

2

Value added by OTArsquos services ()

Figure 2 Equilibrium prices in the integrated system

0 10 20 30 40 50 60 70 800

1

2

3

4

5

6

7

Profi

t

times104

120587lowast

1

120587lowast

2

120587lowast

Value added by OTArsquos services ()

Figure 3 Profits in the integrated system

From the perspective of the supply chain theOTA is expectedto offer more services Despite the rising cost of OTA willlower its profit the hotel can lower the wholesale prices tocoordinate the distribution of profits so as to achieve a win-win situation

In the following we focus on the comparison of differentchannelrsquos profit in each model Figure 6 depicts the curves ofthe total profits of the HAOTA channels in the integratedsystem with respect to V Figure 7 draws the curves of the dif-ferent channelsrsquo profits under both Bertrand and Stackelberggame The profit of the HA channel refers to the profit thatthe hotel derived from the HA channelThe profit of the OTA

0 10 20 30 40 50 60125

13

135

14

145

15

155

16

165

Profi

t

times104

120587Blowast

2

120587Slowast

2

Value added by OTArsquos services ()

Figure 4 OTArsquos profits under two games

0 10 20 30 40 50 60 70 8052

53

54

55

56

57

58

59

6

61

62

Profi

t

times104

120587Blowast

2

120587Slowast

2120587lowast

Value added by OTArsquos services ()

Figure 5 The profit comparison

channel involves the OTArsquos profit and the hotelrsquos profit gainedfrom the OTA channel

As shown in Figures 6 and 7 with the increase of V theprofit of the OTA channel will increase first and will thendecrease This indicates that a high level of service by OTAwill be detrimental to the channel profit That is because ahigh level of service will bring a high cost undoubtedly Forthe integrated model and Bertrand game model this disad-vantage is more evident The OTArsquos service can motivate theactual purchase behavior of customers in the OTA channelWhen V is relatively lower the additional profits from OTArsquos

Discrete Dynamics in Nature and Society 11

0 10 20 30 40 50 60 70 8018

2

22

24

26

28

3

32

34

36

38

4

Profi

t

HA channelOTA channel

times104

Value added by OTArsquos services ()

Figure 6 Channel profits in the integrated system

0 10 20 30 40 50 60 70 8005

1

15

2

25

3

35

4

45

Profi

t

HA channel in Bertrand gameOTA channel in Bertrand gameHA channel in Stackelberg gameOTA channel in Stackelberg game

times104

Value added by OTArsquos services ()

Figure 7 Channel profits in two games

service are enough to compensate for the cost In this casethe hotel and the OTA can get more profit from providing theservice However when V is high the additional profits fromOTArsquos service cannot make up for the high cost In such phe-nomenon the OTA should not increase investment in ser-vice

For both integrated model and Bertrand game modelwith the increase of V the profit of the HA channel willdecrease first and will then increase while in the Stackelberggamemodel the profit of theHA channel will always increase

with V With Figure 2 we can know that when OTA providesmore additional services it tends to increase its price Someof the customers will turn to reserve rooms from the HAbecause of the excessively high price in OTA As a result thehotel can gain more profits from the HA channel

8 Conclusion

With the development of e-commerce the providers oftourism products are more inclined to build dual-channelsIn this paper we consider the direct selling channel of HAand the traditional retail channel ofOTA from the perspectiveof tourism supply chain We develop a two-echelon tourismsupply chain model involving one hotel and one OTA wheretheOTAprovides related service Customers will be refundedpartially in case of cancelation or no-show We investigatethe optimal pricing strategies under several common casesThe integrated operation and the decentralized operationbased on Bertrand and Stackelberg games are studied andcorresponding equilibrium pricing policies are obtained

Our findings demonstrate that the hotel plays a crucialrole in optimizing the benefits of supply chain Consideringthe overall profit of the supply chain the hotel should act as aleader in dual-channel supply chain and formulate reasonablewholesale prices to improve the cooperative enthusiasm ofOTA so as to achieve optimization of the whole supplychain A lower wholesale price can help reduce OTArsquos loss ofprofit because of the opening of HA channel In addition weconsider the overbooking of the hotel and obtain the optimaloverbooking quantity We conclude that the hotel can alwaysobtain higher profits when the overbooking proportion iscontrolledwithin a certain range Otherwise if the overbook-ing proportion is too high the hotel can get extra profits onlywhen the overbooking cost is lower than a certain value

The contribution of this paper is that we extend tourismsupply chain to the dual-channel structure in which the hotelopens its direct channel to sell tourism products And theextant literature only refers to the single channel In additionwe realize that customer cancellations andno-showoccur fre-quently in hotel industry Thus we develop the game modelsbased on such phenomenon At last we derive the conditionsunder which the hotel dominant case is profitable for boththe supply chain members Our results can provide hotelsand OTAs with some new managerial insights under thedual-channel environment

This research can be extended in several directions infuture work For example in this paper we assume that allinformation is known to the hotel and OTA However someinformation could be asymmetric (eg see Chen [37]) Thuswe can explore the Bayesian equilibrium under asymmetricinformation settings Secondly the assumption of lineardemand is a limitation of this paperWe can further study thedynamic pricing in tourism dual-channel supply chain

Appendix

A Proof of Corollary 8

First we set (1199011198711)119861lowast

gt (119901119871

1)119878lowast which can be expressed as

12 Discrete Dynamics in Nature and Society

(1 minus 120582120572) (120579119886119871 + 120579119904119886119871+ 2119887119871119904119886119871+ 120579V120573 + 3119908

1198711205792+ 3119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

gt(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(A1)

The above equation can be simplified as

119908119871gt120579 [(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)]

4119887119871 (1 minus 120582120572) (119887119871 + 120579) (119887

119871+ 2120579)

(A2)

So we can get Corollary 8 B Proof of Corollary 9

If (1199011198941)119878lowast

gt (119901119894

1)119861lowast then

(1 minus 120582120572) (120579119886119894 + 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 2119908

1198941205792+ 2119908119894119887119894120579 minus 1205792V minus 2120579119887

119894V) + 119888120579 (119887

119894+ 120579)

minus (1 minus 120582120572) ((119901119894

1)119878lowast

+ (119901119894

1)119861lowast

) [2 (119887119894+ 120579)2minus 1205792] gt 0

120587119878lowast

1minus 120587119861lowast

1=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

2 (119887119871+ 120579)

((119901119871

1)119878lowast

minus (119901119871

1)119861lowast

)

+(1 minus 120582120572) (120579119886119867 + 120579119904119886

119867+ 2119887119867119904119886119867+ 120579V120573 + 2119908

1198671205792+ 2119908119867119887119867120579 minus 1205792V minus 2120579119887

119867V) + 119888120579 (119887

119867+ 120579)

2 (119887119867+ 120579)

((119901119867

1)119878lowast

minus (119901119867

1)119861lowast

)

minus (1 minus 120582120572)2 (119887119871+ 120579)2minus 1205792

2 (119887119871+ 120579)

[((119901119871

1)119878lowast

)2

minus ((119901119871

1)119861lowast

)2

] minus (1 minus 120582120572)2 (119887119867+ 120579)2minus 1205792

2 (119887119867+ 120579)

[((119901119867

1)119878lowast

)2

minus ((119901119867

1)119861lowast

)2

] gt 0

(B1)

If (1199011198711)119878lowast

lt (119901119871

1)119861lowast and (119901

119867

1)119878lowast

lt (119901119867

1)119861lowast we can prove

120587119878lowast

1gt 120587119861lowast

1similarly

From Propositions 3 and 7 with (3) we obtain that

120587119861lowast

2minus 120587119878lowast

2=

120579

4 (119887119871+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119871 + V (120573 + 120579) minus 119908119871(119887119871+ 120579)]

minus 2119888 (119887119871+ 120579) + 120579 (1 minus 120582120572) ((119901

119871

1)119861lowast

+ (119901119871

1)119878lowast

)

sdot ((119901119871

1)119861lowast

minus (119901119871

1)119878lowast

) +120579

4 (119887119867+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119867 + V (120573 + 120579) minus 119908 (119887119867+ 120579)]

minus 2119888 (119887119867+ 120579) + 120579 (1 minus 120582120572) ((119901

119867

1)119861lowast

+ (119901119867

1)119878lowast

)

sdot ((119901119867

1)119861lowast

minus (119901119867

1)119878lowast

)

(B2)

Note that

119863119894

2= [(1 minus 119904) 119886119894 minus 119887

119894119901119894

2] + 120573V + 120579 (119901

119894

1+ V minus 119901

119894

2) gt 0 (B3)

so we show that

2 (1 minus 120582120572) [(1 minus 119904) 119886119894 + V (120573 + 120579) minus 119908119894(119887119894+ 120579)]

minus 2119888 (119887119894+ 120579) + 120579 (1 minus 120582120572) ((119901

119894

1)119861lowast

+ (119901119894

1)119878lowast

)

gt 0

(B4)

Thus we have the following

(1) 120587119861lowast2

gt 120587119878lowast

2 if (1199011198711)119861lowast

gt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

gt (119901119867

1)119878lowast

(2) 120587119861lowast2

= 120587119878lowast

2 if (1199011198711)119861lowast

= (119901119871

1)119878lowast and (119901

119867

1)119861lowast

= (119901119867

1)119878lowast

(3) 120587119861lowast2

lt 120587119878lowast

2 if (1199011198711)119861lowast

lt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

lt (119901119867

1)119878lowast

Combined with Corollary 8 the proposition is proved

Discrete Dynamics in Nature and Society 13

C Proof of Corollary 10

The profit of hotel from the economy rooms is as follows

120587119871

= [(1 minus 120582120572) (119904119886119871 minus 120579V) minus 119888120579] 119901119871

1

+ [(1 minus 120582120572) (119886119871 minus 119904119886119871+ 120573V + 120579V) + 119888 (119887

119871+ 120579)] 119901

119871

2

+ 2120579 (1 minus 120582120572) 119901119871

1119901119871

2minus (1 minus 120582120572) (119887119871 + 120579) (119901

119871

1)2

minus (1 minus 120582120572) (119887119871 + 120579) (119901119871

2)2

minus (119886119871minus 119904119886119871+ 120573V + 120579V) 119888

(C1)

Define (119901119871

1)119861(119878)

= (119860119871

1)119861(119878)

+ (119861119871

1)119861(119878)

119908119871 (1199011198712)119861(119878)

=

(119860119871

2)119861(119878)

+ (119861119871

2)119861(119878)

119908119871 where

(119861119871

1)119861

=3120579 (119887119871+ 120579)

4 (119887119871+ 120579)2minus 1205792

(119861119871

1)119878

=120579 (119887119871+ 120579)

2 (119887119871+ 120579)2minus 1205792

(119861119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119861119871

1)119861(119878)

+1

2

(119860119871

1)119861

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

(119860119871

1)119878

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(119860119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119860119871

1)119861(119878)

+(1 minus 120582120572) [(1 minus 119904) 119886119871 + V (120579 + 120573)] + 119888 (119887

119871+ 120579)

2 (1 minus 120582120572) (119887119871 + 120579)

(C2)

Let 120597120587119871120597119908 = 0 then we get119908lowast

119871 Similarly we can get119908lowast

119867

D Proof of Proposition 12

Let 120587119889minus 120587119903gt 0 then we can get 119904

0 where the profits of hotel

from HA and OTA are as follows

120587119889= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1)

120587119903= (1 minus 120582120572) (119908119871119863

119871

2+ 119908119867119863119867

2)

(D1)

E Proof of Corollary 11

If Δ119862119871le 120582(1 minus 120582)119876

119871 then the profit of hotel is 120587119871

11 The

derivative of 12058711987111(Δ119862119871) is 120597120587119871

11120597Δ119862119871= (1 minus 120582120572)119901

119871

1gt 0 So

with the increase of Δ119862119871 12058711987111

will increase When Δ119862119871

=

120582(1 minus 120582)119876119871 12058711987111

is maximized If Δ119862119871

ge 120582(1 minus 120582)119876119871

then the profit of hotel is 12058711987112 The derivative of 120587119871

12(Δ119862119871) is

120597120587119871

12120597Δ119862119871= (1 minus 120582120572)119901

119871

1minus (1 minus 120582)(119901

119871

1+ 119888119871) lt 0 So with the

increase of Δ119862119871 12058711987111will decline When Δ119862

119871= 120582(1 minus 120582)119876

119871

120587119871

11is maximizedSimilarly we can get Δ119862lowast

119867

F Proof of Proposition 13

Assume that the overbooking proportion is 120574119871and 120574119867

(1) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) le 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

That is

120574119867lt

120582

1 minus 120582lt 120574119871

le120582119876119871+ 119876119867[1 minus (1 minus 120582) (1 + 120574

119867)]

(1 minus 120582)119876119871

(F1)

Thus the hotel would like to overbook to get more profitrather than room vacancy

(2) Consider (1198631198711+119863119871

2)(1minus120582) lt 119876

119871and (119863119867

1+119863119867

2)(1minus120582) gt

119876119867That is 120574

119871lt 120582(1 minus 120582) lt 120574

119867 Then the profit of hotel is

120587112

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F2)

Thenwhen 119888119867119906

lt (1minus120582120572)119901119867

1(1minus120582) that is120587

112minus120587111

gt 0the hotel would carry out overbooking

(3) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

14 Discrete Dynamics in Nature and Society

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867lt 120582(1 minus 120582) Then the profit of hotel is

120587113

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2+ 119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876]

(F3)

Then when 119888119871

119906lt (1 minus 120582120572)119901

119871

1(1 minus 120582) 120587

113minus120587111

gt 0 thusthe hotel would carry out overbooking

(4) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) gt 119876

119867

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867gt (120582119876

119867+ 119876119871[1 minus (1 minus 120582)(1 + 120574

119871)])(1 minus 120582)119876

119867

Then the profit of hotel is as follows

120587114

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2) (1 minus 120582) minus 119876

119871]

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F4)

Then when 119888119871119906lt (1minus120582120572)119901

119871

1(1minus120582) and 119888119867

119906lt (1minus120582120572)119901

119867

1

(1 minus 120582) 120587114

minus 120587111

gt 0 overbooking is preferred

G Threshold Values

Threshold values are as follows

1198711= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 3119908

1198941205792+ 3119908119894119887119894120579

minus 1205792V minus 2120579119887

119894V

1198712= 2119886119894(119887119894+ 120579) minus 119904119886

119894(2119887119894+ 120579) + 120579

2119908119894+ 2 (120579 + 120573) (119887

119894

+ 120579) V + 2119908119894(119887119894+ 120579)2minus 1205792V

1198713= 4120579V119887

119894120573 minus 120579119904119886

119894119887119894+ 2V1205731198872

119894+ 31198861198941205792+ 4119886119894119887119894120579

minus 21198861198941198872

119894119904 + 3120579

2V120573 + 1205792V119887119894+ 2120579V1198872

119894+ 21198861198941198872

119894

1198714= 3119886119894119887119894120579 + 3120579

2V120573 minus 2120579V1198872119894minus 1205792V119887119894+ 31198861198941205792

+ 21198861198941198872

119894119904 + 119886119887

119894119904120579 + 3119887

119894120573V120579

1198715= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 minus 120579

2V minus 2120579119887119894V

1198661= [(1 minus 120582120572) (119904119886119894 minus 120579V) minus 119888120579] (119861

119894

1)119861(119878)

+ [(1 minus 120582120572) (119886119894 minus 119904119886119894+ 120573V + 120579V) + 119888 (119887

119894+ 120579)]

sdot (119861119894

1)119861(119878)

+ 2120579 (1 minus 120582120572) [(119860119894

1)119861(119878)

(119861119894

2)119861(119878)

+ (119861119894

1)119861(119878)

(119860119894

2)119861(119878)

] minus 2 (1 minus 120582120572) (119887119894 + 120579)

sdot [(119860119894

1)119861(119878)

(119861119894

1)119861(119878)

+ (119860119894

2)119861(119878)

(119861119894

2)119861(119878)

]

1198662= 2 (1 minus 120582120572)

sdot (119887119894+ 120579) [((119861

119894

1)119861(119878)

)

2

+ ((119861119894

2)119861(119878)

)

2

]

minus 2120579 (119861119894

1)119861(119878)

(119861119894

2)119861(119878)

1199040= ((119887119871+ 120579) (119901

119871

1)2

+ (119887119867+ 120579) (119901

119867

1)2

+ 120579119908119871(119901119871

1minus 119901119871

2) + 120579119908

119867(119901119867

1minus 119901119867

2)

+ 120579V (1199011198711+ 119901119867

1) + (119908

119871+ 119908119867) (120573 + 120579) V

+ 119908119871(119886119871minus 119887119871119901119871

2) + 119908119867(119886119867minus 119887119867119901119867

2)

minus 120579 (119901119871

1119901119871

2+ 119901119867

1119901119867

2)) (119886119871(119901119871

1+ 119908119871)

+ 119886119867(119901119867

1+ 119908119867))minus1

(G1)

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The authors thank associate editor and anonymous refereesfor their numerous constructive comments and encourage-ment that have improved their paper greatly The work waspartly supported by (i) the National Natural Science Founda-tion ofChina (71201083 71572058 and 71571100) (ii) the Fun-damental Research Funds for the Central Universities SCUT(2015ZZ057) (iii) Jiangsu Province Science Foundation forYouths (BK2012379) and (iv) the Fundamental ResearchFunds for the Central Universities (NS2015076)

References

[1] J Li W N Zhang H Xu and J Jiang ldquoDynamic competitionand cooperation of road infrastructure investment of multipletourism destinations a case Study of Xidi and Hongcun WorldCulturalHeritagerdquoDiscreteDynamics inNature and Society vol2015 Article ID 962028 10 pages 2015

[2] T Paksoy EOzceylan andG-WWeber ldquoProfit oriented supplychain network optimizationrdquoCentral European Journal of Oper-ations Research vol 21 no 2 pp 455ndash478 2013

[3] X Zhang H Song and G Q Huang ldquoTourism supply chainmanagement a new research agendardquo Tourism Managementvol 30 no 3 pp 345ndash358 2009

[4] Z Yang and J Cai ldquoDo regional factors matter Determinantsof hotel industry performance in Chinardquo TourismManagementvol 52 pp 242ndash253 2016

[5] B Pan L Zhang and R Law ldquoThe complex matter of onlinehotel choicerdquoCornell Hospitality Quarterly vol 54 no 1 pp 74ndash83 2013

[6] L Ling X Guo and C Yang ldquoOpening the online marketplacean examination of hotel pricing and travel agency on-line

Discrete Dynamics in Nature and Society 15

distribution of roomsrdquo Tourism Management vol 45 pp 234ndash243 2014

[7] L Ling Y Dong X Guo and L Liang ldquoAvailability man-agement of hotel rooms under cooperation with online travelagenciesrdquo International Journal of Hospitality Management vol50 pp 145ndash152 2015

[8] J N K Liu andE Y Zhang ldquoAn investigation of factors affectingcustomer selection of online hotel booking channelsrdquo Interna-tional Journal of Hospitality Management vol 39 pp 71ndash832014

[9] L Fox ldquoFour Seasons Unveils $18 Million Website as LuxuryTravel Growsrdquo 2012 httpwwwtnoozcomarticlefour-sea-sons-unveils-18-million-dollar-website-as-luxury-travel-grows

[10] C-M Chen and Y-C Lin ldquoThe influence of uncertain demandon hotel capacityrdquo International Journal of Hospitality Manage-ment vol 34 no 1 pp 462ndash465 2013

[11] S Yang G Q Huang H Song and L Liang ldquoGame-theoreticapproach to competition dynamics in tourism supply chainsrdquoJournal of Travel Research vol 47 no 4 pp 425ndash439 2009

[12] G Q Huang H Song and X Zhang ldquoA comparative analysis ofquantity and price competitions in tourism supply chain net-works for package holidaysrdquo Service Industries Journal vol 30no 10 pp 1593ndash1606 2010

[13] Y Huang H Song G Q Huang and J Lou ldquoA comparativestudy of tourism supply chains with quantity competitionrdquoJournal of Travel Research vol 51 no 6 pp 717ndash729 2012

[14] H K Lee and Y Fernando ldquoThe antecedents and outcomes ofthe medical tourism supply chainrdquo Tourism Management vol46 pp 148ndash157 2015

[15] W-Y K Chiang D Chhajed and J D Hess ldquoDirect marketingindirect profits a strategic analysis of dual-channel supply-chain designrdquoManagement Science vol 49 no 1 pp 1ndash20 2003

[16] A A Tsay and N Agrawal ldquoChannel conflict and coordinationin the E-commerce agerdquo Production and Operations Manage-ment vol 13 no 1 pp 93ndash110 2004

[17] Q-H Li and B Li ldquoDual-channel supply chain equilibriumproblems regarding retail services and fairness concernsrdquoApplied Mathematical Modelling 2016

[18] S Panda N M Modak S S Sana and M Basu ldquoPricingand replenishment policies in dual-channel supply chain undercontinuous unit cost decreaserdquo Applied Mathematics and Com-putation vol 256 pp 913ndash929 2015

[19] Y Liu C Ding C Fan and X Chen ldquoPricing decision underdual-channel structure considering fairness and free-ridingbehaviorrdquo Discrete Dynamics in Nature and Society vol 2014Article ID 536576 10 pages 2014

[20] J Chen H Zhang and Y Sun ldquoImplementing coordinationcontracts in a manufacturer Stackelberg dual-channel supplychainrdquo Omega vol 40 no 5 pp 571ndash583 2012

[21] Q Ding C Dong and Z Pan ldquoA hierarchical pricing decisionprocess on a dual-channel problem with one manufacturer andone retailerrdquo International Journal of Production Economics vol175 pp 197ndash212 2016

[22] B Rodriguez and G Aydin ldquoPricing and assortment decisionsfor a manufacturer selling through dual channelsrdquo EuropeanJournal of Operational Research vol 242 no 3 pp 901ndash9092015

[23] T Lockyer ldquoThe perceived importance of price as one hotelselection dimensionrdquo Tourism Management vol 26 no 4 pp529ndash537 2005

[24] C-M Chen H-W Yang E Y Li and C-C Liu ldquoHow doeshotel pricing influence guest satisfaction by the moderatinginfluence of room occupancyrdquo International Journal of Hospi-tality Management vol 49 pp 136ndash138 2015

[25] J-M Espinet M Fluvia R Rigall-I-Torrent and A Salo ldquoHotelcharacteristics and seasonality in prices an analysis usingSpanish tour operatorsrsquo brochuresrdquo Tourism Economics vol 18no 4 pp 749ndash767 2012

[26] C Juaneda J M Raya and F Sastre ldquoPricing the time and loca-tion of a stay at a hotel or apartmentrdquo Tourism Economics vol17 no 2 pp 321ndash338 2011

[27] G Abrate G Fraquelli and G Viglia ldquoDynamic pricing strate-gies evidence from European hotelsrdquo International Journal ofHospitality Management vol 31 no 1 pp 160ndash168 2012

[28] D Q Yao and J J Liu ldquoCompetitive pricing of mixed retail ande-tail distribution channelsrdquo Omega vol 33 no 3 pp 235ndash2472005

[29] J Zhao and L Wang ldquoPricing and retail service decisionsin fuzzy uncertainty environmentsrdquo Applied Mathematics andComputation vol 250 pp 580ndash592 2015

[30] A A Tsay and N Agrawal ldquoChannel dynamics under priceand service competitionrdquo Manufacturing amp Service OperationsManagement vol 2 no 4 pp 372ndash391 2000

[31] S C Choi ldquoPrice competition in a duopoly common retailerchannelrdquo Journal of Retailing vol 72 no 2 pp 117ndash134 1996

[32] Y Bakos andE Brynjolfsson ldquoBundling and competition on theinternetrdquoMarketing Science vol 19 no 1 pp 63ndash82 2000

[33] H Song J H Kim and S Yang ldquoConfidence intervals fortourism demand elasticityrdquo Annals of Tourism Research vol 37no 2 pp 377ndash396 2010

[34] DMHanssens L J Parsons andR L SchultzMarket ResponseModels Econometric and Time Series Analysis Kluwer Aca-demic Publishers Boston Mass USA 2nd edition 2001

[35] H Kurata D-Q Yao and J J Liu ldquoPricing policies under directvs indirect channel competition and national vs store brandcompetitionrdquo European Journal of Operational Research vol180 no 1 pp 262ndash281 2007

[36] R Law and C Cheung ldquoA study of the perceived importance ofthe overall website quality of different classes of hotelsrdquo Inter-national Journal of Hospitality Management vol 25 no 3 pp525ndash531 2006

[37] K B Chen ldquoProcurement strategies and coordination mecha-nism of the supply chain with one manufacturer and multiplesuppliersrdquo International Journal of Production Economics vol138 no 1 pp 125ndash135 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Discrete Dynamics in Nature and Society 3

Liu et al [19] investigated the pricing decisions under dual-channel structure In their model fairness and free-ridingbehavior are considered They detected that manufacturerrsquosequilibrium price based on channel fairness is below its equi-librium price ignoring fairness More related articles on thisissue have been presented by Chen et al [20] Ding et al [21]and Rodriguez and Aydin [22]

23 RevenueManagement Revenuemanagement whichwasoriginated in the airline industry is also widely used in thehotel industry That is because airline and hotel have similarcharacteristics (eg perishable service or product fixedcapacity distinct customer segmentation and price differen-tiation) In this aspect the room pricing decision has beenstudied extensively since price has an important influence oncustomerrsquos accommodation selection decisions [23] It is alsorelevant to our study

Chen et al [24] examined the impact of hotel pricing onguest satisfaction Their results imply that at the low pricelevel room price and food and beverage price lead to anincrease in guest satisfaction whereas the high price levelcould have just the opposite effect Ling et al [6] consid-ered the case that customers can make reservations directlythrough the distribution channel of the hotel or indirectlythrough the OTA Although the background of the studyis similar to that in our model they aim to find a methodfor hotels to manage their room availability for cooperativeOTAs Espinet et al [25] analyzed how hotel characteristicsaffect seasonality in prices and find that more hotel servicesand higher star ratings are associated with fewer seasonalvariations in hotel prices Juaneda et al [26] investigated theprice component of physical characteristics and the locationof apartments and hotels and compare their effect on thefinal price of both types of accommodation Abrate et al [27]collected data from almost 1000 hotels in Europe to analyzethe dynamic pricing strategies of hotels they showed thatthe intertemporal pricing structure primarily depends on thetype of customer the star rating and the number of supplierswith available rooms

The extant literature about revenuemanagement ismostlyfrom the perspective of the hotel itself However nowadaysthe competition among tourism enterprises turns to begradually and distinctly embodied in the competition amongtheir tourism supply chains In contrast to the above papersour model is more practical by considering pricing strategiesfrom the perspective of tourism dual-channel supply chain

This papermakes the following contributions Firstly thispaper introduces the tourism products into the dual-channelsupply chain framework while the aforementioned literatureignores this point Secondly the rooms in our research areclassified into economic and luxury type which can be betterto reflect the reality Thirdly this paper aims to illustrate thepricing decisions under several common cases which canprovide a valuable reference for hotels and OTAs

3 Model Setup and Notations

We consider a tourism supply chain model involving onehotel and one OTA (Figure 1) The hotel and OTA are both

Upstream(hotel)

Downstream(traveler)

Hotel alliance

Service agentseLong and Ctrip

wL wH pL

2 pH

2

pL

1 pH

1

Figure 1 Tourism dual-channel supply chain model diagram

risk neutral and completely rational The hotel is requiredto sign a cooperation agreement to join a HA HoweverHA charges the hotel trivial commissions Thus HA can betreated as a hotelrsquos direct sales platform and HArsquos price isdecided by the hotel directlyTherefore it is negligible to con-sider the contractual relationship between the hotel and HA

For the hotel customers are usually divided into twotypes business travelers and leisure travelers Leisure travel-ers aremore sensitive to roomprice than business ones so thatthey oftenmake a reservation before a long time Accordinglyhotels prefer to sell luxury rooms to business travelers Cor-respondingly the hotel rooms are usually classified accordingto different customersrsquo need such as luxury rooms economyrooms standard rooms and business roomsThrough settingdifferent rates for different rooms hotels are able to selldifferent types of rooms to specific target customers Basedon the above background in our model the hotel rooms areclassified into economic and luxury type In this paper hotelsells roommeans that hotel sells the right for guest to use theroom that is the hotel rents the room to guest for a periodof time The hotel sells the economy (luxury) rooms with theprice of 119901119871

1(1199011198671) to the customer directly and it sells rooms to

OTA with the wholesale prices of 119908119871(119908119867) respectively Pro-

viding combination of products and additional services OTAsells rooms to customers with the prices of 119901119871

2and 119901

119867

2

According to international practice in order to reducethe phenomenon of no-show customers must provide hotelreservation deposit with credit card or prepay the fee whenthey make reservation If customers cancel the booking orchoose no-show the hotel can deduct all or part of the roomcharge Take for example Ctripcom the orders can bedivided into two types orders that cannot be cancelled andtime-limited orders When customers choose the orders thatcannot be cancelled they cannot cancel the order after theyconform the booking if not the reservation deposit orprepaid fee will not be returnedThis kind of situation usuallyoccurs when guest room resources are intense The time-limited order means that customers can cancel the order forfree before the deadline (usually 1 to 3 days before check-in) Ifcustomers cancel the booking after the deadline or choose no-show Ctripcom will charge the customers for the first dayrsquosroom fee as a punishment This also means that when thecustomer reserves a room for more than one day he willreceive partial refund Such methods are also adopted byBookingcom and eLongcom Based on reality we assumethat customers must provide full guarantee with credit cardwhen they make reservation but if the customers cancel

4 Discrete Dynamics in Nature and Society

the booking or choose no-show finally the hotel would onlyreturn certain expense rate of 120572 (0 le 120572 le 1) If a customeris booking through OTA then OTA would return to thecustomer with the proportion of the retail prices At the sametime the hotel would return to OTA with the proportionof the wholesale prices We assume that the proportion thathotel returns to the customer the proportion that hotelreturns to OTA and the proportion that OTA returns to thecustomer are the same

We list the following notations where 119894 (119894 = 119871119867) insubscripts or superscripts are for economic (low price) andluxury (high price) rooms respectively

119876 the total number of rooms provided for renting toguests119876119894 the total number of economicluxury rooms

119863119894

1 the reservation amount of economicluxury room

booking through HA119863119894

2 the reservation amount of economicluxury room

booking through OTA119886119894 the market base demand of economicluxury

room119886 the total market base demand of rooms (119886 = 119886

119871+

119886119867)

119904 themarket share of HA in the tourism dual-channelsupply chain119901119894

1 HArsquos price of economicluxury rooms that is the

direct selling prices119901119894

2 OTArsquos price of economicluxury rooms that is the

retail prices119908119894 the wholesale price of economicluxury rooms

119887119894 the price sensitivity coefficient of 119894 price rooms

(119887119871gt 119887119867)

120579 the diffusion intensity which describes the shiftbetween two channels with regard to the price andvalue120582 the proportion of customer cancellations and no-show120572 the return expense proportion of customer cancel-lations and no-show (0 le 120572 le 1)120573 the services elasticity of demandV the value added by OTArsquos services120578 the coefficient of service cost119888(V) the function of service cost 119888(V) = 120578V221205871 the profit of the hotel

1205872 the profit of the OTA

In the model we do not consider the marginal sales costof the hotel since it is very low In reality OTA will firstlyintroduce to customers the hotelsrsquo facilities and quota andafterwards confirm the booking and finally book rooms fromthe hotel for customersTherefore the rooms sold by HA and

OTA are homogeneous In addition to providing hotel reser-vations OTA also provides other related services as wellsuch as offering plane ticket booking holiday booking andtravel information OTA aims to provide a full range of travelprogram for travelers In order to provide such services OTAneeds to pay for additional operating costs The customerswho want to get more tourist information and services willprefer to reserve rooms through OTA By contrast HA onlyprovides hotel room information for customers For instancecustomers cannot book the suitable hotel and air ticket at thesame time through the HA platform Consequently in orderto distinguish the influence of different information servicesto customerrsquos channel choice we suppose that OTA providesadditional service and the value added from the services is VFurther the cost for providing service is 119888(V) = 120578V22 wherethe parameter 120578measures the cost effectiveness of the serviceSuch cost function is commonly adopted in previous litera-ture and canwell describe the relationship between additionalservices and cost [28 29] When OTA does not provide theservice the cost should be zero

According to the process of demand function in Tsay andAgrawal [30] andChoi [31] the demands of economicluxuryrooms through each channel are expressed as follows

119863119894

1= (119904119886119894minus 119887119894119901119894

1) + 120579 (119901

119894

2minus V minus 119901

119894

1)

119863119894

2= [(1 minus 119904) 119886119894 minus 119887

119894119901119894

2] + 120573V + 120579 (119901

119894

1+ V minus 119901

119894

2)

(1)

Such linear demand functions are used because they canachieve approximate and satisfactory fit to certain types ofdemand and they are tractable and widely used in marketingand supply chain management literature [32] In our modelthe parameter 119887 represents the price sensitivity coefficientIt describes the marginal channel demand per respectivechannel price The own price elasticity is normally negative[33] And the parameter 120573measures the marginal demand ofOTA per service value added In addition the parameter 120579 isunderstood as the diffusion intensity (cross-price sensitivity)and describes the shift between two channels with regard tothe price and the value Suchmodelingmethod can guaranteethat the self-price sensitivity in absolute value is strongerthan the cross-price sensitivity which is proved by Hanssenset al [34] and used by Yao and Liu [28] Choi [31] and Kurataet al [35]

Now consider the situation without overbooking that is119863119871

1+ 119863119871

2le 119876119871and 119863

119867

1+ 119863119867

2le 119876119867 Thus the reservation

amount can be regarded as the final demandThe total profit for the hotel OTA and the whole supply

chain can be expressed as follows

1205871= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2) (2)

1205872= [(1 minus 120582120572) (119901

119871

2minus 119908119871) minus 119888 (V)]119863119871

2

+ [(1 minus 120582120572) (119901119867

2minus 119908119867) minus 119888 (V)]119863119867

2

(3)

120587 = 1205871+ 1205872 (4)

Discrete Dynamics in Nature and Society 5

4 Integrated System

As a benchmark we first consider an integrated systemwherethe common goal of supply chain upstream and downstreammembers is tomaximize the overall profit of the supply chainThis is an ideal model that the members in the supply chainoperate as an entirety In such an integratedmodel of tourismsupply chain the hotel and OTA cooperate to determine thepricing strategies

Proposition 1 In the integrated system the optimal pricingdecisions of HA and OTA are as follows

119901119894lowast

1=119886119894(119887119894119904 + 120579) + 120579V (120573 minus 119887

119894)

2 (119887119894)2+ 4119887119894120579

119901119894lowast

2=(119887119894+ 120579 minus 119887

119894119904) 119886119894+ 119887119894120573V + 120579V (120573 + 119887

119894)

2 (119887119894)2+ 4119887119894120579

+119888 (V)

2 (1 minus 120582120572)

119894 = 119871119867

(5)

From Proposition 1 the optimal prices shown above canexplain that in the integrated system the optimal prices of HAwill not be affected by the proportion of customer cancella-tions and no-show (120582) or the return expense proportion (120572)On the other hand with the increase of 120582 or 120572 the optimalprices for OTAwill increaseThis is reasonable because whenOTA faces unstable demand or it should return more tocustomersrsquo cancellation or no-show it would like to increasethe price to guarantee its profit

Corollary 2 119901119871lowast2

and 119901119867lowast2

are increasing in V Moreover

(1) if 120573 gt 119887119871gt 119887119867 then 120597119901

119871lowast

1120597V gt 0 120597119901119867lowast

1120597V gt 0

(2) if 119887119871gt 120573 gt 119887

119867 then 120597119901

119871lowast

1120597V lt 0 120597119901119867lowast

1120597V gt 0

(3) if 119887119871gt 119887119867gt 120573 then 120597119901

119871lowast

1120597V lt 0 120597119901119867lowast

1120597V lt 0

From Corollary 2 we can know that when OTA offersmore services OTArsquos optimal price will be increased accord-ingly It is reasonable that if V increases the cost of OTA willalso definitely increase So there is always a positive correla-tion between OTArsquos optimal prices and the added value

If 120573 gt 119887119871

gt 119887119867 the market of economy rooms and

that of luxury rooms are both service-oriented rather thanprice-oriented The implication is that the effective servicewill increase the optimal price of HAWhenOTA offersmoreeffective service its price will increase But some customerswant to enjoy the additional services so they are willingto make a booking through OTA despite spending moremoneyTherefore the demand inOTAwill increase while thedemand in HA will decrease

If 119887119871gt 120573 gt 119887

119867 the market of economy rooms is service-

oriented while the market of luxury rooms is price-orientedThe HArsquos optimal price of economy rooms will decrease withrespect to V Conversely the HArsquos optimal price of luxuryrooms will increase with respect to V For examples the

change of price has a great impact on leisure travelersrsquo deci-sions but for business travelers the price is not themost con-cern If the price ofOTA increasesOTArsquos demandof economyrooms will significantly reduce and the HArsquos demand willincrease thus the HArsquos optimal price will decline On theother hand for luxury rooms if OTA provides more effectiveservice the customer would be willing to pay higher pricesfor value-added service This will bring the increase in OTArsquosdemand and the reduction of HArsquos demand thus the optimalprice of HA will increase

If 119887119871gt 119887119867gt 120573 the market of economy rooms and that of

luxury rooms are both price-oriented than service-orientedThe HArsquos optimal price of both economy rooms and luxuryrooms will decrease with the increase of V When the marketis price-oriented the promotion of price in OTAwill lead to areduction in OTArsquos demandThereby the demand in HA willincrease and optimal price in HA will decline

5 Two Game Models

In the tourism dual-channel supply chain the relationshipbetween hotel and OTA is cooperative as well as competitiveIn the decentralized decision-making model they are morecompetitive than cooperative Their purposes are to maxi-mize their own profits In reality hotel can choose whether toinform the price ofHAor not forHA is competingwithOTAUninformed of the prices inHAOTAcan predict the range ofprice onHAby the star-rated and room type of the hotel but itcannot know the exact priceTherefore this section examinesthe pricing equilibrium between the hotel and OTA undertwo types of games namely the Bertrand and Stackelberggames For the Bertrand game both of the participantsregard price as a decision variable the hotel and OTA areuncooperative For the Stackelberg game the participantsare divided into two roles the leader and the follower Asa leader in tourism supply chain the hotel will provide thepolicy to maximize its interests As a follower OTA accepts ifprofitable By comparing the two models we can understandhow the behavior of hotel influences the pricing decisions

51 Bertrand Game In a Bertrand game the procedure isas follows keeping the wholesale price unchanged the hoteldetermines HArsquos prices 119901119871

1and 119901

119867

1 so as to maximize profit

1205871 Uninformed of the prices of HA OTA decides prices 119901119871

2

and 119901119867

2 so as to maximize his profit 120587

2 Let (119901119894

1)119861 (1199011198942)119861(119894 =

119871119867) denote HArsquos and OTArsquos prices under a Bertrand modelrespectively

In the following 119871119899(119899 = 1 2 5) 119904

0 and 119866

119898(119898 =

1 2) are the threshold values and are given in Appendix G

Proposition 3 There exist Bertrand equilibrium prices(119901119894

1)119861lowast (119901119894

2)119861lowast

(119894 = 119871119867) where

(119901119894

1)119861lowast

=(1 minus 120582120572) 1198711 + 119888120579 (119887

119894+ 120579)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

2)119861lowast

=(1 minus 120582120572) 1198712 + 2119888 (119887

119894+ 120579)2

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(6)

6 Discrete Dynamics in Nature and Society

From Proposition 3 in the Bertrand model the equilib-rium prices for hotel and OTA are both affected by 120572 and 120582With the increase of 120572 or 120582 both (119901

119894

1)119861lowast and (119901

119894

2)119861lowast will be

higher In otherwords with higher uncertainty of roomoccu-pancy the hotel and OTA tend to increase prices to protecttheir own profits

Denote 1198881= (1 minus 120582120572)(2119887

119871+ 120579 minus 120573)(119887

119871+ 120579) and 119888

2= (1 minus

120582120572)(2119887119867+ 120579 minus 120573)(119887

119867+ 120579) then 119888

1gt 1198882

Corollary 4 (1199011198712)119861lowast and (119901

119867

2)119861lowast are increasing in V (119901119871

1)119861lowast

and (119901119867

1)119861lowast have the following relationships with respect to

OTArsquos service

(1) if 1198881015840(V) gt 1198881 then 120597(119901

119871

1)119861lowast120597V gt 0 120597(119901119867

1)119861lowast120597V gt 0

(2) if 1198881gt 1198881015840(V) gt 119888

2 then 120597(119901

119871

1)119861lowast120597V lt 0 120597(119901119867

1)119861lowast120597V gt

0(3) if 1198881015840(V) lt 119888

2 then 120597(119901

119871

1)119861lowast120597V lt 0 120597(119901119867

1)119861lowast120597V lt 0

From Corollary 4 when OTA offers more effective ser-vices its optimal prices will increase due to the incrementin the cost Marginal cost measures the input costs and theoutput value per unit If the marginal cost is greater than1198881 then the costs of OTA to provide additional services are

higher So the equilibrium prices of HA will increase as thevalue added by OTArsquos services increases When the marginalcost is between 119888

1and 1198882 HArsquos equilibrium price of economy

rooms and the value added by OTArsquos service have a negativecorrelation but HArsquos equilibrium price of luxury roomswould increase with the increment of V In addition when themarginal cost is less than 119888

2 the costs of OTA to provide addi-

tional service are lower And the equilibriumprices ofHAwilldecrease when V increases

Corollary 5 There exist threshold unit wholesale prices 1199080119894

1199081

119894(119894 = 119871119867) such that

(1) (1199011198941)lowastlt (119901119894

1)119861lowast if 119908

119894gt 1199080

119894 (1199011198941)lowast= (119901119894

1)119861lowast if 119908

119894= 1199080

119894

(119901119894

1)lowastgt (119901119894

1)119861lowast if 119908

119894lt 1199080

119894

(2) (1199011198942)lowastlt (119901119894

2)119861lowast if 119908

119894gt 1199081

119894 (1199011198942)lowast= (119901119894

2)119861lowast if 119908

119894= 1199081

119894

(119901119894

2)lowastgt (119901119894

2)119861lowast if 119908

119894lt 1199081

119894

where

1199080

119894=

1198713

6119887119894(119887119894+ 120579) (119887

119894+ 2120579)

minus119888

3 (1 minus 120582120572)

1199081

119894=

120579 [(1 minus 120582120572) 1198714 minus 119888119887119894120579 (119887119894+ 2120579)]

2119887119894 (1 minus 120582120572) (119887119894 + 2120579) (31205792 + 21198872

119894+ 2119887119894120579)

(7)

FromProposition 1 it is easy to know that the equilibriumprices in the integrated system are not affected by the whole-sale prices However from Proposition 3 in the Bertrandmodel there is a positive correlation between the equilibriumprices and the wholesale prices Corollary 5 shows that theequilibrium price of HA in the Bertrand game is higherthan that in the integrated system if the wholesale price isgreater than a certain critical point (1199080

119894) Additionally if the

wholesale price is greater than1199081119894 then the equilibrium price

of OTA in Bertrand model will be higher than that in theintegrated model

Corollary 6 There exists a threshold unit wholesale price1199082

119894(119894 = 119871119867) such that if119908

119894gt 1199082

119894 then119863lowast

119894gt 119863119861lowast

119894(119894 = 119871119867)

where

1199082

119894=120579 [(1 minus 120582120572) (V120573 + 119886

119894) minus 119887119894119888]

2119887119894 (1 minus 120582120572) (119887119894 + 2120579)

(8)

Corollary 6 shows that when thewholesale price is greaterthan 119908

2

119894 the high price will lead to a lower demand in the

Bertrand game That is the reservation amount of Bertrandmodel is less than that in the integrated model The highersale price in OTA results from the higher wholesale priceThus the above result is reasonable because travelers are pricesensitive especially for leisure travelers the increase of pricewill bring the decline of reservation amount When the rela-tionship between the hotel and OTA is modeled as a Stackel-berg game the hotel canmotivate customers to reserve roomsthrough a reasonable wholesale price If the wholesale price isgreater than the threshold the sales volume in the centralizedcase is lower than that in the Bertrand case

52 Stackelberg Game In a Stackelberg game the procedureis as follows keeping thewholesale price unchanged the hotel(as the leader) announces HArsquos prices 119901119871

1and 119901119867

1of two types

of rooms respectively in order to maximize its profit 1205871 In

response to HArsquos prices OTA (as the follower) determinesprices 119901

119871

2and 119901

119867

2to maximize its profit 120587

2 Let (119901

119894

1)119878

(119901119894

2)119878(119894 = 119871119867) denote respectively HArsquos and OTArsquos prices

under a Stackelberg game

Proposition 7 The optimal prices are (119901119894

1)119878lowast (119901119894

2)119878lowast

(119894 =

119871119867) and there exists a threshold unit wholesale price 1199083119894(119894 =

119871119867) such that if 119908119894gt 1199083

119894 then (119901

119894

1)lowastlt (119901119894

1)119878lowast where

(119901119894

1)119878lowast

=(1 minus 120582120572) (1198711 minus 119908

1198941205792minus 119908119894119887119894120579) + 119888120579 (119887

119894+ 120579)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 21205792]

(119901119894

2)119878lowast

=120579 (119901119894

1)119878lowast

+ (1 minus 119904) 119886119894 + V (120579 + 120573) + 119908119894(119887119894+ 120579)

2 (119887119894+ 120579)

+119888

2 (1 minus 120582120572)

1199083

119894

=119887119894V120573 + 119886119887

119894+ 120579V119887119894+ 119886119894120579 + 120579V120573 minus 119886

119894119887119894119904

2119887119894(119887119894+ 2120579)

minus119888

2 (1 minus 120582120572)

(9)

Similar to the Bertrand competition the equilibriumprices in Stackelberg game will increase with the increase of

Discrete Dynamics in Nature and Society 7

the return expense proportion (120572) or the cancellations andno-show proportion (120582)

From Proposition 7 we can see that the Stackelbergmodel is similar to the Bertrand model that the equilibriumprices would increase with the increase of wholesale pricesFurthermore when thewholesale price is greater than1199083

119894 the

equilibrium price of HA in Stackelberg model will be higherthan that in the integrated model

In the Stackelberg game if OTA offers more effective ser-vices the equilibrium prices of OTA would increase accord-ingly The relationship between the Stackelberg equilibriumprices and V is similar to that in the Bertrand model

53 Contrastive Analysis of Bertrand and Stackelberg GamesBased on the equilibrium prices obtained in the previoussection we in this section compare the equilibriumprices andoptimal profit under Bertrand and Stackelberg games

Corollary 8 There exists a threshold unit wholesale price1199084

119894(119894 = 119871119867) such that

(1) (1199011198941)119861lowast

gt (119901119894

1)119878lowast and (119901119894

2)119861lowast

gt (119901119894

2)119878lowast if 119908

119894gt 1199084

119894

(2) (1199011198941)119861lowast

= (119901119894

1)119878lowast and (119901119894

2)119861lowast

= (119901119894

2)119878lowast if 119908

119894= 1199084

119894

(3) (1199011198941)119861lowast

lt (119901119894

1)119878lowast and (119901119894

2)119861lowast

lt (119901119894

2)119878lowast if 119908

119894lt 1199084

119894

where

1199084

119894=

120579 [(1 minus 120582120572) 1198715 + 119888120579 (119887119894+ 120579)]

4119887119894 (1 minus 120582120572) (119887119894 + 120579) (119887

119894+ 2120579)

(10)

Corollary 8 compares the equilibrium prices under theBertrand and Stackelberg game with respect to the wholesaleprice It shows that if the wholesale price is greater than1199084

119894 the pricing equilibrium under the Bertrand is higher

than that under the Stackelberg game Conversely the pricingequilibrium is lower if the wholesale price is less than 119908

4

119894

In the decentralized case both the manufacturer and theretailer want to maximize their profit A high wholesale pricecould be passed on to customersTherefore the above resultsexist In addition how to share the profit between the manu-facturer and the retailer depends on their bargaining powers

Corollary 9 If 119908119894

= 1199084

119894(119894 = 119871119867) then 120587

119878lowast

1gt 120587119861lowast

1 OTArsquos

profit has the following relationship with respect to 1199084119894

(1) 120587119861lowast2

gt 120587119878lowast

2if 119908119871gt 1199084

119871and 119908

119867gt 1199084

119867

(2) 120587119861lowast2

= 120587119878lowast

2if 119908119871= 1199084

119871and 119908

119867= 1199084

119867

(3) 120587119861lowast2

lt 120587119878lowast

2if 119908119871lt 1199084

119871and 119908

119867lt 1199084

119867

Thehotel is the leader in Stackelberg game and can alwaysbenefit from it except for the critical point1199084

119894 Comparedwith

the Bertrand game the hotel can get higher profits in Stackel-berg gamewhen the wholesale price is not equal to1199084

119894There-

fore in decentralized decision-making model the hotel willbe more inclined to be the price leader in order to ensure thatit can achieve higher profits

Corollary 9 indicates that the Stackelberg model is supe-rior to the Bertrand model when the wholesale price is less

than the critical point1199084119894 Not only the hotel but alsoOTA can

gain more profit from the Stackelberg game Though OTA isa follower in Stackelberg game the profit will not be reducedbecause the lower wholesale prices can compensate for theloss of profit caused by the opening of HA channel Conse-quently the hotel should play the role of the price leader inthe supply chain and develop reasonable wholesale prices toachieve optimization of the whole supply chain profit whileoptimizing its own profit

Corollary 10 Under either Bertrand or Stackelberg equi-librium channel prices there exists optimal wholesale price119908lowast

119894(119894 = 119871119867) that maximizes the total equilibrium channel

profit where 119908lowast119894= 11986611198662

According to Corollary 10 there exists optimal wholesaleprice 119908

lowast

119894(119894 = 119871119867) that maximizes the total equilibrium

channel profit under either Bertrand or Stackelberg gameThe optimal wholesale price will optimize the decentralizeddecision-making supply chainMeanwhile both the hotel andtheOTA can benefit from the optimal wholesale priceThere-fore the reasonable wholesale price can help promotemutualcooperation and communication between the supply chainmembers

54 Contrastive Analysis of Two Channels in the Supply Chain

Corollary 11 There exists a threshold unit market share of HAin the tourism dual-channel supply chain (119904

0) such that when

119904 gt 1199040 the hotelrsquos profit from HA is higher than that from OTA

Keeping the wholesale prices and sales prices unchangedwhen the market share of HA in the tourism dual-channelsupply chain exceeds a certain value 119904

0 the hotelrsquos profit from

HA is higher than that from OTA The result is suitable forthe integrated system Bertrand and Stackelberg games Fromthe perspective of hotelrsquos revenue the hotel should explorethe channel for direct selling actively Also the hotel canstrengthen the promotion of HA channel to improve thecustomerrsquos understanding and preference for theHA channelBut the premise is that the profit growth from the promotioncan compensate for the cost According to the statistical datafrom the hotel price competitiveness analysis report in thefirst half of 2012 we know that the booking cost from directselling channel is about 1 dollar per night but that fromOTAis about 10 dollars per night Booking cost can be reducedby 46 if the direct selling level is doubled Then improvingthe market share of direct selling will greatly reduce the costMore comparisons of different channelrsquos profits in eachmodelcan be found in part of numerical analysis

6 Overbooking

This section extends to consider the overbooking caseRegarding overbooking in the hospitality industry the com-mon practice is that the hotel upgrades the room type ortransfers customers to other hotels nearby that have the samelevel and same type In airline industry if customers aredenied boarding after arriving at the airport the airline will

8 Discrete Dynamics in Nature and Society

provide a free upgrade endorse the ticket or provide com-pensation for the customers according to specific situationCompared to the hotels the airlines cannot transfer cus-tomers to other companies The air ticket alteration will usu-ally disrupt customersrsquo traveling schedule Though the over-booking by airlines has been well studied in the literature ourresearch is new in the hospitality industry by considering theoverbooking withwithout room transfer with the hope thatcertain implications can be enlightened to the hotel man-agers

The hotel wants to increase the occupancy rates toincrease the profits through overbooking However over-booking will lead to the risk that the actual occupancyamount is greater than the number of hotel roomsThereforethe hotel has to provide compensation to travelers who can-not check in that is overbooking cost The greater the num-bers of overbooking the less the probability of room vacancybut at the same time travelers are more likely to be refusedby the hotel Therefore the hotel must balance between thevacancy lost and the overbooking costs We develop a modelto analyze the overbooking choice

In reality the OTA is always a crucial partner of hotelsfor it can attract a large number of customers for hotelsand improve their occupancy rates [36] Spontaneously theOTA plays an increasingly significant role in the distributionsystems of hotels [5 7] By contrast the HA mainly providesa platform for individual guest Compared with individualcustomers hotel pays more attention to the long-term coop-eration relationship with the OTA Therefore in our modelwe assume that when the market demand is greater than thesupply and the hotel does not carry out overbooking the hotelwould give priority to customers who are booking fromOTA

61 Without Room Transfer Here we consider the casewith no room transfer When the actual occupancy amountexceeds the total quantity of rooms the hotel does not arrangeother alternative accommodation for the customers who can-not check in But the hotel must pay the loss of goodwill costSuppose that the overbooking quantity of economy and lux-ury rooms isΔ119862

119871andΔ119862

119867and the overbooking cost is 119888

119871and

119888119867 respectivelyWe discuss economy roomsrsquo overbooking The actual

occupancy can be either of the following two cases (1) when119876119871

lt 119863119871

1+ 119863119871

2le 119876119871+ Δ119862

119871 the reservation amount of

rooms is 1198631198711+ 119863119871

2 so the actual occupancy amount is (119863119871

1+

119863119871

2)(1 minus 120582) (2) when119863

119871

1+ 119863119871

2gt 119876119871+ Δ119862

119871 the reservation

amount is 119876119871+ Δ119862119871 then the actual occupancy amount is

(119876119871+Δ119862119871)(1 minus 120582) Therefore if (119876

119871+Δ119862119871)(1 minus 120582) le 119876

119871 that

is Δ119862119871le 120582119876119871(1 minus 120582) the profit of hotel is

120587119871

11= (1 minus 120582120572) [119901

119871

1(119876119871+ Δ119862119871minus 119863119871

2) + 119908119871119863119871

2] (11)

If (119876119871+ Δ119862119871)(1 minus 120582) ge 119876

119871 that is Δ119862

119871ge 120582119876119871(1 minus 120582)

the economy roomsrsquo actual occupancy amount exceeds theeconomy roomsrsquo number in the hotel so the hotel must paythe overbooking cost then the profit of hotel is

120587119871

12= (1 minus 120582120572) [119901

119871

1(119876119871+ Δ119862119871minus 119863119871

2) + 119908119871119863119871

2]

minus (119901119871

1+ 119888119871) [(119876119871+ Δ119862119871) (1 minus 120582) minus 119876

119871]

(12)

Proposition 12 Without considering roomsrsquo transfer the opti-mal overbooking quantity of economy rooms and luxury roomsis

Δ119862lowast

119894=

120582

1 minus 120582119876119894 119894 = 119871119867 (13)

FromProposition 12 we know that the higher the propor-tion of customer cancellations and no-show is the larger theoptimal overbooking quantity of the hotel will be With theincrease of 120572 the penalty that customers need to pay for theircancellation or no-show decreases Two following extremesituations are considered When 120572 = 1 the hotel will returnall the guarantee fee in case of customersrsquo cancellation or no-showThat is the same as the hotel does not charge customersany guarantee fee when customers book the rooms Undersuch circumstances customers can book rooms for severaldays firstly after they identify a specific itinerary they cancancel the extra rooms for they do not suffer any loss It is nodoubt that such regulation will increase the cancellation andno-show rate On the other hand if 120572 = 1 all the guaranteefee will not be returned after cancellation or no-show In thiscase customers need to reserve a room cautiously If it is notnecessary customers will not choose cancellation or no-showbecause the penalty cost is too high Such policy will reducethe cancellation and no-show rate Spontaneously to someextent 120572 and 120582 are positive correlation When the hotelincreases proportion 120572 it would like to increase the over-booking quantity so as to increase the actual occupancy rateNowadays the time-limited orders are widely used amonghotels Such regulation cannot only reduce customersrsquo lossfor the change of schedule but also help the hotel confirmthe orders so as to handle the overbooking phenomenon inadvance

In addition the risk of overbooking the economy roomsis relatively lower than the luxury rooms Compared toeconomic rooms it is more difficult for the hotel to findalternative luxury rooms to satisfy the customers Naturallyoverbooking cost of luxury room is higher For instance ifeconomy rooms are overbooked the hotel can transfer thecustomers to luxury rooms and the customers are willingto accept By contrast if luxury rooms are overbooked cus-tomers are not willing to accept the adjustment from luxuryrooms to economic rooms This implies that the hotel has topay a higher default costTherefore the hotel should be morecareful to choose the overbooking quantity of luxury rooms

62 With Room Transfer The following discusses the casewith room transfer Firstly when the economy rooms areinsufficient and luxury rooms have a surplus customers cancheck in the hotelrsquos luxury rooms with the price of economyrooms Customers spend the same money and can enjoybetter service so they are willing to accept this adjustmentSecondly when the luxury roomsrsquo actual occupancy amountexceeds the number of luxury rooms in the hotel the hotelusually transfers customers to other hotels nearby that havethe same level and same type because the customers whobook luxury room have a high requirement Customers canenjoy the same service so they are willing to accept this trans-fer However the hotelrsquos credibility in customersrsquo mind will be

Discrete Dynamics in Nature and Society 9

damaged and it must pay the additional costsThirdly if boththe economy rooms and luxury rooms are unable to meetthe demand the hotel usually transfers the customers whocannot check in to other hotels Note that when119863119894

1+119863119894

2gt 119876119894

119894 = 119871119867 if the hotel does not overbook its profit is

120587111

= (1 minus 120582120572) [119901119871

1(119876119871minus 119863119871

2) + 119901119867

1(119876119867minus 119863119867

2)

+ 119908119871119863119871

2+ 119908119867119863119867

2]

(14)

Proposition 13 With room transfer there exists threshold unitoverbooking cost 119888

1198940 such that if 119888

119894lt 1198881198940 then overbooking is

profitable for the hotel where

1198881198940=(1 minus 120582120572) 119901

119894

1

1 minus 120582 119894 = 119871119867 (15)

From Propositions 12 and 13 we conclude that the hotelshould control the overbooking quantity in a certain rangeto prevent lacking of rooms If the overbooking proportionis too large then the hotel may face a loss Only when theoverbooking cost is low the hotel can obtain additional profitOtherwise if the overbooking cost exceeds a certain valuethe hotelrsquos profit would be lower when it carries out over-booking As the market demand increases the supply is closeto saturation and then the overbooking costs will be higherTherefore when the market demand is excessive the hotelshould strictly control the proportion of overbooking Inaddition if the number of hotels that have the same level andtype in the same region is little that is the possibility to trans-fer customer is small then the hotel should lower the propor-tion of overbooking

The proportion of overbooking depends on the propor-tion of customer cancellations andno-showaswell as the totalnumber of hotel rooms so the hotel can analyze the historicaldata to develop an appropriate overbooking proportion so asto maximize the hotelrsquos expected profit

Proposition 14 When the economy rooms and luxury roomsare both overbooked the optimal centralized prices are asfollows 119894 = 119871119867

119901119894lowast

14= 119901119894lowast

1+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

119901119894lowast

24= 119901119894lowast

2+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

(16)

Bertrand and Stackelberg prices are as follows

(119901119894

14)119861lowast

= (119901119894

1)119861lowast

+2119888119894

119906119887119894(119887119894+ 120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

24)119861lowast

= (119901119894

2)119861lowast

+120579119888119894

119906119887119894 (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

14)119878lowast

= (119901119894

1)119878lowast

+119888119894

119906119887119894(2119887119894+ 3120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 21205792]

(119901119894

24)119878lowast

=120579 (119901119894

14)119878lowast

+ (1 minus 119904) 119886119894 + V (120579 + 120573) + 119908119894(119887119894+ 120579)

2 (119887119894+ 120579)

+119888

2 (1 minus 120582120572)

(17)

For the hotel the premise to overbook rooms is that themarket demand is greater than the supply When the hotelfaces the risk of overbooking the equilibrium prices in bothcentralized and decentralized decision-making supply chainwill improve In the busy season in order to reduce the riskof overbooking the hotel would increase the prices and theincrement will increase as the transfer cost increases From(16) and (17) we can know that the increment in centralizeddecision-making model is the greatest and that in Bertrandgame is the smallest

7 Numerical Analysis

In this section we do some numerical experiment to gainmore insights According to the China Hotel Sales Chan-nel Report by I-Research (httpreportiresearchcnreport2013031892shtml) there are 381 of the hotels that aresuitable for high-end travelers and 619 of the hotels thatare suitable for low-end travelersTherefore this part assumesthat the proportion of the economical rooms and the luxuryrooms is 4 6 that is 119886

119871= 06119886 119886

119867= 04119886 Other parameter

settings are made as follows 119886 = 600 119904 = 05 and 119887119871= 06

119887119867= 02 120573 = 120579 = 05 120578 = 004 120572 = 08 120582 = 01 119908

119894= 05119901

119894

1

(119894 = 119871119867) In the following we investigate the impact of V onthe optimal prices and profits

When V = 0 that is the OTA does not offer any servicethen the optimal prices of HA are equal to the prices ofOTA Since 119887

119871gt 120573 gt 119887

119867 then the market of economy

rooms is service-oriented while the market of luxury roomsis price-oriented FromFigure 2 we can know that whenOTAoffers more services OTArsquos optimal price will be increasedaccordingly It is reasonable that if V increases the cost ofOTAwill also definitely increase With the increase of V 119901119871lowast

1will

decline slowly while 119901119867lowast1

will increaseThe OTArsquos profit status becomes better with the improve-

ment of its price But as the V increases the cost of OTA willalso definitely increase When V is equal to 27 then the profitof OTA is the highest If V is larger then the high costs willreduce the profits of OTAWhen V is equal to 34 the profit ofthewhole supply chain is the highest So from the perspectiveof the supply chain V is expected to be 34 rather than 27Similarly for the integrated system the profit of the OTAalso rises first and then declines with the increase of V Aftercalculationwe can get thatwhen V = 27 both120587119861lowast

2and120587119878lowast2will

be the highest From Figures 3 and 4 we know that the OTAwould tend to offer service that valued 27 so as to maximizeits own profit

After calculation we can conclude that when V = 34 then120587119861lowast is highest when V = 35 then 120587

119878lowast is highest (Figure 5)

10 Discrete Dynamics in Nature and Society

0 10 20 30 40 50 60 70 80100

150

200

250

300

350

400

450

Pric

e

pLlowast

1

pLlowast

2

pHlowast

1

pHlowast

2

Value added by OTArsquos services ()

Figure 2 Equilibrium prices in the integrated system

0 10 20 30 40 50 60 70 800

1

2

3

4

5

6

7

Profi

t

times104

120587lowast

1

120587lowast

2

120587lowast

Value added by OTArsquos services ()

Figure 3 Profits in the integrated system

From the perspective of the supply chain theOTA is expectedto offer more services Despite the rising cost of OTA willlower its profit the hotel can lower the wholesale prices tocoordinate the distribution of profits so as to achieve a win-win situation

In the following we focus on the comparison of differentchannelrsquos profit in each model Figure 6 depicts the curves ofthe total profits of the HAOTA channels in the integratedsystem with respect to V Figure 7 draws the curves of the dif-ferent channelsrsquo profits under both Bertrand and Stackelberggame The profit of the HA channel refers to the profit thatthe hotel derived from the HA channelThe profit of the OTA

0 10 20 30 40 50 60125

13

135

14

145

15

155

16

165

Profi

t

times104

120587Blowast

2

120587Slowast

2

Value added by OTArsquos services ()

Figure 4 OTArsquos profits under two games

0 10 20 30 40 50 60 70 8052

53

54

55

56

57

58

59

6

61

62

Profi

t

times104

120587Blowast

2

120587Slowast

2120587lowast

Value added by OTArsquos services ()

Figure 5 The profit comparison

channel involves the OTArsquos profit and the hotelrsquos profit gainedfrom the OTA channel

As shown in Figures 6 and 7 with the increase of V theprofit of the OTA channel will increase first and will thendecrease This indicates that a high level of service by OTAwill be detrimental to the channel profit That is because ahigh level of service will bring a high cost undoubtedly Forthe integrated model and Bertrand game model this disad-vantage is more evident The OTArsquos service can motivate theactual purchase behavior of customers in the OTA channelWhen V is relatively lower the additional profits from OTArsquos

Discrete Dynamics in Nature and Society 11

0 10 20 30 40 50 60 70 8018

2

22

24

26

28

3

32

34

36

38

4

Profi

t

HA channelOTA channel

times104

Value added by OTArsquos services ()

Figure 6 Channel profits in the integrated system

0 10 20 30 40 50 60 70 8005

1

15

2

25

3

35

4

45

Profi

t

HA channel in Bertrand gameOTA channel in Bertrand gameHA channel in Stackelberg gameOTA channel in Stackelberg game

times104

Value added by OTArsquos services ()

Figure 7 Channel profits in two games

service are enough to compensate for the cost In this casethe hotel and the OTA can get more profit from providing theservice However when V is high the additional profits fromOTArsquos service cannot make up for the high cost In such phe-nomenon the OTA should not increase investment in ser-vice

For both integrated model and Bertrand game modelwith the increase of V the profit of the HA channel willdecrease first and will then increase while in the Stackelberggamemodel the profit of theHA channel will always increase

with V With Figure 2 we can know that when OTA providesmore additional services it tends to increase its price Someof the customers will turn to reserve rooms from the HAbecause of the excessively high price in OTA As a result thehotel can gain more profits from the HA channel

8 Conclusion

With the development of e-commerce the providers oftourism products are more inclined to build dual-channelsIn this paper we consider the direct selling channel of HAand the traditional retail channel ofOTA from the perspectiveof tourism supply chain We develop a two-echelon tourismsupply chain model involving one hotel and one OTA wheretheOTAprovides related service Customers will be refundedpartially in case of cancelation or no-show We investigatethe optimal pricing strategies under several common casesThe integrated operation and the decentralized operationbased on Bertrand and Stackelberg games are studied andcorresponding equilibrium pricing policies are obtained

Our findings demonstrate that the hotel plays a crucialrole in optimizing the benefits of supply chain Consideringthe overall profit of the supply chain the hotel should act as aleader in dual-channel supply chain and formulate reasonablewholesale prices to improve the cooperative enthusiasm ofOTA so as to achieve optimization of the whole supplychain A lower wholesale price can help reduce OTArsquos loss ofprofit because of the opening of HA channel In addition weconsider the overbooking of the hotel and obtain the optimaloverbooking quantity We conclude that the hotel can alwaysobtain higher profits when the overbooking proportion iscontrolledwithin a certain range Otherwise if the overbook-ing proportion is too high the hotel can get extra profits onlywhen the overbooking cost is lower than a certain value

The contribution of this paper is that we extend tourismsupply chain to the dual-channel structure in which the hotelopens its direct channel to sell tourism products And theextant literature only refers to the single channel In additionwe realize that customer cancellations andno-showoccur fre-quently in hotel industry Thus we develop the game modelsbased on such phenomenon At last we derive the conditionsunder which the hotel dominant case is profitable for boththe supply chain members Our results can provide hotelsand OTAs with some new managerial insights under thedual-channel environment

This research can be extended in several directions infuture work For example in this paper we assume that allinformation is known to the hotel and OTA However someinformation could be asymmetric (eg see Chen [37]) Thuswe can explore the Bayesian equilibrium under asymmetricinformation settings Secondly the assumption of lineardemand is a limitation of this paperWe can further study thedynamic pricing in tourism dual-channel supply chain

Appendix

A Proof of Corollary 8

First we set (1199011198711)119861lowast

gt (119901119871

1)119878lowast which can be expressed as

12 Discrete Dynamics in Nature and Society

(1 minus 120582120572) (120579119886119871 + 120579119904119886119871+ 2119887119871119904119886119871+ 120579V120573 + 3119908

1198711205792+ 3119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

gt(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(A1)

The above equation can be simplified as

119908119871gt120579 [(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)]

4119887119871 (1 minus 120582120572) (119887119871 + 120579) (119887

119871+ 2120579)

(A2)

So we can get Corollary 8 B Proof of Corollary 9

If (1199011198941)119878lowast

gt (119901119894

1)119861lowast then

(1 minus 120582120572) (120579119886119894 + 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 2119908

1198941205792+ 2119908119894119887119894120579 minus 1205792V minus 2120579119887

119894V) + 119888120579 (119887

119894+ 120579)

minus (1 minus 120582120572) ((119901119894

1)119878lowast

+ (119901119894

1)119861lowast

) [2 (119887119894+ 120579)2minus 1205792] gt 0

120587119878lowast

1minus 120587119861lowast

1=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

2 (119887119871+ 120579)

((119901119871

1)119878lowast

minus (119901119871

1)119861lowast

)

+(1 minus 120582120572) (120579119886119867 + 120579119904119886

119867+ 2119887119867119904119886119867+ 120579V120573 + 2119908

1198671205792+ 2119908119867119887119867120579 minus 1205792V minus 2120579119887

119867V) + 119888120579 (119887

119867+ 120579)

2 (119887119867+ 120579)

((119901119867

1)119878lowast

minus (119901119867

1)119861lowast

)

minus (1 minus 120582120572)2 (119887119871+ 120579)2minus 1205792

2 (119887119871+ 120579)

[((119901119871

1)119878lowast

)2

minus ((119901119871

1)119861lowast

)2

] minus (1 minus 120582120572)2 (119887119867+ 120579)2minus 1205792

2 (119887119867+ 120579)

[((119901119867

1)119878lowast

)2

minus ((119901119867

1)119861lowast

)2

] gt 0

(B1)

If (1199011198711)119878lowast

lt (119901119871

1)119861lowast and (119901

119867

1)119878lowast

lt (119901119867

1)119861lowast we can prove

120587119878lowast

1gt 120587119861lowast

1similarly

From Propositions 3 and 7 with (3) we obtain that

120587119861lowast

2minus 120587119878lowast

2=

120579

4 (119887119871+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119871 + V (120573 + 120579) minus 119908119871(119887119871+ 120579)]

minus 2119888 (119887119871+ 120579) + 120579 (1 minus 120582120572) ((119901

119871

1)119861lowast

+ (119901119871

1)119878lowast

)

sdot ((119901119871

1)119861lowast

minus (119901119871

1)119878lowast

) +120579

4 (119887119867+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119867 + V (120573 + 120579) minus 119908 (119887119867+ 120579)]

minus 2119888 (119887119867+ 120579) + 120579 (1 minus 120582120572) ((119901

119867

1)119861lowast

+ (119901119867

1)119878lowast

)

sdot ((119901119867

1)119861lowast

minus (119901119867

1)119878lowast

)

(B2)

Note that

119863119894

2= [(1 minus 119904) 119886119894 minus 119887

119894119901119894

2] + 120573V + 120579 (119901

119894

1+ V minus 119901

119894

2) gt 0 (B3)

so we show that

2 (1 minus 120582120572) [(1 minus 119904) 119886119894 + V (120573 + 120579) minus 119908119894(119887119894+ 120579)]

minus 2119888 (119887119894+ 120579) + 120579 (1 minus 120582120572) ((119901

119894

1)119861lowast

+ (119901119894

1)119878lowast

)

gt 0

(B4)

Thus we have the following

(1) 120587119861lowast2

gt 120587119878lowast

2 if (1199011198711)119861lowast

gt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

gt (119901119867

1)119878lowast

(2) 120587119861lowast2

= 120587119878lowast

2 if (1199011198711)119861lowast

= (119901119871

1)119878lowast and (119901

119867

1)119861lowast

= (119901119867

1)119878lowast

(3) 120587119861lowast2

lt 120587119878lowast

2 if (1199011198711)119861lowast

lt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

lt (119901119867

1)119878lowast

Combined with Corollary 8 the proposition is proved

Discrete Dynamics in Nature and Society 13

C Proof of Corollary 10

The profit of hotel from the economy rooms is as follows

120587119871

= [(1 minus 120582120572) (119904119886119871 minus 120579V) minus 119888120579] 119901119871

1

+ [(1 minus 120582120572) (119886119871 minus 119904119886119871+ 120573V + 120579V) + 119888 (119887

119871+ 120579)] 119901

119871

2

+ 2120579 (1 minus 120582120572) 119901119871

1119901119871

2minus (1 minus 120582120572) (119887119871 + 120579) (119901

119871

1)2

minus (1 minus 120582120572) (119887119871 + 120579) (119901119871

2)2

minus (119886119871minus 119904119886119871+ 120573V + 120579V) 119888

(C1)

Define (119901119871

1)119861(119878)

= (119860119871

1)119861(119878)

+ (119861119871

1)119861(119878)

119908119871 (1199011198712)119861(119878)

=

(119860119871

2)119861(119878)

+ (119861119871

2)119861(119878)

119908119871 where

(119861119871

1)119861

=3120579 (119887119871+ 120579)

4 (119887119871+ 120579)2minus 1205792

(119861119871

1)119878

=120579 (119887119871+ 120579)

2 (119887119871+ 120579)2minus 1205792

(119861119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119861119871

1)119861(119878)

+1

2

(119860119871

1)119861

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

(119860119871

1)119878

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(119860119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119860119871

1)119861(119878)

+(1 minus 120582120572) [(1 minus 119904) 119886119871 + V (120579 + 120573)] + 119888 (119887

119871+ 120579)

2 (1 minus 120582120572) (119887119871 + 120579)

(C2)

Let 120597120587119871120597119908 = 0 then we get119908lowast

119871 Similarly we can get119908lowast

119867

D Proof of Proposition 12

Let 120587119889minus 120587119903gt 0 then we can get 119904

0 where the profits of hotel

from HA and OTA are as follows

120587119889= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1)

120587119903= (1 minus 120582120572) (119908119871119863

119871

2+ 119908119867119863119867

2)

(D1)

E Proof of Corollary 11

If Δ119862119871le 120582(1 minus 120582)119876

119871 then the profit of hotel is 120587119871

11 The

derivative of 12058711987111(Δ119862119871) is 120597120587119871

11120597Δ119862119871= (1 minus 120582120572)119901

119871

1gt 0 So

with the increase of Δ119862119871 12058711987111

will increase When Δ119862119871

=

120582(1 minus 120582)119876119871 12058711987111

is maximized If Δ119862119871

ge 120582(1 minus 120582)119876119871

then the profit of hotel is 12058711987112 The derivative of 120587119871

12(Δ119862119871) is

120597120587119871

12120597Δ119862119871= (1 minus 120582120572)119901

119871

1minus (1 minus 120582)(119901

119871

1+ 119888119871) lt 0 So with the

increase of Δ119862119871 12058711987111will decline When Δ119862

119871= 120582(1 minus 120582)119876

119871

120587119871

11is maximizedSimilarly we can get Δ119862lowast

119867

F Proof of Proposition 13

Assume that the overbooking proportion is 120574119871and 120574119867

(1) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) le 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

That is

120574119867lt

120582

1 minus 120582lt 120574119871

le120582119876119871+ 119876119867[1 minus (1 minus 120582) (1 + 120574

119867)]

(1 minus 120582)119876119871

(F1)

Thus the hotel would like to overbook to get more profitrather than room vacancy

(2) Consider (1198631198711+119863119871

2)(1minus120582) lt 119876

119871and (119863119867

1+119863119867

2)(1minus120582) gt

119876119867That is 120574

119871lt 120582(1 minus 120582) lt 120574

119867 Then the profit of hotel is

120587112

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F2)

Thenwhen 119888119867119906

lt (1minus120582120572)119901119867

1(1minus120582) that is120587

112minus120587111

gt 0the hotel would carry out overbooking

(3) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

14 Discrete Dynamics in Nature and Society

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867lt 120582(1 minus 120582) Then the profit of hotel is

120587113

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2+ 119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876]

(F3)

Then when 119888119871

119906lt (1 minus 120582120572)119901

119871

1(1 minus 120582) 120587

113minus120587111

gt 0 thusthe hotel would carry out overbooking

(4) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) gt 119876

119867

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867gt (120582119876

119867+ 119876119871[1 minus (1 minus 120582)(1 + 120574

119871)])(1 minus 120582)119876

119867

Then the profit of hotel is as follows

120587114

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2) (1 minus 120582) minus 119876

119871]

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F4)

Then when 119888119871119906lt (1minus120582120572)119901

119871

1(1minus120582) and 119888119867

119906lt (1minus120582120572)119901

119867

1

(1 minus 120582) 120587114

minus 120587111

gt 0 overbooking is preferred

G Threshold Values

Threshold values are as follows

1198711= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 3119908

1198941205792+ 3119908119894119887119894120579

minus 1205792V minus 2120579119887

119894V

1198712= 2119886119894(119887119894+ 120579) minus 119904119886

119894(2119887119894+ 120579) + 120579

2119908119894+ 2 (120579 + 120573) (119887

119894

+ 120579) V + 2119908119894(119887119894+ 120579)2minus 1205792V

1198713= 4120579V119887

119894120573 minus 120579119904119886

119894119887119894+ 2V1205731198872

119894+ 31198861198941205792+ 4119886119894119887119894120579

minus 21198861198941198872

119894119904 + 3120579

2V120573 + 1205792V119887119894+ 2120579V1198872

119894+ 21198861198941198872

119894

1198714= 3119886119894119887119894120579 + 3120579

2V120573 minus 2120579V1198872119894minus 1205792V119887119894+ 31198861198941205792

+ 21198861198941198872

119894119904 + 119886119887

119894119904120579 + 3119887

119894120573V120579

1198715= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 minus 120579

2V minus 2120579119887119894V

1198661= [(1 minus 120582120572) (119904119886119894 minus 120579V) minus 119888120579] (119861

119894

1)119861(119878)

+ [(1 minus 120582120572) (119886119894 minus 119904119886119894+ 120573V + 120579V) + 119888 (119887

119894+ 120579)]

sdot (119861119894

1)119861(119878)

+ 2120579 (1 minus 120582120572) [(119860119894

1)119861(119878)

(119861119894

2)119861(119878)

+ (119861119894

1)119861(119878)

(119860119894

2)119861(119878)

] minus 2 (1 minus 120582120572) (119887119894 + 120579)

sdot [(119860119894

1)119861(119878)

(119861119894

1)119861(119878)

+ (119860119894

2)119861(119878)

(119861119894

2)119861(119878)

]

1198662= 2 (1 minus 120582120572)

sdot (119887119894+ 120579) [((119861

119894

1)119861(119878)

)

2

+ ((119861119894

2)119861(119878)

)

2

]

minus 2120579 (119861119894

1)119861(119878)

(119861119894

2)119861(119878)

1199040= ((119887119871+ 120579) (119901

119871

1)2

+ (119887119867+ 120579) (119901

119867

1)2

+ 120579119908119871(119901119871

1minus 119901119871

2) + 120579119908

119867(119901119867

1minus 119901119867

2)

+ 120579V (1199011198711+ 119901119867

1) + (119908

119871+ 119908119867) (120573 + 120579) V

+ 119908119871(119886119871minus 119887119871119901119871

2) + 119908119867(119886119867minus 119887119867119901119867

2)

minus 120579 (119901119871

1119901119871

2+ 119901119867

1119901119867

2)) (119886119871(119901119871

1+ 119908119871)

+ 119886119867(119901119867

1+ 119908119867))minus1

(G1)

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The authors thank associate editor and anonymous refereesfor their numerous constructive comments and encourage-ment that have improved their paper greatly The work waspartly supported by (i) the National Natural Science Founda-tion ofChina (71201083 71572058 and 71571100) (ii) the Fun-damental Research Funds for the Central Universities SCUT(2015ZZ057) (iii) Jiangsu Province Science Foundation forYouths (BK2012379) and (iv) the Fundamental ResearchFunds for the Central Universities (NS2015076)

References

[1] J Li W N Zhang H Xu and J Jiang ldquoDynamic competitionand cooperation of road infrastructure investment of multipletourism destinations a case Study of Xidi and Hongcun WorldCulturalHeritagerdquoDiscreteDynamics inNature and Society vol2015 Article ID 962028 10 pages 2015

[2] T Paksoy EOzceylan andG-WWeber ldquoProfit oriented supplychain network optimizationrdquoCentral European Journal of Oper-ations Research vol 21 no 2 pp 455ndash478 2013

[3] X Zhang H Song and G Q Huang ldquoTourism supply chainmanagement a new research agendardquo Tourism Managementvol 30 no 3 pp 345ndash358 2009

[4] Z Yang and J Cai ldquoDo regional factors matter Determinantsof hotel industry performance in Chinardquo TourismManagementvol 52 pp 242ndash253 2016

[5] B Pan L Zhang and R Law ldquoThe complex matter of onlinehotel choicerdquoCornell Hospitality Quarterly vol 54 no 1 pp 74ndash83 2013

[6] L Ling X Guo and C Yang ldquoOpening the online marketplacean examination of hotel pricing and travel agency on-line

Discrete Dynamics in Nature and Society 15

distribution of roomsrdquo Tourism Management vol 45 pp 234ndash243 2014

[7] L Ling Y Dong X Guo and L Liang ldquoAvailability man-agement of hotel rooms under cooperation with online travelagenciesrdquo International Journal of Hospitality Management vol50 pp 145ndash152 2015

[8] J N K Liu andE Y Zhang ldquoAn investigation of factors affectingcustomer selection of online hotel booking channelsrdquo Interna-tional Journal of Hospitality Management vol 39 pp 71ndash832014

[9] L Fox ldquoFour Seasons Unveils $18 Million Website as LuxuryTravel Growsrdquo 2012 httpwwwtnoozcomarticlefour-sea-sons-unveils-18-million-dollar-website-as-luxury-travel-grows

[10] C-M Chen and Y-C Lin ldquoThe influence of uncertain demandon hotel capacityrdquo International Journal of Hospitality Manage-ment vol 34 no 1 pp 462ndash465 2013

[11] S Yang G Q Huang H Song and L Liang ldquoGame-theoreticapproach to competition dynamics in tourism supply chainsrdquoJournal of Travel Research vol 47 no 4 pp 425ndash439 2009

[12] G Q Huang H Song and X Zhang ldquoA comparative analysis ofquantity and price competitions in tourism supply chain net-works for package holidaysrdquo Service Industries Journal vol 30no 10 pp 1593ndash1606 2010

[13] Y Huang H Song G Q Huang and J Lou ldquoA comparativestudy of tourism supply chains with quantity competitionrdquoJournal of Travel Research vol 51 no 6 pp 717ndash729 2012

[14] H K Lee and Y Fernando ldquoThe antecedents and outcomes ofthe medical tourism supply chainrdquo Tourism Management vol46 pp 148ndash157 2015

[15] W-Y K Chiang D Chhajed and J D Hess ldquoDirect marketingindirect profits a strategic analysis of dual-channel supply-chain designrdquoManagement Science vol 49 no 1 pp 1ndash20 2003

[16] A A Tsay and N Agrawal ldquoChannel conflict and coordinationin the E-commerce agerdquo Production and Operations Manage-ment vol 13 no 1 pp 93ndash110 2004

[17] Q-H Li and B Li ldquoDual-channel supply chain equilibriumproblems regarding retail services and fairness concernsrdquoApplied Mathematical Modelling 2016

[18] S Panda N M Modak S S Sana and M Basu ldquoPricingand replenishment policies in dual-channel supply chain undercontinuous unit cost decreaserdquo Applied Mathematics and Com-putation vol 256 pp 913ndash929 2015

[19] Y Liu C Ding C Fan and X Chen ldquoPricing decision underdual-channel structure considering fairness and free-ridingbehaviorrdquo Discrete Dynamics in Nature and Society vol 2014Article ID 536576 10 pages 2014

[20] J Chen H Zhang and Y Sun ldquoImplementing coordinationcontracts in a manufacturer Stackelberg dual-channel supplychainrdquo Omega vol 40 no 5 pp 571ndash583 2012

[21] Q Ding C Dong and Z Pan ldquoA hierarchical pricing decisionprocess on a dual-channel problem with one manufacturer andone retailerrdquo International Journal of Production Economics vol175 pp 197ndash212 2016

[22] B Rodriguez and G Aydin ldquoPricing and assortment decisionsfor a manufacturer selling through dual channelsrdquo EuropeanJournal of Operational Research vol 242 no 3 pp 901ndash9092015

[23] T Lockyer ldquoThe perceived importance of price as one hotelselection dimensionrdquo Tourism Management vol 26 no 4 pp529ndash537 2005

[24] C-M Chen H-W Yang E Y Li and C-C Liu ldquoHow doeshotel pricing influence guest satisfaction by the moderatinginfluence of room occupancyrdquo International Journal of Hospi-tality Management vol 49 pp 136ndash138 2015

[25] J-M Espinet M Fluvia R Rigall-I-Torrent and A Salo ldquoHotelcharacteristics and seasonality in prices an analysis usingSpanish tour operatorsrsquo brochuresrdquo Tourism Economics vol 18no 4 pp 749ndash767 2012

[26] C Juaneda J M Raya and F Sastre ldquoPricing the time and loca-tion of a stay at a hotel or apartmentrdquo Tourism Economics vol17 no 2 pp 321ndash338 2011

[27] G Abrate G Fraquelli and G Viglia ldquoDynamic pricing strate-gies evidence from European hotelsrdquo International Journal ofHospitality Management vol 31 no 1 pp 160ndash168 2012

[28] D Q Yao and J J Liu ldquoCompetitive pricing of mixed retail ande-tail distribution channelsrdquo Omega vol 33 no 3 pp 235ndash2472005

[29] J Zhao and L Wang ldquoPricing and retail service decisionsin fuzzy uncertainty environmentsrdquo Applied Mathematics andComputation vol 250 pp 580ndash592 2015

[30] A A Tsay and N Agrawal ldquoChannel dynamics under priceand service competitionrdquo Manufacturing amp Service OperationsManagement vol 2 no 4 pp 372ndash391 2000

[31] S C Choi ldquoPrice competition in a duopoly common retailerchannelrdquo Journal of Retailing vol 72 no 2 pp 117ndash134 1996

[32] Y Bakos andE Brynjolfsson ldquoBundling and competition on theinternetrdquoMarketing Science vol 19 no 1 pp 63ndash82 2000

[33] H Song J H Kim and S Yang ldquoConfidence intervals fortourism demand elasticityrdquo Annals of Tourism Research vol 37no 2 pp 377ndash396 2010

[34] DMHanssens L J Parsons andR L SchultzMarket ResponseModels Econometric and Time Series Analysis Kluwer Aca-demic Publishers Boston Mass USA 2nd edition 2001

[35] H Kurata D-Q Yao and J J Liu ldquoPricing policies under directvs indirect channel competition and national vs store brandcompetitionrdquo European Journal of Operational Research vol180 no 1 pp 262ndash281 2007

[36] R Law and C Cheung ldquoA study of the perceived importance ofthe overall website quality of different classes of hotelsrdquo Inter-national Journal of Hospitality Management vol 25 no 3 pp525ndash531 2006

[37] K B Chen ldquoProcurement strategies and coordination mecha-nism of the supply chain with one manufacturer and multiplesuppliersrdquo International Journal of Production Economics vol138 no 1 pp 125ndash135 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Discrete Dynamics in Nature and Society

the booking or choose no-show finally the hotel would onlyreturn certain expense rate of 120572 (0 le 120572 le 1) If a customeris booking through OTA then OTA would return to thecustomer with the proportion of the retail prices At the sametime the hotel would return to OTA with the proportionof the wholesale prices We assume that the proportion thathotel returns to the customer the proportion that hotelreturns to OTA and the proportion that OTA returns to thecustomer are the same

We list the following notations where 119894 (119894 = 119871119867) insubscripts or superscripts are for economic (low price) andluxury (high price) rooms respectively

119876 the total number of rooms provided for renting toguests119876119894 the total number of economicluxury rooms

119863119894

1 the reservation amount of economicluxury room

booking through HA119863119894

2 the reservation amount of economicluxury room

booking through OTA119886119894 the market base demand of economicluxury

room119886 the total market base demand of rooms (119886 = 119886

119871+

119886119867)

119904 themarket share of HA in the tourism dual-channelsupply chain119901119894

1 HArsquos price of economicluxury rooms that is the

direct selling prices119901119894

2 OTArsquos price of economicluxury rooms that is the

retail prices119908119894 the wholesale price of economicluxury rooms

119887119894 the price sensitivity coefficient of 119894 price rooms

(119887119871gt 119887119867)

120579 the diffusion intensity which describes the shiftbetween two channels with regard to the price andvalue120582 the proportion of customer cancellations and no-show120572 the return expense proportion of customer cancel-lations and no-show (0 le 120572 le 1)120573 the services elasticity of demandV the value added by OTArsquos services120578 the coefficient of service cost119888(V) the function of service cost 119888(V) = 120578V221205871 the profit of the hotel

1205872 the profit of the OTA

In the model we do not consider the marginal sales costof the hotel since it is very low In reality OTA will firstlyintroduce to customers the hotelsrsquo facilities and quota andafterwards confirm the booking and finally book rooms fromthe hotel for customersTherefore the rooms sold by HA and

OTA are homogeneous In addition to providing hotel reser-vations OTA also provides other related services as wellsuch as offering plane ticket booking holiday booking andtravel information OTA aims to provide a full range of travelprogram for travelers In order to provide such services OTAneeds to pay for additional operating costs The customerswho want to get more tourist information and services willprefer to reserve rooms through OTA By contrast HA onlyprovides hotel room information for customers For instancecustomers cannot book the suitable hotel and air ticket at thesame time through the HA platform Consequently in orderto distinguish the influence of different information servicesto customerrsquos channel choice we suppose that OTA providesadditional service and the value added from the services is VFurther the cost for providing service is 119888(V) = 120578V22 wherethe parameter 120578measures the cost effectiveness of the serviceSuch cost function is commonly adopted in previous litera-ture and canwell describe the relationship between additionalservices and cost [28 29] When OTA does not provide theservice the cost should be zero

According to the process of demand function in Tsay andAgrawal [30] andChoi [31] the demands of economicluxuryrooms through each channel are expressed as follows

119863119894

1= (119904119886119894minus 119887119894119901119894

1) + 120579 (119901

119894

2minus V minus 119901

119894

1)

119863119894

2= [(1 minus 119904) 119886119894 minus 119887

119894119901119894

2] + 120573V + 120579 (119901

119894

1+ V minus 119901

119894

2)

(1)

Such linear demand functions are used because they canachieve approximate and satisfactory fit to certain types ofdemand and they are tractable and widely used in marketingand supply chain management literature [32] In our modelthe parameter 119887 represents the price sensitivity coefficientIt describes the marginal channel demand per respectivechannel price The own price elasticity is normally negative[33] And the parameter 120573measures the marginal demand ofOTA per service value added In addition the parameter 120579 isunderstood as the diffusion intensity (cross-price sensitivity)and describes the shift between two channels with regard tothe price and the value Suchmodelingmethod can guaranteethat the self-price sensitivity in absolute value is strongerthan the cross-price sensitivity which is proved by Hanssenset al [34] and used by Yao and Liu [28] Choi [31] and Kurataet al [35]

Now consider the situation without overbooking that is119863119871

1+ 119863119871

2le 119876119871and 119863

119867

1+ 119863119867

2le 119876119867 Thus the reservation

amount can be regarded as the final demandThe total profit for the hotel OTA and the whole supply

chain can be expressed as follows

1205871= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2) (2)

1205872= [(1 minus 120582120572) (119901

119871

2minus 119908119871) minus 119888 (V)]119863119871

2

+ [(1 minus 120582120572) (119901119867

2minus 119908119867) minus 119888 (V)]119863119867

2

(3)

120587 = 1205871+ 1205872 (4)

Discrete Dynamics in Nature and Society 5

4 Integrated System

As a benchmark we first consider an integrated systemwherethe common goal of supply chain upstream and downstreammembers is tomaximize the overall profit of the supply chainThis is an ideal model that the members in the supply chainoperate as an entirety In such an integratedmodel of tourismsupply chain the hotel and OTA cooperate to determine thepricing strategies

Proposition 1 In the integrated system the optimal pricingdecisions of HA and OTA are as follows

119901119894lowast

1=119886119894(119887119894119904 + 120579) + 120579V (120573 minus 119887

119894)

2 (119887119894)2+ 4119887119894120579

119901119894lowast

2=(119887119894+ 120579 minus 119887

119894119904) 119886119894+ 119887119894120573V + 120579V (120573 + 119887

119894)

2 (119887119894)2+ 4119887119894120579

+119888 (V)

2 (1 minus 120582120572)

119894 = 119871119867

(5)

From Proposition 1 the optimal prices shown above canexplain that in the integrated system the optimal prices of HAwill not be affected by the proportion of customer cancella-tions and no-show (120582) or the return expense proportion (120572)On the other hand with the increase of 120582 or 120572 the optimalprices for OTAwill increaseThis is reasonable because whenOTA faces unstable demand or it should return more tocustomersrsquo cancellation or no-show it would like to increasethe price to guarantee its profit

Corollary 2 119901119871lowast2

and 119901119867lowast2

are increasing in V Moreover

(1) if 120573 gt 119887119871gt 119887119867 then 120597119901

119871lowast

1120597V gt 0 120597119901119867lowast

1120597V gt 0

(2) if 119887119871gt 120573 gt 119887

119867 then 120597119901

119871lowast

1120597V lt 0 120597119901119867lowast

1120597V gt 0

(3) if 119887119871gt 119887119867gt 120573 then 120597119901

119871lowast

1120597V lt 0 120597119901119867lowast

1120597V lt 0

From Corollary 2 we can know that when OTA offersmore services OTArsquos optimal price will be increased accord-ingly It is reasonable that if V increases the cost of OTA willalso definitely increase So there is always a positive correla-tion between OTArsquos optimal prices and the added value

If 120573 gt 119887119871

gt 119887119867 the market of economy rooms and

that of luxury rooms are both service-oriented rather thanprice-oriented The implication is that the effective servicewill increase the optimal price of HAWhenOTA offersmoreeffective service its price will increase But some customerswant to enjoy the additional services so they are willingto make a booking through OTA despite spending moremoneyTherefore the demand inOTAwill increase while thedemand in HA will decrease

If 119887119871gt 120573 gt 119887

119867 the market of economy rooms is service-

oriented while the market of luxury rooms is price-orientedThe HArsquos optimal price of economy rooms will decrease withrespect to V Conversely the HArsquos optimal price of luxuryrooms will increase with respect to V For examples the

change of price has a great impact on leisure travelersrsquo deci-sions but for business travelers the price is not themost con-cern If the price ofOTA increasesOTArsquos demandof economyrooms will significantly reduce and the HArsquos demand willincrease thus the HArsquos optimal price will decline On theother hand for luxury rooms if OTA provides more effectiveservice the customer would be willing to pay higher pricesfor value-added service This will bring the increase in OTArsquosdemand and the reduction of HArsquos demand thus the optimalprice of HA will increase

If 119887119871gt 119887119867gt 120573 the market of economy rooms and that of

luxury rooms are both price-oriented than service-orientedThe HArsquos optimal price of both economy rooms and luxuryrooms will decrease with the increase of V When the marketis price-oriented the promotion of price in OTAwill lead to areduction in OTArsquos demandThereby the demand in HA willincrease and optimal price in HA will decline

5 Two Game Models

In the tourism dual-channel supply chain the relationshipbetween hotel and OTA is cooperative as well as competitiveIn the decentralized decision-making model they are morecompetitive than cooperative Their purposes are to maxi-mize their own profits In reality hotel can choose whether toinform the price ofHAor not forHA is competingwithOTAUninformed of the prices inHAOTAcan predict the range ofprice onHAby the star-rated and room type of the hotel but itcannot know the exact priceTherefore this section examinesthe pricing equilibrium between the hotel and OTA undertwo types of games namely the Bertrand and Stackelberggames For the Bertrand game both of the participantsregard price as a decision variable the hotel and OTA areuncooperative For the Stackelberg game the participantsare divided into two roles the leader and the follower Asa leader in tourism supply chain the hotel will provide thepolicy to maximize its interests As a follower OTA accepts ifprofitable By comparing the two models we can understandhow the behavior of hotel influences the pricing decisions

51 Bertrand Game In a Bertrand game the procedure isas follows keeping the wholesale price unchanged the hoteldetermines HArsquos prices 119901119871

1and 119901

119867

1 so as to maximize profit

1205871 Uninformed of the prices of HA OTA decides prices 119901119871

2

and 119901119867

2 so as to maximize his profit 120587

2 Let (119901119894

1)119861 (1199011198942)119861(119894 =

119871119867) denote HArsquos and OTArsquos prices under a Bertrand modelrespectively

In the following 119871119899(119899 = 1 2 5) 119904

0 and 119866

119898(119898 =

1 2) are the threshold values and are given in Appendix G

Proposition 3 There exist Bertrand equilibrium prices(119901119894

1)119861lowast (119901119894

2)119861lowast

(119894 = 119871119867) where

(119901119894

1)119861lowast

=(1 minus 120582120572) 1198711 + 119888120579 (119887

119894+ 120579)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

2)119861lowast

=(1 minus 120582120572) 1198712 + 2119888 (119887

119894+ 120579)2

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(6)

6 Discrete Dynamics in Nature and Society

From Proposition 3 in the Bertrand model the equilib-rium prices for hotel and OTA are both affected by 120572 and 120582With the increase of 120572 or 120582 both (119901

119894

1)119861lowast and (119901

119894

2)119861lowast will be

higher In otherwords with higher uncertainty of roomoccu-pancy the hotel and OTA tend to increase prices to protecttheir own profits

Denote 1198881= (1 minus 120582120572)(2119887

119871+ 120579 minus 120573)(119887

119871+ 120579) and 119888

2= (1 minus

120582120572)(2119887119867+ 120579 minus 120573)(119887

119867+ 120579) then 119888

1gt 1198882

Corollary 4 (1199011198712)119861lowast and (119901

119867

2)119861lowast are increasing in V (119901119871

1)119861lowast

and (119901119867

1)119861lowast have the following relationships with respect to

OTArsquos service

(1) if 1198881015840(V) gt 1198881 then 120597(119901

119871

1)119861lowast120597V gt 0 120597(119901119867

1)119861lowast120597V gt 0

(2) if 1198881gt 1198881015840(V) gt 119888

2 then 120597(119901

119871

1)119861lowast120597V lt 0 120597(119901119867

1)119861lowast120597V gt

0(3) if 1198881015840(V) lt 119888

2 then 120597(119901

119871

1)119861lowast120597V lt 0 120597(119901119867

1)119861lowast120597V lt 0

From Corollary 4 when OTA offers more effective ser-vices its optimal prices will increase due to the incrementin the cost Marginal cost measures the input costs and theoutput value per unit If the marginal cost is greater than1198881 then the costs of OTA to provide additional services are

higher So the equilibrium prices of HA will increase as thevalue added by OTArsquos services increases When the marginalcost is between 119888

1and 1198882 HArsquos equilibrium price of economy

rooms and the value added by OTArsquos service have a negativecorrelation but HArsquos equilibrium price of luxury roomswould increase with the increment of V In addition when themarginal cost is less than 119888

2 the costs of OTA to provide addi-

tional service are lower And the equilibriumprices ofHAwilldecrease when V increases

Corollary 5 There exist threshold unit wholesale prices 1199080119894

1199081

119894(119894 = 119871119867) such that

(1) (1199011198941)lowastlt (119901119894

1)119861lowast if 119908

119894gt 1199080

119894 (1199011198941)lowast= (119901119894

1)119861lowast if 119908

119894= 1199080

119894

(119901119894

1)lowastgt (119901119894

1)119861lowast if 119908

119894lt 1199080

119894

(2) (1199011198942)lowastlt (119901119894

2)119861lowast if 119908

119894gt 1199081

119894 (1199011198942)lowast= (119901119894

2)119861lowast if 119908

119894= 1199081

119894

(119901119894

2)lowastgt (119901119894

2)119861lowast if 119908

119894lt 1199081

119894

where

1199080

119894=

1198713

6119887119894(119887119894+ 120579) (119887

119894+ 2120579)

minus119888

3 (1 minus 120582120572)

1199081

119894=

120579 [(1 minus 120582120572) 1198714 minus 119888119887119894120579 (119887119894+ 2120579)]

2119887119894 (1 minus 120582120572) (119887119894 + 2120579) (31205792 + 21198872

119894+ 2119887119894120579)

(7)

FromProposition 1 it is easy to know that the equilibriumprices in the integrated system are not affected by the whole-sale prices However from Proposition 3 in the Bertrandmodel there is a positive correlation between the equilibriumprices and the wholesale prices Corollary 5 shows that theequilibrium price of HA in the Bertrand game is higherthan that in the integrated system if the wholesale price isgreater than a certain critical point (1199080

119894) Additionally if the

wholesale price is greater than1199081119894 then the equilibrium price

of OTA in Bertrand model will be higher than that in theintegrated model

Corollary 6 There exists a threshold unit wholesale price1199082

119894(119894 = 119871119867) such that if119908

119894gt 1199082

119894 then119863lowast

119894gt 119863119861lowast

119894(119894 = 119871119867)

where

1199082

119894=120579 [(1 minus 120582120572) (V120573 + 119886

119894) minus 119887119894119888]

2119887119894 (1 minus 120582120572) (119887119894 + 2120579)

(8)

Corollary 6 shows that when thewholesale price is greaterthan 119908

2

119894 the high price will lead to a lower demand in the

Bertrand game That is the reservation amount of Bertrandmodel is less than that in the integrated model The highersale price in OTA results from the higher wholesale priceThus the above result is reasonable because travelers are pricesensitive especially for leisure travelers the increase of pricewill bring the decline of reservation amount When the rela-tionship between the hotel and OTA is modeled as a Stackel-berg game the hotel canmotivate customers to reserve roomsthrough a reasonable wholesale price If the wholesale price isgreater than the threshold the sales volume in the centralizedcase is lower than that in the Bertrand case

52 Stackelberg Game In a Stackelberg game the procedureis as follows keeping thewholesale price unchanged the hotel(as the leader) announces HArsquos prices 119901119871

1and 119901119867

1of two types

of rooms respectively in order to maximize its profit 1205871 In

response to HArsquos prices OTA (as the follower) determinesprices 119901

119871

2and 119901

119867

2to maximize its profit 120587

2 Let (119901

119894

1)119878

(119901119894

2)119878(119894 = 119871119867) denote respectively HArsquos and OTArsquos prices

under a Stackelberg game

Proposition 7 The optimal prices are (119901119894

1)119878lowast (119901119894

2)119878lowast

(119894 =

119871119867) and there exists a threshold unit wholesale price 1199083119894(119894 =

119871119867) such that if 119908119894gt 1199083

119894 then (119901

119894

1)lowastlt (119901119894

1)119878lowast where

(119901119894

1)119878lowast

=(1 minus 120582120572) (1198711 minus 119908

1198941205792minus 119908119894119887119894120579) + 119888120579 (119887

119894+ 120579)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 21205792]

(119901119894

2)119878lowast

=120579 (119901119894

1)119878lowast

+ (1 minus 119904) 119886119894 + V (120579 + 120573) + 119908119894(119887119894+ 120579)

2 (119887119894+ 120579)

+119888

2 (1 minus 120582120572)

1199083

119894

=119887119894V120573 + 119886119887

119894+ 120579V119887119894+ 119886119894120579 + 120579V120573 minus 119886

119894119887119894119904

2119887119894(119887119894+ 2120579)

minus119888

2 (1 minus 120582120572)

(9)

Similar to the Bertrand competition the equilibriumprices in Stackelberg game will increase with the increase of

Discrete Dynamics in Nature and Society 7

the return expense proportion (120572) or the cancellations andno-show proportion (120582)

From Proposition 7 we can see that the Stackelbergmodel is similar to the Bertrand model that the equilibriumprices would increase with the increase of wholesale pricesFurthermore when thewholesale price is greater than1199083

119894 the

equilibrium price of HA in Stackelberg model will be higherthan that in the integrated model

In the Stackelberg game if OTA offers more effective ser-vices the equilibrium prices of OTA would increase accord-ingly The relationship between the Stackelberg equilibriumprices and V is similar to that in the Bertrand model

53 Contrastive Analysis of Bertrand and Stackelberg GamesBased on the equilibrium prices obtained in the previoussection we in this section compare the equilibriumprices andoptimal profit under Bertrand and Stackelberg games

Corollary 8 There exists a threshold unit wholesale price1199084

119894(119894 = 119871119867) such that

(1) (1199011198941)119861lowast

gt (119901119894

1)119878lowast and (119901119894

2)119861lowast

gt (119901119894

2)119878lowast if 119908

119894gt 1199084

119894

(2) (1199011198941)119861lowast

= (119901119894

1)119878lowast and (119901119894

2)119861lowast

= (119901119894

2)119878lowast if 119908

119894= 1199084

119894

(3) (1199011198941)119861lowast

lt (119901119894

1)119878lowast and (119901119894

2)119861lowast

lt (119901119894

2)119878lowast if 119908

119894lt 1199084

119894

where

1199084

119894=

120579 [(1 minus 120582120572) 1198715 + 119888120579 (119887119894+ 120579)]

4119887119894 (1 minus 120582120572) (119887119894 + 120579) (119887

119894+ 2120579)

(10)

Corollary 8 compares the equilibrium prices under theBertrand and Stackelberg game with respect to the wholesaleprice It shows that if the wholesale price is greater than1199084

119894 the pricing equilibrium under the Bertrand is higher

than that under the Stackelberg game Conversely the pricingequilibrium is lower if the wholesale price is less than 119908

4

119894

In the decentralized case both the manufacturer and theretailer want to maximize their profit A high wholesale pricecould be passed on to customersTherefore the above resultsexist In addition how to share the profit between the manu-facturer and the retailer depends on their bargaining powers

Corollary 9 If 119908119894

= 1199084

119894(119894 = 119871119867) then 120587

119878lowast

1gt 120587119861lowast

1 OTArsquos

profit has the following relationship with respect to 1199084119894

(1) 120587119861lowast2

gt 120587119878lowast

2if 119908119871gt 1199084

119871and 119908

119867gt 1199084

119867

(2) 120587119861lowast2

= 120587119878lowast

2if 119908119871= 1199084

119871and 119908

119867= 1199084

119867

(3) 120587119861lowast2

lt 120587119878lowast

2if 119908119871lt 1199084

119871and 119908

119867lt 1199084

119867

Thehotel is the leader in Stackelberg game and can alwaysbenefit from it except for the critical point1199084

119894 Comparedwith

the Bertrand game the hotel can get higher profits in Stackel-berg gamewhen the wholesale price is not equal to1199084

119894There-

fore in decentralized decision-making model the hotel willbe more inclined to be the price leader in order to ensure thatit can achieve higher profits

Corollary 9 indicates that the Stackelberg model is supe-rior to the Bertrand model when the wholesale price is less

than the critical point1199084119894 Not only the hotel but alsoOTA can

gain more profit from the Stackelberg game Though OTA isa follower in Stackelberg game the profit will not be reducedbecause the lower wholesale prices can compensate for theloss of profit caused by the opening of HA channel Conse-quently the hotel should play the role of the price leader inthe supply chain and develop reasonable wholesale prices toachieve optimization of the whole supply chain profit whileoptimizing its own profit

Corollary 10 Under either Bertrand or Stackelberg equi-librium channel prices there exists optimal wholesale price119908lowast

119894(119894 = 119871119867) that maximizes the total equilibrium channel

profit where 119908lowast119894= 11986611198662

According to Corollary 10 there exists optimal wholesaleprice 119908

lowast

119894(119894 = 119871119867) that maximizes the total equilibrium

channel profit under either Bertrand or Stackelberg gameThe optimal wholesale price will optimize the decentralizeddecision-making supply chainMeanwhile both the hotel andtheOTA can benefit from the optimal wholesale priceThere-fore the reasonable wholesale price can help promotemutualcooperation and communication between the supply chainmembers

54 Contrastive Analysis of Two Channels in the Supply Chain

Corollary 11 There exists a threshold unit market share of HAin the tourism dual-channel supply chain (119904

0) such that when

119904 gt 1199040 the hotelrsquos profit from HA is higher than that from OTA

Keeping the wholesale prices and sales prices unchangedwhen the market share of HA in the tourism dual-channelsupply chain exceeds a certain value 119904

0 the hotelrsquos profit from

HA is higher than that from OTA The result is suitable forthe integrated system Bertrand and Stackelberg games Fromthe perspective of hotelrsquos revenue the hotel should explorethe channel for direct selling actively Also the hotel canstrengthen the promotion of HA channel to improve thecustomerrsquos understanding and preference for theHA channelBut the premise is that the profit growth from the promotioncan compensate for the cost According to the statistical datafrom the hotel price competitiveness analysis report in thefirst half of 2012 we know that the booking cost from directselling channel is about 1 dollar per night but that fromOTAis about 10 dollars per night Booking cost can be reducedby 46 if the direct selling level is doubled Then improvingthe market share of direct selling will greatly reduce the costMore comparisons of different channelrsquos profits in eachmodelcan be found in part of numerical analysis

6 Overbooking

This section extends to consider the overbooking caseRegarding overbooking in the hospitality industry the com-mon practice is that the hotel upgrades the room type ortransfers customers to other hotels nearby that have the samelevel and same type In airline industry if customers aredenied boarding after arriving at the airport the airline will

8 Discrete Dynamics in Nature and Society

provide a free upgrade endorse the ticket or provide com-pensation for the customers according to specific situationCompared to the hotels the airlines cannot transfer cus-tomers to other companies The air ticket alteration will usu-ally disrupt customersrsquo traveling schedule Though the over-booking by airlines has been well studied in the literature ourresearch is new in the hospitality industry by considering theoverbooking withwithout room transfer with the hope thatcertain implications can be enlightened to the hotel man-agers

The hotel wants to increase the occupancy rates toincrease the profits through overbooking However over-booking will lead to the risk that the actual occupancyamount is greater than the number of hotel roomsThereforethe hotel has to provide compensation to travelers who can-not check in that is overbooking cost The greater the num-bers of overbooking the less the probability of room vacancybut at the same time travelers are more likely to be refusedby the hotel Therefore the hotel must balance between thevacancy lost and the overbooking costs We develop a modelto analyze the overbooking choice

In reality the OTA is always a crucial partner of hotelsfor it can attract a large number of customers for hotelsand improve their occupancy rates [36] Spontaneously theOTA plays an increasingly significant role in the distributionsystems of hotels [5 7] By contrast the HA mainly providesa platform for individual guest Compared with individualcustomers hotel pays more attention to the long-term coop-eration relationship with the OTA Therefore in our modelwe assume that when the market demand is greater than thesupply and the hotel does not carry out overbooking the hotelwould give priority to customers who are booking fromOTA

61 Without Room Transfer Here we consider the casewith no room transfer When the actual occupancy amountexceeds the total quantity of rooms the hotel does not arrangeother alternative accommodation for the customers who can-not check in But the hotel must pay the loss of goodwill costSuppose that the overbooking quantity of economy and lux-ury rooms isΔ119862

119871andΔ119862

119867and the overbooking cost is 119888

119871and

119888119867 respectivelyWe discuss economy roomsrsquo overbooking The actual

occupancy can be either of the following two cases (1) when119876119871

lt 119863119871

1+ 119863119871

2le 119876119871+ Δ119862

119871 the reservation amount of

rooms is 1198631198711+ 119863119871

2 so the actual occupancy amount is (119863119871

1+

119863119871

2)(1 minus 120582) (2) when119863

119871

1+ 119863119871

2gt 119876119871+ Δ119862

119871 the reservation

amount is 119876119871+ Δ119862119871 then the actual occupancy amount is

(119876119871+Δ119862119871)(1 minus 120582) Therefore if (119876

119871+Δ119862119871)(1 minus 120582) le 119876

119871 that

is Δ119862119871le 120582119876119871(1 minus 120582) the profit of hotel is

120587119871

11= (1 minus 120582120572) [119901

119871

1(119876119871+ Δ119862119871minus 119863119871

2) + 119908119871119863119871

2] (11)

If (119876119871+ Δ119862119871)(1 minus 120582) ge 119876

119871 that is Δ119862

119871ge 120582119876119871(1 minus 120582)

the economy roomsrsquo actual occupancy amount exceeds theeconomy roomsrsquo number in the hotel so the hotel must paythe overbooking cost then the profit of hotel is

120587119871

12= (1 minus 120582120572) [119901

119871

1(119876119871+ Δ119862119871minus 119863119871

2) + 119908119871119863119871

2]

minus (119901119871

1+ 119888119871) [(119876119871+ Δ119862119871) (1 minus 120582) minus 119876

119871]

(12)

Proposition 12 Without considering roomsrsquo transfer the opti-mal overbooking quantity of economy rooms and luxury roomsis

Δ119862lowast

119894=

120582

1 minus 120582119876119894 119894 = 119871119867 (13)

FromProposition 12 we know that the higher the propor-tion of customer cancellations and no-show is the larger theoptimal overbooking quantity of the hotel will be With theincrease of 120572 the penalty that customers need to pay for theircancellation or no-show decreases Two following extremesituations are considered When 120572 = 1 the hotel will returnall the guarantee fee in case of customersrsquo cancellation or no-showThat is the same as the hotel does not charge customersany guarantee fee when customers book the rooms Undersuch circumstances customers can book rooms for severaldays firstly after they identify a specific itinerary they cancancel the extra rooms for they do not suffer any loss It is nodoubt that such regulation will increase the cancellation andno-show rate On the other hand if 120572 = 1 all the guaranteefee will not be returned after cancellation or no-show In thiscase customers need to reserve a room cautiously If it is notnecessary customers will not choose cancellation or no-showbecause the penalty cost is too high Such policy will reducethe cancellation and no-show rate Spontaneously to someextent 120572 and 120582 are positive correlation When the hotelincreases proportion 120572 it would like to increase the over-booking quantity so as to increase the actual occupancy rateNowadays the time-limited orders are widely used amonghotels Such regulation cannot only reduce customersrsquo lossfor the change of schedule but also help the hotel confirmthe orders so as to handle the overbooking phenomenon inadvance

In addition the risk of overbooking the economy roomsis relatively lower than the luxury rooms Compared toeconomic rooms it is more difficult for the hotel to findalternative luxury rooms to satisfy the customers Naturallyoverbooking cost of luxury room is higher For instance ifeconomy rooms are overbooked the hotel can transfer thecustomers to luxury rooms and the customers are willingto accept By contrast if luxury rooms are overbooked cus-tomers are not willing to accept the adjustment from luxuryrooms to economic rooms This implies that the hotel has topay a higher default costTherefore the hotel should be morecareful to choose the overbooking quantity of luxury rooms

62 With Room Transfer The following discusses the casewith room transfer Firstly when the economy rooms areinsufficient and luxury rooms have a surplus customers cancheck in the hotelrsquos luxury rooms with the price of economyrooms Customers spend the same money and can enjoybetter service so they are willing to accept this adjustmentSecondly when the luxury roomsrsquo actual occupancy amountexceeds the number of luxury rooms in the hotel the hotelusually transfers customers to other hotels nearby that havethe same level and same type because the customers whobook luxury room have a high requirement Customers canenjoy the same service so they are willing to accept this trans-fer However the hotelrsquos credibility in customersrsquo mind will be

Discrete Dynamics in Nature and Society 9

damaged and it must pay the additional costsThirdly if boththe economy rooms and luxury rooms are unable to meetthe demand the hotel usually transfers the customers whocannot check in to other hotels Note that when119863119894

1+119863119894

2gt 119876119894

119894 = 119871119867 if the hotel does not overbook its profit is

120587111

= (1 minus 120582120572) [119901119871

1(119876119871minus 119863119871

2) + 119901119867

1(119876119867minus 119863119867

2)

+ 119908119871119863119871

2+ 119908119867119863119867

2]

(14)

Proposition 13 With room transfer there exists threshold unitoverbooking cost 119888

1198940 such that if 119888

119894lt 1198881198940 then overbooking is

profitable for the hotel where

1198881198940=(1 minus 120582120572) 119901

119894

1

1 minus 120582 119894 = 119871119867 (15)

From Propositions 12 and 13 we conclude that the hotelshould control the overbooking quantity in a certain rangeto prevent lacking of rooms If the overbooking proportionis too large then the hotel may face a loss Only when theoverbooking cost is low the hotel can obtain additional profitOtherwise if the overbooking cost exceeds a certain valuethe hotelrsquos profit would be lower when it carries out over-booking As the market demand increases the supply is closeto saturation and then the overbooking costs will be higherTherefore when the market demand is excessive the hotelshould strictly control the proportion of overbooking Inaddition if the number of hotels that have the same level andtype in the same region is little that is the possibility to trans-fer customer is small then the hotel should lower the propor-tion of overbooking

The proportion of overbooking depends on the propor-tion of customer cancellations andno-showaswell as the totalnumber of hotel rooms so the hotel can analyze the historicaldata to develop an appropriate overbooking proportion so asto maximize the hotelrsquos expected profit

Proposition 14 When the economy rooms and luxury roomsare both overbooked the optimal centralized prices are asfollows 119894 = 119871119867

119901119894lowast

14= 119901119894lowast

1+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

119901119894lowast

24= 119901119894lowast

2+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

(16)

Bertrand and Stackelberg prices are as follows

(119901119894

14)119861lowast

= (119901119894

1)119861lowast

+2119888119894

119906119887119894(119887119894+ 120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

24)119861lowast

= (119901119894

2)119861lowast

+120579119888119894

119906119887119894 (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

14)119878lowast

= (119901119894

1)119878lowast

+119888119894

119906119887119894(2119887119894+ 3120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 21205792]

(119901119894

24)119878lowast

=120579 (119901119894

14)119878lowast

+ (1 minus 119904) 119886119894 + V (120579 + 120573) + 119908119894(119887119894+ 120579)

2 (119887119894+ 120579)

+119888

2 (1 minus 120582120572)

(17)

For the hotel the premise to overbook rooms is that themarket demand is greater than the supply When the hotelfaces the risk of overbooking the equilibrium prices in bothcentralized and decentralized decision-making supply chainwill improve In the busy season in order to reduce the riskof overbooking the hotel would increase the prices and theincrement will increase as the transfer cost increases From(16) and (17) we can know that the increment in centralizeddecision-making model is the greatest and that in Bertrandgame is the smallest

7 Numerical Analysis

In this section we do some numerical experiment to gainmore insights According to the China Hotel Sales Chan-nel Report by I-Research (httpreportiresearchcnreport2013031892shtml) there are 381 of the hotels that aresuitable for high-end travelers and 619 of the hotels thatare suitable for low-end travelersTherefore this part assumesthat the proportion of the economical rooms and the luxuryrooms is 4 6 that is 119886

119871= 06119886 119886

119867= 04119886 Other parameter

settings are made as follows 119886 = 600 119904 = 05 and 119887119871= 06

119887119867= 02 120573 = 120579 = 05 120578 = 004 120572 = 08 120582 = 01 119908

119894= 05119901

119894

1

(119894 = 119871119867) In the following we investigate the impact of V onthe optimal prices and profits

When V = 0 that is the OTA does not offer any servicethen the optimal prices of HA are equal to the prices ofOTA Since 119887

119871gt 120573 gt 119887

119867 then the market of economy

rooms is service-oriented while the market of luxury roomsis price-oriented FromFigure 2 we can know that whenOTAoffers more services OTArsquos optimal price will be increasedaccordingly It is reasonable that if V increases the cost ofOTAwill also definitely increase With the increase of V 119901119871lowast

1will

decline slowly while 119901119867lowast1

will increaseThe OTArsquos profit status becomes better with the improve-

ment of its price But as the V increases the cost of OTA willalso definitely increase When V is equal to 27 then the profitof OTA is the highest If V is larger then the high costs willreduce the profits of OTAWhen V is equal to 34 the profit ofthewhole supply chain is the highest So from the perspectiveof the supply chain V is expected to be 34 rather than 27Similarly for the integrated system the profit of the OTAalso rises first and then declines with the increase of V Aftercalculationwe can get thatwhen V = 27 both120587119861lowast

2and120587119878lowast2will

be the highest From Figures 3 and 4 we know that the OTAwould tend to offer service that valued 27 so as to maximizeits own profit

After calculation we can conclude that when V = 34 then120587119861lowast is highest when V = 35 then 120587

119878lowast is highest (Figure 5)

10 Discrete Dynamics in Nature and Society

0 10 20 30 40 50 60 70 80100

150

200

250

300

350

400

450

Pric

e

pLlowast

1

pLlowast

2

pHlowast

1

pHlowast

2

Value added by OTArsquos services ()

Figure 2 Equilibrium prices in the integrated system

0 10 20 30 40 50 60 70 800

1

2

3

4

5

6

7

Profi

t

times104

120587lowast

1

120587lowast

2

120587lowast

Value added by OTArsquos services ()

Figure 3 Profits in the integrated system

From the perspective of the supply chain theOTA is expectedto offer more services Despite the rising cost of OTA willlower its profit the hotel can lower the wholesale prices tocoordinate the distribution of profits so as to achieve a win-win situation

In the following we focus on the comparison of differentchannelrsquos profit in each model Figure 6 depicts the curves ofthe total profits of the HAOTA channels in the integratedsystem with respect to V Figure 7 draws the curves of the dif-ferent channelsrsquo profits under both Bertrand and Stackelberggame The profit of the HA channel refers to the profit thatthe hotel derived from the HA channelThe profit of the OTA

0 10 20 30 40 50 60125

13

135

14

145

15

155

16

165

Profi

t

times104

120587Blowast

2

120587Slowast

2

Value added by OTArsquos services ()

Figure 4 OTArsquos profits under two games

0 10 20 30 40 50 60 70 8052

53

54

55

56

57

58

59

6

61

62

Profi

t

times104

120587Blowast

2

120587Slowast

2120587lowast

Value added by OTArsquos services ()

Figure 5 The profit comparison

channel involves the OTArsquos profit and the hotelrsquos profit gainedfrom the OTA channel

As shown in Figures 6 and 7 with the increase of V theprofit of the OTA channel will increase first and will thendecrease This indicates that a high level of service by OTAwill be detrimental to the channel profit That is because ahigh level of service will bring a high cost undoubtedly Forthe integrated model and Bertrand game model this disad-vantage is more evident The OTArsquos service can motivate theactual purchase behavior of customers in the OTA channelWhen V is relatively lower the additional profits from OTArsquos

Discrete Dynamics in Nature and Society 11

0 10 20 30 40 50 60 70 8018

2

22

24

26

28

3

32

34

36

38

4

Profi

t

HA channelOTA channel

times104

Value added by OTArsquos services ()

Figure 6 Channel profits in the integrated system

0 10 20 30 40 50 60 70 8005

1

15

2

25

3

35

4

45

Profi

t

HA channel in Bertrand gameOTA channel in Bertrand gameHA channel in Stackelberg gameOTA channel in Stackelberg game

times104

Value added by OTArsquos services ()

Figure 7 Channel profits in two games

service are enough to compensate for the cost In this casethe hotel and the OTA can get more profit from providing theservice However when V is high the additional profits fromOTArsquos service cannot make up for the high cost In such phe-nomenon the OTA should not increase investment in ser-vice

For both integrated model and Bertrand game modelwith the increase of V the profit of the HA channel willdecrease first and will then increase while in the Stackelberggamemodel the profit of theHA channel will always increase

with V With Figure 2 we can know that when OTA providesmore additional services it tends to increase its price Someof the customers will turn to reserve rooms from the HAbecause of the excessively high price in OTA As a result thehotel can gain more profits from the HA channel

8 Conclusion

With the development of e-commerce the providers oftourism products are more inclined to build dual-channelsIn this paper we consider the direct selling channel of HAand the traditional retail channel ofOTA from the perspectiveof tourism supply chain We develop a two-echelon tourismsupply chain model involving one hotel and one OTA wheretheOTAprovides related service Customers will be refundedpartially in case of cancelation or no-show We investigatethe optimal pricing strategies under several common casesThe integrated operation and the decentralized operationbased on Bertrand and Stackelberg games are studied andcorresponding equilibrium pricing policies are obtained

Our findings demonstrate that the hotel plays a crucialrole in optimizing the benefits of supply chain Consideringthe overall profit of the supply chain the hotel should act as aleader in dual-channel supply chain and formulate reasonablewholesale prices to improve the cooperative enthusiasm ofOTA so as to achieve optimization of the whole supplychain A lower wholesale price can help reduce OTArsquos loss ofprofit because of the opening of HA channel In addition weconsider the overbooking of the hotel and obtain the optimaloverbooking quantity We conclude that the hotel can alwaysobtain higher profits when the overbooking proportion iscontrolledwithin a certain range Otherwise if the overbook-ing proportion is too high the hotel can get extra profits onlywhen the overbooking cost is lower than a certain value

The contribution of this paper is that we extend tourismsupply chain to the dual-channel structure in which the hotelopens its direct channel to sell tourism products And theextant literature only refers to the single channel In additionwe realize that customer cancellations andno-showoccur fre-quently in hotel industry Thus we develop the game modelsbased on such phenomenon At last we derive the conditionsunder which the hotel dominant case is profitable for boththe supply chain members Our results can provide hotelsand OTAs with some new managerial insights under thedual-channel environment

This research can be extended in several directions infuture work For example in this paper we assume that allinformation is known to the hotel and OTA However someinformation could be asymmetric (eg see Chen [37]) Thuswe can explore the Bayesian equilibrium under asymmetricinformation settings Secondly the assumption of lineardemand is a limitation of this paperWe can further study thedynamic pricing in tourism dual-channel supply chain

Appendix

A Proof of Corollary 8

First we set (1199011198711)119861lowast

gt (119901119871

1)119878lowast which can be expressed as

12 Discrete Dynamics in Nature and Society

(1 minus 120582120572) (120579119886119871 + 120579119904119886119871+ 2119887119871119904119886119871+ 120579V120573 + 3119908

1198711205792+ 3119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

gt(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(A1)

The above equation can be simplified as

119908119871gt120579 [(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)]

4119887119871 (1 minus 120582120572) (119887119871 + 120579) (119887

119871+ 2120579)

(A2)

So we can get Corollary 8 B Proof of Corollary 9

If (1199011198941)119878lowast

gt (119901119894

1)119861lowast then

(1 minus 120582120572) (120579119886119894 + 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 2119908

1198941205792+ 2119908119894119887119894120579 minus 1205792V minus 2120579119887

119894V) + 119888120579 (119887

119894+ 120579)

minus (1 minus 120582120572) ((119901119894

1)119878lowast

+ (119901119894

1)119861lowast

) [2 (119887119894+ 120579)2minus 1205792] gt 0

120587119878lowast

1minus 120587119861lowast

1=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

2 (119887119871+ 120579)

((119901119871

1)119878lowast

minus (119901119871

1)119861lowast

)

+(1 minus 120582120572) (120579119886119867 + 120579119904119886

119867+ 2119887119867119904119886119867+ 120579V120573 + 2119908

1198671205792+ 2119908119867119887119867120579 minus 1205792V minus 2120579119887

119867V) + 119888120579 (119887

119867+ 120579)

2 (119887119867+ 120579)

((119901119867

1)119878lowast

minus (119901119867

1)119861lowast

)

minus (1 minus 120582120572)2 (119887119871+ 120579)2minus 1205792

2 (119887119871+ 120579)

[((119901119871

1)119878lowast

)2

minus ((119901119871

1)119861lowast

)2

] minus (1 minus 120582120572)2 (119887119867+ 120579)2minus 1205792

2 (119887119867+ 120579)

[((119901119867

1)119878lowast

)2

minus ((119901119867

1)119861lowast

)2

] gt 0

(B1)

If (1199011198711)119878lowast

lt (119901119871

1)119861lowast and (119901

119867

1)119878lowast

lt (119901119867

1)119861lowast we can prove

120587119878lowast

1gt 120587119861lowast

1similarly

From Propositions 3 and 7 with (3) we obtain that

120587119861lowast

2minus 120587119878lowast

2=

120579

4 (119887119871+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119871 + V (120573 + 120579) minus 119908119871(119887119871+ 120579)]

minus 2119888 (119887119871+ 120579) + 120579 (1 minus 120582120572) ((119901

119871

1)119861lowast

+ (119901119871

1)119878lowast

)

sdot ((119901119871

1)119861lowast

minus (119901119871

1)119878lowast

) +120579

4 (119887119867+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119867 + V (120573 + 120579) minus 119908 (119887119867+ 120579)]

minus 2119888 (119887119867+ 120579) + 120579 (1 minus 120582120572) ((119901

119867

1)119861lowast

+ (119901119867

1)119878lowast

)

sdot ((119901119867

1)119861lowast

minus (119901119867

1)119878lowast

)

(B2)

Note that

119863119894

2= [(1 minus 119904) 119886119894 minus 119887

119894119901119894

2] + 120573V + 120579 (119901

119894

1+ V minus 119901

119894

2) gt 0 (B3)

so we show that

2 (1 minus 120582120572) [(1 minus 119904) 119886119894 + V (120573 + 120579) minus 119908119894(119887119894+ 120579)]

minus 2119888 (119887119894+ 120579) + 120579 (1 minus 120582120572) ((119901

119894

1)119861lowast

+ (119901119894

1)119878lowast

)

gt 0

(B4)

Thus we have the following

(1) 120587119861lowast2

gt 120587119878lowast

2 if (1199011198711)119861lowast

gt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

gt (119901119867

1)119878lowast

(2) 120587119861lowast2

= 120587119878lowast

2 if (1199011198711)119861lowast

= (119901119871

1)119878lowast and (119901

119867

1)119861lowast

= (119901119867

1)119878lowast

(3) 120587119861lowast2

lt 120587119878lowast

2 if (1199011198711)119861lowast

lt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

lt (119901119867

1)119878lowast

Combined with Corollary 8 the proposition is proved

Discrete Dynamics in Nature and Society 13

C Proof of Corollary 10

The profit of hotel from the economy rooms is as follows

120587119871

= [(1 minus 120582120572) (119904119886119871 minus 120579V) minus 119888120579] 119901119871

1

+ [(1 minus 120582120572) (119886119871 minus 119904119886119871+ 120573V + 120579V) + 119888 (119887

119871+ 120579)] 119901

119871

2

+ 2120579 (1 minus 120582120572) 119901119871

1119901119871

2minus (1 minus 120582120572) (119887119871 + 120579) (119901

119871

1)2

minus (1 minus 120582120572) (119887119871 + 120579) (119901119871

2)2

minus (119886119871minus 119904119886119871+ 120573V + 120579V) 119888

(C1)

Define (119901119871

1)119861(119878)

= (119860119871

1)119861(119878)

+ (119861119871

1)119861(119878)

119908119871 (1199011198712)119861(119878)

=

(119860119871

2)119861(119878)

+ (119861119871

2)119861(119878)

119908119871 where

(119861119871

1)119861

=3120579 (119887119871+ 120579)

4 (119887119871+ 120579)2minus 1205792

(119861119871

1)119878

=120579 (119887119871+ 120579)

2 (119887119871+ 120579)2minus 1205792

(119861119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119861119871

1)119861(119878)

+1

2

(119860119871

1)119861

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

(119860119871

1)119878

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(119860119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119860119871

1)119861(119878)

+(1 minus 120582120572) [(1 minus 119904) 119886119871 + V (120579 + 120573)] + 119888 (119887

119871+ 120579)

2 (1 minus 120582120572) (119887119871 + 120579)

(C2)

Let 120597120587119871120597119908 = 0 then we get119908lowast

119871 Similarly we can get119908lowast

119867

D Proof of Proposition 12

Let 120587119889minus 120587119903gt 0 then we can get 119904

0 where the profits of hotel

from HA and OTA are as follows

120587119889= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1)

120587119903= (1 minus 120582120572) (119908119871119863

119871

2+ 119908119867119863119867

2)

(D1)

E Proof of Corollary 11

If Δ119862119871le 120582(1 minus 120582)119876

119871 then the profit of hotel is 120587119871

11 The

derivative of 12058711987111(Δ119862119871) is 120597120587119871

11120597Δ119862119871= (1 minus 120582120572)119901

119871

1gt 0 So

with the increase of Δ119862119871 12058711987111

will increase When Δ119862119871

=

120582(1 minus 120582)119876119871 12058711987111

is maximized If Δ119862119871

ge 120582(1 minus 120582)119876119871

then the profit of hotel is 12058711987112 The derivative of 120587119871

12(Δ119862119871) is

120597120587119871

12120597Δ119862119871= (1 minus 120582120572)119901

119871

1minus (1 minus 120582)(119901

119871

1+ 119888119871) lt 0 So with the

increase of Δ119862119871 12058711987111will decline When Δ119862

119871= 120582(1 minus 120582)119876

119871

120587119871

11is maximizedSimilarly we can get Δ119862lowast

119867

F Proof of Proposition 13

Assume that the overbooking proportion is 120574119871and 120574119867

(1) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) le 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

That is

120574119867lt

120582

1 minus 120582lt 120574119871

le120582119876119871+ 119876119867[1 minus (1 minus 120582) (1 + 120574

119867)]

(1 minus 120582)119876119871

(F1)

Thus the hotel would like to overbook to get more profitrather than room vacancy

(2) Consider (1198631198711+119863119871

2)(1minus120582) lt 119876

119871and (119863119867

1+119863119867

2)(1minus120582) gt

119876119867That is 120574

119871lt 120582(1 minus 120582) lt 120574

119867 Then the profit of hotel is

120587112

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F2)

Thenwhen 119888119867119906

lt (1minus120582120572)119901119867

1(1minus120582) that is120587

112minus120587111

gt 0the hotel would carry out overbooking

(3) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

14 Discrete Dynamics in Nature and Society

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867lt 120582(1 minus 120582) Then the profit of hotel is

120587113

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2+ 119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876]

(F3)

Then when 119888119871

119906lt (1 minus 120582120572)119901

119871

1(1 minus 120582) 120587

113minus120587111

gt 0 thusthe hotel would carry out overbooking

(4) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) gt 119876

119867

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867gt (120582119876

119867+ 119876119871[1 minus (1 minus 120582)(1 + 120574

119871)])(1 minus 120582)119876

119867

Then the profit of hotel is as follows

120587114

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2) (1 minus 120582) minus 119876

119871]

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F4)

Then when 119888119871119906lt (1minus120582120572)119901

119871

1(1minus120582) and 119888119867

119906lt (1minus120582120572)119901

119867

1

(1 minus 120582) 120587114

minus 120587111

gt 0 overbooking is preferred

G Threshold Values

Threshold values are as follows

1198711= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 3119908

1198941205792+ 3119908119894119887119894120579

minus 1205792V minus 2120579119887

119894V

1198712= 2119886119894(119887119894+ 120579) minus 119904119886

119894(2119887119894+ 120579) + 120579

2119908119894+ 2 (120579 + 120573) (119887

119894

+ 120579) V + 2119908119894(119887119894+ 120579)2minus 1205792V

1198713= 4120579V119887

119894120573 minus 120579119904119886

119894119887119894+ 2V1205731198872

119894+ 31198861198941205792+ 4119886119894119887119894120579

minus 21198861198941198872

119894119904 + 3120579

2V120573 + 1205792V119887119894+ 2120579V1198872

119894+ 21198861198941198872

119894

1198714= 3119886119894119887119894120579 + 3120579

2V120573 minus 2120579V1198872119894minus 1205792V119887119894+ 31198861198941205792

+ 21198861198941198872

119894119904 + 119886119887

119894119904120579 + 3119887

119894120573V120579

1198715= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 minus 120579

2V minus 2120579119887119894V

1198661= [(1 minus 120582120572) (119904119886119894 minus 120579V) minus 119888120579] (119861

119894

1)119861(119878)

+ [(1 minus 120582120572) (119886119894 minus 119904119886119894+ 120573V + 120579V) + 119888 (119887

119894+ 120579)]

sdot (119861119894

1)119861(119878)

+ 2120579 (1 minus 120582120572) [(119860119894

1)119861(119878)

(119861119894

2)119861(119878)

+ (119861119894

1)119861(119878)

(119860119894

2)119861(119878)

] minus 2 (1 minus 120582120572) (119887119894 + 120579)

sdot [(119860119894

1)119861(119878)

(119861119894

1)119861(119878)

+ (119860119894

2)119861(119878)

(119861119894

2)119861(119878)

]

1198662= 2 (1 minus 120582120572)

sdot (119887119894+ 120579) [((119861

119894

1)119861(119878)

)

2

+ ((119861119894

2)119861(119878)

)

2

]

minus 2120579 (119861119894

1)119861(119878)

(119861119894

2)119861(119878)

1199040= ((119887119871+ 120579) (119901

119871

1)2

+ (119887119867+ 120579) (119901

119867

1)2

+ 120579119908119871(119901119871

1minus 119901119871

2) + 120579119908

119867(119901119867

1minus 119901119867

2)

+ 120579V (1199011198711+ 119901119867

1) + (119908

119871+ 119908119867) (120573 + 120579) V

+ 119908119871(119886119871minus 119887119871119901119871

2) + 119908119867(119886119867minus 119887119867119901119867

2)

minus 120579 (119901119871

1119901119871

2+ 119901119867

1119901119867

2)) (119886119871(119901119871

1+ 119908119871)

+ 119886119867(119901119867

1+ 119908119867))minus1

(G1)

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The authors thank associate editor and anonymous refereesfor their numerous constructive comments and encourage-ment that have improved their paper greatly The work waspartly supported by (i) the National Natural Science Founda-tion ofChina (71201083 71572058 and 71571100) (ii) the Fun-damental Research Funds for the Central Universities SCUT(2015ZZ057) (iii) Jiangsu Province Science Foundation forYouths (BK2012379) and (iv) the Fundamental ResearchFunds for the Central Universities (NS2015076)

References

[1] J Li W N Zhang H Xu and J Jiang ldquoDynamic competitionand cooperation of road infrastructure investment of multipletourism destinations a case Study of Xidi and Hongcun WorldCulturalHeritagerdquoDiscreteDynamics inNature and Society vol2015 Article ID 962028 10 pages 2015

[2] T Paksoy EOzceylan andG-WWeber ldquoProfit oriented supplychain network optimizationrdquoCentral European Journal of Oper-ations Research vol 21 no 2 pp 455ndash478 2013

[3] X Zhang H Song and G Q Huang ldquoTourism supply chainmanagement a new research agendardquo Tourism Managementvol 30 no 3 pp 345ndash358 2009

[4] Z Yang and J Cai ldquoDo regional factors matter Determinantsof hotel industry performance in Chinardquo TourismManagementvol 52 pp 242ndash253 2016

[5] B Pan L Zhang and R Law ldquoThe complex matter of onlinehotel choicerdquoCornell Hospitality Quarterly vol 54 no 1 pp 74ndash83 2013

[6] L Ling X Guo and C Yang ldquoOpening the online marketplacean examination of hotel pricing and travel agency on-line

Discrete Dynamics in Nature and Society 15

distribution of roomsrdquo Tourism Management vol 45 pp 234ndash243 2014

[7] L Ling Y Dong X Guo and L Liang ldquoAvailability man-agement of hotel rooms under cooperation with online travelagenciesrdquo International Journal of Hospitality Management vol50 pp 145ndash152 2015

[8] J N K Liu andE Y Zhang ldquoAn investigation of factors affectingcustomer selection of online hotel booking channelsrdquo Interna-tional Journal of Hospitality Management vol 39 pp 71ndash832014

[9] L Fox ldquoFour Seasons Unveils $18 Million Website as LuxuryTravel Growsrdquo 2012 httpwwwtnoozcomarticlefour-sea-sons-unveils-18-million-dollar-website-as-luxury-travel-grows

[10] C-M Chen and Y-C Lin ldquoThe influence of uncertain demandon hotel capacityrdquo International Journal of Hospitality Manage-ment vol 34 no 1 pp 462ndash465 2013

[11] S Yang G Q Huang H Song and L Liang ldquoGame-theoreticapproach to competition dynamics in tourism supply chainsrdquoJournal of Travel Research vol 47 no 4 pp 425ndash439 2009

[12] G Q Huang H Song and X Zhang ldquoA comparative analysis ofquantity and price competitions in tourism supply chain net-works for package holidaysrdquo Service Industries Journal vol 30no 10 pp 1593ndash1606 2010

[13] Y Huang H Song G Q Huang and J Lou ldquoA comparativestudy of tourism supply chains with quantity competitionrdquoJournal of Travel Research vol 51 no 6 pp 717ndash729 2012

[14] H K Lee and Y Fernando ldquoThe antecedents and outcomes ofthe medical tourism supply chainrdquo Tourism Management vol46 pp 148ndash157 2015

[15] W-Y K Chiang D Chhajed and J D Hess ldquoDirect marketingindirect profits a strategic analysis of dual-channel supply-chain designrdquoManagement Science vol 49 no 1 pp 1ndash20 2003

[16] A A Tsay and N Agrawal ldquoChannel conflict and coordinationin the E-commerce agerdquo Production and Operations Manage-ment vol 13 no 1 pp 93ndash110 2004

[17] Q-H Li and B Li ldquoDual-channel supply chain equilibriumproblems regarding retail services and fairness concernsrdquoApplied Mathematical Modelling 2016

[18] S Panda N M Modak S S Sana and M Basu ldquoPricingand replenishment policies in dual-channel supply chain undercontinuous unit cost decreaserdquo Applied Mathematics and Com-putation vol 256 pp 913ndash929 2015

[19] Y Liu C Ding C Fan and X Chen ldquoPricing decision underdual-channel structure considering fairness and free-ridingbehaviorrdquo Discrete Dynamics in Nature and Society vol 2014Article ID 536576 10 pages 2014

[20] J Chen H Zhang and Y Sun ldquoImplementing coordinationcontracts in a manufacturer Stackelberg dual-channel supplychainrdquo Omega vol 40 no 5 pp 571ndash583 2012

[21] Q Ding C Dong and Z Pan ldquoA hierarchical pricing decisionprocess on a dual-channel problem with one manufacturer andone retailerrdquo International Journal of Production Economics vol175 pp 197ndash212 2016

[22] B Rodriguez and G Aydin ldquoPricing and assortment decisionsfor a manufacturer selling through dual channelsrdquo EuropeanJournal of Operational Research vol 242 no 3 pp 901ndash9092015

[23] T Lockyer ldquoThe perceived importance of price as one hotelselection dimensionrdquo Tourism Management vol 26 no 4 pp529ndash537 2005

[24] C-M Chen H-W Yang E Y Li and C-C Liu ldquoHow doeshotel pricing influence guest satisfaction by the moderatinginfluence of room occupancyrdquo International Journal of Hospi-tality Management vol 49 pp 136ndash138 2015

[25] J-M Espinet M Fluvia R Rigall-I-Torrent and A Salo ldquoHotelcharacteristics and seasonality in prices an analysis usingSpanish tour operatorsrsquo brochuresrdquo Tourism Economics vol 18no 4 pp 749ndash767 2012

[26] C Juaneda J M Raya and F Sastre ldquoPricing the time and loca-tion of a stay at a hotel or apartmentrdquo Tourism Economics vol17 no 2 pp 321ndash338 2011

[27] G Abrate G Fraquelli and G Viglia ldquoDynamic pricing strate-gies evidence from European hotelsrdquo International Journal ofHospitality Management vol 31 no 1 pp 160ndash168 2012

[28] D Q Yao and J J Liu ldquoCompetitive pricing of mixed retail ande-tail distribution channelsrdquo Omega vol 33 no 3 pp 235ndash2472005

[29] J Zhao and L Wang ldquoPricing and retail service decisionsin fuzzy uncertainty environmentsrdquo Applied Mathematics andComputation vol 250 pp 580ndash592 2015

[30] A A Tsay and N Agrawal ldquoChannel dynamics under priceand service competitionrdquo Manufacturing amp Service OperationsManagement vol 2 no 4 pp 372ndash391 2000

[31] S C Choi ldquoPrice competition in a duopoly common retailerchannelrdquo Journal of Retailing vol 72 no 2 pp 117ndash134 1996

[32] Y Bakos andE Brynjolfsson ldquoBundling and competition on theinternetrdquoMarketing Science vol 19 no 1 pp 63ndash82 2000

[33] H Song J H Kim and S Yang ldquoConfidence intervals fortourism demand elasticityrdquo Annals of Tourism Research vol 37no 2 pp 377ndash396 2010

[34] DMHanssens L J Parsons andR L SchultzMarket ResponseModels Econometric and Time Series Analysis Kluwer Aca-demic Publishers Boston Mass USA 2nd edition 2001

[35] H Kurata D-Q Yao and J J Liu ldquoPricing policies under directvs indirect channel competition and national vs store brandcompetitionrdquo European Journal of Operational Research vol180 no 1 pp 262ndash281 2007

[36] R Law and C Cheung ldquoA study of the perceived importance ofthe overall website quality of different classes of hotelsrdquo Inter-national Journal of Hospitality Management vol 25 no 3 pp525ndash531 2006

[37] K B Chen ldquoProcurement strategies and coordination mecha-nism of the supply chain with one manufacturer and multiplesuppliersrdquo International Journal of Production Economics vol138 no 1 pp 125ndash135 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Discrete Dynamics in Nature and Society 5

4 Integrated System

As a benchmark we first consider an integrated systemwherethe common goal of supply chain upstream and downstreammembers is tomaximize the overall profit of the supply chainThis is an ideal model that the members in the supply chainoperate as an entirety In such an integratedmodel of tourismsupply chain the hotel and OTA cooperate to determine thepricing strategies

Proposition 1 In the integrated system the optimal pricingdecisions of HA and OTA are as follows

119901119894lowast

1=119886119894(119887119894119904 + 120579) + 120579V (120573 minus 119887

119894)

2 (119887119894)2+ 4119887119894120579

119901119894lowast

2=(119887119894+ 120579 minus 119887

119894119904) 119886119894+ 119887119894120573V + 120579V (120573 + 119887

119894)

2 (119887119894)2+ 4119887119894120579

+119888 (V)

2 (1 minus 120582120572)

119894 = 119871119867

(5)

From Proposition 1 the optimal prices shown above canexplain that in the integrated system the optimal prices of HAwill not be affected by the proportion of customer cancella-tions and no-show (120582) or the return expense proportion (120572)On the other hand with the increase of 120582 or 120572 the optimalprices for OTAwill increaseThis is reasonable because whenOTA faces unstable demand or it should return more tocustomersrsquo cancellation or no-show it would like to increasethe price to guarantee its profit

Corollary 2 119901119871lowast2

and 119901119867lowast2

are increasing in V Moreover

(1) if 120573 gt 119887119871gt 119887119867 then 120597119901

119871lowast

1120597V gt 0 120597119901119867lowast

1120597V gt 0

(2) if 119887119871gt 120573 gt 119887

119867 then 120597119901

119871lowast

1120597V lt 0 120597119901119867lowast

1120597V gt 0

(3) if 119887119871gt 119887119867gt 120573 then 120597119901

119871lowast

1120597V lt 0 120597119901119867lowast

1120597V lt 0

From Corollary 2 we can know that when OTA offersmore services OTArsquos optimal price will be increased accord-ingly It is reasonable that if V increases the cost of OTA willalso definitely increase So there is always a positive correla-tion between OTArsquos optimal prices and the added value

If 120573 gt 119887119871

gt 119887119867 the market of economy rooms and

that of luxury rooms are both service-oriented rather thanprice-oriented The implication is that the effective servicewill increase the optimal price of HAWhenOTA offersmoreeffective service its price will increase But some customerswant to enjoy the additional services so they are willingto make a booking through OTA despite spending moremoneyTherefore the demand inOTAwill increase while thedemand in HA will decrease

If 119887119871gt 120573 gt 119887

119867 the market of economy rooms is service-

oriented while the market of luxury rooms is price-orientedThe HArsquos optimal price of economy rooms will decrease withrespect to V Conversely the HArsquos optimal price of luxuryrooms will increase with respect to V For examples the

change of price has a great impact on leisure travelersrsquo deci-sions but for business travelers the price is not themost con-cern If the price ofOTA increasesOTArsquos demandof economyrooms will significantly reduce and the HArsquos demand willincrease thus the HArsquos optimal price will decline On theother hand for luxury rooms if OTA provides more effectiveservice the customer would be willing to pay higher pricesfor value-added service This will bring the increase in OTArsquosdemand and the reduction of HArsquos demand thus the optimalprice of HA will increase

If 119887119871gt 119887119867gt 120573 the market of economy rooms and that of

luxury rooms are both price-oriented than service-orientedThe HArsquos optimal price of both economy rooms and luxuryrooms will decrease with the increase of V When the marketis price-oriented the promotion of price in OTAwill lead to areduction in OTArsquos demandThereby the demand in HA willincrease and optimal price in HA will decline

5 Two Game Models

In the tourism dual-channel supply chain the relationshipbetween hotel and OTA is cooperative as well as competitiveIn the decentralized decision-making model they are morecompetitive than cooperative Their purposes are to maxi-mize their own profits In reality hotel can choose whether toinform the price ofHAor not forHA is competingwithOTAUninformed of the prices inHAOTAcan predict the range ofprice onHAby the star-rated and room type of the hotel but itcannot know the exact priceTherefore this section examinesthe pricing equilibrium between the hotel and OTA undertwo types of games namely the Bertrand and Stackelberggames For the Bertrand game both of the participantsregard price as a decision variable the hotel and OTA areuncooperative For the Stackelberg game the participantsare divided into two roles the leader and the follower Asa leader in tourism supply chain the hotel will provide thepolicy to maximize its interests As a follower OTA accepts ifprofitable By comparing the two models we can understandhow the behavior of hotel influences the pricing decisions

51 Bertrand Game In a Bertrand game the procedure isas follows keeping the wholesale price unchanged the hoteldetermines HArsquos prices 119901119871

1and 119901

119867

1 so as to maximize profit

1205871 Uninformed of the prices of HA OTA decides prices 119901119871

2

and 119901119867

2 so as to maximize his profit 120587

2 Let (119901119894

1)119861 (1199011198942)119861(119894 =

119871119867) denote HArsquos and OTArsquos prices under a Bertrand modelrespectively

In the following 119871119899(119899 = 1 2 5) 119904

0 and 119866

119898(119898 =

1 2) are the threshold values and are given in Appendix G

Proposition 3 There exist Bertrand equilibrium prices(119901119894

1)119861lowast (119901119894

2)119861lowast

(119894 = 119871119867) where

(119901119894

1)119861lowast

=(1 minus 120582120572) 1198711 + 119888120579 (119887

119894+ 120579)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

2)119861lowast

=(1 minus 120582120572) 1198712 + 2119888 (119887

119894+ 120579)2

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(6)

6 Discrete Dynamics in Nature and Society

From Proposition 3 in the Bertrand model the equilib-rium prices for hotel and OTA are both affected by 120572 and 120582With the increase of 120572 or 120582 both (119901

119894

1)119861lowast and (119901

119894

2)119861lowast will be

higher In otherwords with higher uncertainty of roomoccu-pancy the hotel and OTA tend to increase prices to protecttheir own profits

Denote 1198881= (1 minus 120582120572)(2119887

119871+ 120579 minus 120573)(119887

119871+ 120579) and 119888

2= (1 minus

120582120572)(2119887119867+ 120579 minus 120573)(119887

119867+ 120579) then 119888

1gt 1198882

Corollary 4 (1199011198712)119861lowast and (119901

119867

2)119861lowast are increasing in V (119901119871

1)119861lowast

and (119901119867

1)119861lowast have the following relationships with respect to

OTArsquos service

(1) if 1198881015840(V) gt 1198881 then 120597(119901

119871

1)119861lowast120597V gt 0 120597(119901119867

1)119861lowast120597V gt 0

(2) if 1198881gt 1198881015840(V) gt 119888

2 then 120597(119901

119871

1)119861lowast120597V lt 0 120597(119901119867

1)119861lowast120597V gt

0(3) if 1198881015840(V) lt 119888

2 then 120597(119901

119871

1)119861lowast120597V lt 0 120597(119901119867

1)119861lowast120597V lt 0

From Corollary 4 when OTA offers more effective ser-vices its optimal prices will increase due to the incrementin the cost Marginal cost measures the input costs and theoutput value per unit If the marginal cost is greater than1198881 then the costs of OTA to provide additional services are

higher So the equilibrium prices of HA will increase as thevalue added by OTArsquos services increases When the marginalcost is between 119888

1and 1198882 HArsquos equilibrium price of economy

rooms and the value added by OTArsquos service have a negativecorrelation but HArsquos equilibrium price of luxury roomswould increase with the increment of V In addition when themarginal cost is less than 119888

2 the costs of OTA to provide addi-

tional service are lower And the equilibriumprices ofHAwilldecrease when V increases

Corollary 5 There exist threshold unit wholesale prices 1199080119894

1199081

119894(119894 = 119871119867) such that

(1) (1199011198941)lowastlt (119901119894

1)119861lowast if 119908

119894gt 1199080

119894 (1199011198941)lowast= (119901119894

1)119861lowast if 119908

119894= 1199080

119894

(119901119894

1)lowastgt (119901119894

1)119861lowast if 119908

119894lt 1199080

119894

(2) (1199011198942)lowastlt (119901119894

2)119861lowast if 119908

119894gt 1199081

119894 (1199011198942)lowast= (119901119894

2)119861lowast if 119908

119894= 1199081

119894

(119901119894

2)lowastgt (119901119894

2)119861lowast if 119908

119894lt 1199081

119894

where

1199080

119894=

1198713

6119887119894(119887119894+ 120579) (119887

119894+ 2120579)

minus119888

3 (1 minus 120582120572)

1199081

119894=

120579 [(1 minus 120582120572) 1198714 minus 119888119887119894120579 (119887119894+ 2120579)]

2119887119894 (1 minus 120582120572) (119887119894 + 2120579) (31205792 + 21198872

119894+ 2119887119894120579)

(7)

FromProposition 1 it is easy to know that the equilibriumprices in the integrated system are not affected by the whole-sale prices However from Proposition 3 in the Bertrandmodel there is a positive correlation between the equilibriumprices and the wholesale prices Corollary 5 shows that theequilibrium price of HA in the Bertrand game is higherthan that in the integrated system if the wholesale price isgreater than a certain critical point (1199080

119894) Additionally if the

wholesale price is greater than1199081119894 then the equilibrium price

of OTA in Bertrand model will be higher than that in theintegrated model

Corollary 6 There exists a threshold unit wholesale price1199082

119894(119894 = 119871119867) such that if119908

119894gt 1199082

119894 then119863lowast

119894gt 119863119861lowast

119894(119894 = 119871119867)

where

1199082

119894=120579 [(1 minus 120582120572) (V120573 + 119886

119894) minus 119887119894119888]

2119887119894 (1 minus 120582120572) (119887119894 + 2120579)

(8)

Corollary 6 shows that when thewholesale price is greaterthan 119908

2

119894 the high price will lead to a lower demand in the

Bertrand game That is the reservation amount of Bertrandmodel is less than that in the integrated model The highersale price in OTA results from the higher wholesale priceThus the above result is reasonable because travelers are pricesensitive especially for leisure travelers the increase of pricewill bring the decline of reservation amount When the rela-tionship between the hotel and OTA is modeled as a Stackel-berg game the hotel canmotivate customers to reserve roomsthrough a reasonable wholesale price If the wholesale price isgreater than the threshold the sales volume in the centralizedcase is lower than that in the Bertrand case

52 Stackelberg Game In a Stackelberg game the procedureis as follows keeping thewholesale price unchanged the hotel(as the leader) announces HArsquos prices 119901119871

1and 119901119867

1of two types

of rooms respectively in order to maximize its profit 1205871 In

response to HArsquos prices OTA (as the follower) determinesprices 119901

119871

2and 119901

119867

2to maximize its profit 120587

2 Let (119901

119894

1)119878

(119901119894

2)119878(119894 = 119871119867) denote respectively HArsquos and OTArsquos prices

under a Stackelberg game

Proposition 7 The optimal prices are (119901119894

1)119878lowast (119901119894

2)119878lowast

(119894 =

119871119867) and there exists a threshold unit wholesale price 1199083119894(119894 =

119871119867) such that if 119908119894gt 1199083

119894 then (119901

119894

1)lowastlt (119901119894

1)119878lowast where

(119901119894

1)119878lowast

=(1 minus 120582120572) (1198711 minus 119908

1198941205792minus 119908119894119887119894120579) + 119888120579 (119887

119894+ 120579)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 21205792]

(119901119894

2)119878lowast

=120579 (119901119894

1)119878lowast

+ (1 minus 119904) 119886119894 + V (120579 + 120573) + 119908119894(119887119894+ 120579)

2 (119887119894+ 120579)

+119888

2 (1 minus 120582120572)

1199083

119894

=119887119894V120573 + 119886119887

119894+ 120579V119887119894+ 119886119894120579 + 120579V120573 minus 119886

119894119887119894119904

2119887119894(119887119894+ 2120579)

minus119888

2 (1 minus 120582120572)

(9)

Similar to the Bertrand competition the equilibriumprices in Stackelberg game will increase with the increase of

Discrete Dynamics in Nature and Society 7

the return expense proportion (120572) or the cancellations andno-show proportion (120582)

From Proposition 7 we can see that the Stackelbergmodel is similar to the Bertrand model that the equilibriumprices would increase with the increase of wholesale pricesFurthermore when thewholesale price is greater than1199083

119894 the

equilibrium price of HA in Stackelberg model will be higherthan that in the integrated model

In the Stackelberg game if OTA offers more effective ser-vices the equilibrium prices of OTA would increase accord-ingly The relationship between the Stackelberg equilibriumprices and V is similar to that in the Bertrand model

53 Contrastive Analysis of Bertrand and Stackelberg GamesBased on the equilibrium prices obtained in the previoussection we in this section compare the equilibriumprices andoptimal profit under Bertrand and Stackelberg games

Corollary 8 There exists a threshold unit wholesale price1199084

119894(119894 = 119871119867) such that

(1) (1199011198941)119861lowast

gt (119901119894

1)119878lowast and (119901119894

2)119861lowast

gt (119901119894

2)119878lowast if 119908

119894gt 1199084

119894

(2) (1199011198941)119861lowast

= (119901119894

1)119878lowast and (119901119894

2)119861lowast

= (119901119894

2)119878lowast if 119908

119894= 1199084

119894

(3) (1199011198941)119861lowast

lt (119901119894

1)119878lowast and (119901119894

2)119861lowast

lt (119901119894

2)119878lowast if 119908

119894lt 1199084

119894

where

1199084

119894=

120579 [(1 minus 120582120572) 1198715 + 119888120579 (119887119894+ 120579)]

4119887119894 (1 minus 120582120572) (119887119894 + 120579) (119887

119894+ 2120579)

(10)

Corollary 8 compares the equilibrium prices under theBertrand and Stackelberg game with respect to the wholesaleprice It shows that if the wholesale price is greater than1199084

119894 the pricing equilibrium under the Bertrand is higher

than that under the Stackelberg game Conversely the pricingequilibrium is lower if the wholesale price is less than 119908

4

119894

In the decentralized case both the manufacturer and theretailer want to maximize their profit A high wholesale pricecould be passed on to customersTherefore the above resultsexist In addition how to share the profit between the manu-facturer and the retailer depends on their bargaining powers

Corollary 9 If 119908119894

= 1199084

119894(119894 = 119871119867) then 120587

119878lowast

1gt 120587119861lowast

1 OTArsquos

profit has the following relationship with respect to 1199084119894

(1) 120587119861lowast2

gt 120587119878lowast

2if 119908119871gt 1199084

119871and 119908

119867gt 1199084

119867

(2) 120587119861lowast2

= 120587119878lowast

2if 119908119871= 1199084

119871and 119908

119867= 1199084

119867

(3) 120587119861lowast2

lt 120587119878lowast

2if 119908119871lt 1199084

119871and 119908

119867lt 1199084

119867

Thehotel is the leader in Stackelberg game and can alwaysbenefit from it except for the critical point1199084

119894 Comparedwith

the Bertrand game the hotel can get higher profits in Stackel-berg gamewhen the wholesale price is not equal to1199084

119894There-

fore in decentralized decision-making model the hotel willbe more inclined to be the price leader in order to ensure thatit can achieve higher profits

Corollary 9 indicates that the Stackelberg model is supe-rior to the Bertrand model when the wholesale price is less

than the critical point1199084119894 Not only the hotel but alsoOTA can

gain more profit from the Stackelberg game Though OTA isa follower in Stackelberg game the profit will not be reducedbecause the lower wholesale prices can compensate for theloss of profit caused by the opening of HA channel Conse-quently the hotel should play the role of the price leader inthe supply chain and develop reasonable wholesale prices toachieve optimization of the whole supply chain profit whileoptimizing its own profit

Corollary 10 Under either Bertrand or Stackelberg equi-librium channel prices there exists optimal wholesale price119908lowast

119894(119894 = 119871119867) that maximizes the total equilibrium channel

profit where 119908lowast119894= 11986611198662

According to Corollary 10 there exists optimal wholesaleprice 119908

lowast

119894(119894 = 119871119867) that maximizes the total equilibrium

channel profit under either Bertrand or Stackelberg gameThe optimal wholesale price will optimize the decentralizeddecision-making supply chainMeanwhile both the hotel andtheOTA can benefit from the optimal wholesale priceThere-fore the reasonable wholesale price can help promotemutualcooperation and communication between the supply chainmembers

54 Contrastive Analysis of Two Channels in the Supply Chain

Corollary 11 There exists a threshold unit market share of HAin the tourism dual-channel supply chain (119904

0) such that when

119904 gt 1199040 the hotelrsquos profit from HA is higher than that from OTA

Keeping the wholesale prices and sales prices unchangedwhen the market share of HA in the tourism dual-channelsupply chain exceeds a certain value 119904

0 the hotelrsquos profit from

HA is higher than that from OTA The result is suitable forthe integrated system Bertrand and Stackelberg games Fromthe perspective of hotelrsquos revenue the hotel should explorethe channel for direct selling actively Also the hotel canstrengthen the promotion of HA channel to improve thecustomerrsquos understanding and preference for theHA channelBut the premise is that the profit growth from the promotioncan compensate for the cost According to the statistical datafrom the hotel price competitiveness analysis report in thefirst half of 2012 we know that the booking cost from directselling channel is about 1 dollar per night but that fromOTAis about 10 dollars per night Booking cost can be reducedby 46 if the direct selling level is doubled Then improvingthe market share of direct selling will greatly reduce the costMore comparisons of different channelrsquos profits in eachmodelcan be found in part of numerical analysis

6 Overbooking

This section extends to consider the overbooking caseRegarding overbooking in the hospitality industry the com-mon practice is that the hotel upgrades the room type ortransfers customers to other hotels nearby that have the samelevel and same type In airline industry if customers aredenied boarding after arriving at the airport the airline will

8 Discrete Dynamics in Nature and Society

provide a free upgrade endorse the ticket or provide com-pensation for the customers according to specific situationCompared to the hotels the airlines cannot transfer cus-tomers to other companies The air ticket alteration will usu-ally disrupt customersrsquo traveling schedule Though the over-booking by airlines has been well studied in the literature ourresearch is new in the hospitality industry by considering theoverbooking withwithout room transfer with the hope thatcertain implications can be enlightened to the hotel man-agers

The hotel wants to increase the occupancy rates toincrease the profits through overbooking However over-booking will lead to the risk that the actual occupancyamount is greater than the number of hotel roomsThereforethe hotel has to provide compensation to travelers who can-not check in that is overbooking cost The greater the num-bers of overbooking the less the probability of room vacancybut at the same time travelers are more likely to be refusedby the hotel Therefore the hotel must balance between thevacancy lost and the overbooking costs We develop a modelto analyze the overbooking choice

In reality the OTA is always a crucial partner of hotelsfor it can attract a large number of customers for hotelsand improve their occupancy rates [36] Spontaneously theOTA plays an increasingly significant role in the distributionsystems of hotels [5 7] By contrast the HA mainly providesa platform for individual guest Compared with individualcustomers hotel pays more attention to the long-term coop-eration relationship with the OTA Therefore in our modelwe assume that when the market demand is greater than thesupply and the hotel does not carry out overbooking the hotelwould give priority to customers who are booking fromOTA

61 Without Room Transfer Here we consider the casewith no room transfer When the actual occupancy amountexceeds the total quantity of rooms the hotel does not arrangeother alternative accommodation for the customers who can-not check in But the hotel must pay the loss of goodwill costSuppose that the overbooking quantity of economy and lux-ury rooms isΔ119862

119871andΔ119862

119867and the overbooking cost is 119888

119871and

119888119867 respectivelyWe discuss economy roomsrsquo overbooking The actual

occupancy can be either of the following two cases (1) when119876119871

lt 119863119871

1+ 119863119871

2le 119876119871+ Δ119862

119871 the reservation amount of

rooms is 1198631198711+ 119863119871

2 so the actual occupancy amount is (119863119871

1+

119863119871

2)(1 minus 120582) (2) when119863

119871

1+ 119863119871

2gt 119876119871+ Δ119862

119871 the reservation

amount is 119876119871+ Δ119862119871 then the actual occupancy amount is

(119876119871+Δ119862119871)(1 minus 120582) Therefore if (119876

119871+Δ119862119871)(1 minus 120582) le 119876

119871 that

is Δ119862119871le 120582119876119871(1 minus 120582) the profit of hotel is

120587119871

11= (1 minus 120582120572) [119901

119871

1(119876119871+ Δ119862119871minus 119863119871

2) + 119908119871119863119871

2] (11)

If (119876119871+ Δ119862119871)(1 minus 120582) ge 119876

119871 that is Δ119862

119871ge 120582119876119871(1 minus 120582)

the economy roomsrsquo actual occupancy amount exceeds theeconomy roomsrsquo number in the hotel so the hotel must paythe overbooking cost then the profit of hotel is

120587119871

12= (1 minus 120582120572) [119901

119871

1(119876119871+ Δ119862119871minus 119863119871

2) + 119908119871119863119871

2]

minus (119901119871

1+ 119888119871) [(119876119871+ Δ119862119871) (1 minus 120582) minus 119876

119871]

(12)

Proposition 12 Without considering roomsrsquo transfer the opti-mal overbooking quantity of economy rooms and luxury roomsis

Δ119862lowast

119894=

120582

1 minus 120582119876119894 119894 = 119871119867 (13)

FromProposition 12 we know that the higher the propor-tion of customer cancellations and no-show is the larger theoptimal overbooking quantity of the hotel will be With theincrease of 120572 the penalty that customers need to pay for theircancellation or no-show decreases Two following extremesituations are considered When 120572 = 1 the hotel will returnall the guarantee fee in case of customersrsquo cancellation or no-showThat is the same as the hotel does not charge customersany guarantee fee when customers book the rooms Undersuch circumstances customers can book rooms for severaldays firstly after they identify a specific itinerary they cancancel the extra rooms for they do not suffer any loss It is nodoubt that such regulation will increase the cancellation andno-show rate On the other hand if 120572 = 1 all the guaranteefee will not be returned after cancellation or no-show In thiscase customers need to reserve a room cautiously If it is notnecessary customers will not choose cancellation or no-showbecause the penalty cost is too high Such policy will reducethe cancellation and no-show rate Spontaneously to someextent 120572 and 120582 are positive correlation When the hotelincreases proportion 120572 it would like to increase the over-booking quantity so as to increase the actual occupancy rateNowadays the time-limited orders are widely used amonghotels Such regulation cannot only reduce customersrsquo lossfor the change of schedule but also help the hotel confirmthe orders so as to handle the overbooking phenomenon inadvance

In addition the risk of overbooking the economy roomsis relatively lower than the luxury rooms Compared toeconomic rooms it is more difficult for the hotel to findalternative luxury rooms to satisfy the customers Naturallyoverbooking cost of luxury room is higher For instance ifeconomy rooms are overbooked the hotel can transfer thecustomers to luxury rooms and the customers are willingto accept By contrast if luxury rooms are overbooked cus-tomers are not willing to accept the adjustment from luxuryrooms to economic rooms This implies that the hotel has topay a higher default costTherefore the hotel should be morecareful to choose the overbooking quantity of luxury rooms

62 With Room Transfer The following discusses the casewith room transfer Firstly when the economy rooms areinsufficient and luxury rooms have a surplus customers cancheck in the hotelrsquos luxury rooms with the price of economyrooms Customers spend the same money and can enjoybetter service so they are willing to accept this adjustmentSecondly when the luxury roomsrsquo actual occupancy amountexceeds the number of luxury rooms in the hotel the hotelusually transfers customers to other hotels nearby that havethe same level and same type because the customers whobook luxury room have a high requirement Customers canenjoy the same service so they are willing to accept this trans-fer However the hotelrsquos credibility in customersrsquo mind will be

Discrete Dynamics in Nature and Society 9

damaged and it must pay the additional costsThirdly if boththe economy rooms and luxury rooms are unable to meetthe demand the hotel usually transfers the customers whocannot check in to other hotels Note that when119863119894

1+119863119894

2gt 119876119894

119894 = 119871119867 if the hotel does not overbook its profit is

120587111

= (1 minus 120582120572) [119901119871

1(119876119871minus 119863119871

2) + 119901119867

1(119876119867minus 119863119867

2)

+ 119908119871119863119871

2+ 119908119867119863119867

2]

(14)

Proposition 13 With room transfer there exists threshold unitoverbooking cost 119888

1198940 such that if 119888

119894lt 1198881198940 then overbooking is

profitable for the hotel where

1198881198940=(1 minus 120582120572) 119901

119894

1

1 minus 120582 119894 = 119871119867 (15)

From Propositions 12 and 13 we conclude that the hotelshould control the overbooking quantity in a certain rangeto prevent lacking of rooms If the overbooking proportionis too large then the hotel may face a loss Only when theoverbooking cost is low the hotel can obtain additional profitOtherwise if the overbooking cost exceeds a certain valuethe hotelrsquos profit would be lower when it carries out over-booking As the market demand increases the supply is closeto saturation and then the overbooking costs will be higherTherefore when the market demand is excessive the hotelshould strictly control the proportion of overbooking Inaddition if the number of hotels that have the same level andtype in the same region is little that is the possibility to trans-fer customer is small then the hotel should lower the propor-tion of overbooking

The proportion of overbooking depends on the propor-tion of customer cancellations andno-showaswell as the totalnumber of hotel rooms so the hotel can analyze the historicaldata to develop an appropriate overbooking proportion so asto maximize the hotelrsquos expected profit

Proposition 14 When the economy rooms and luxury roomsare both overbooked the optimal centralized prices are asfollows 119894 = 119871119867

119901119894lowast

14= 119901119894lowast

1+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

119901119894lowast

24= 119901119894lowast

2+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

(16)

Bertrand and Stackelberg prices are as follows

(119901119894

14)119861lowast

= (119901119894

1)119861lowast

+2119888119894

119906119887119894(119887119894+ 120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

24)119861lowast

= (119901119894

2)119861lowast

+120579119888119894

119906119887119894 (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

14)119878lowast

= (119901119894

1)119878lowast

+119888119894

119906119887119894(2119887119894+ 3120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 21205792]

(119901119894

24)119878lowast

=120579 (119901119894

14)119878lowast

+ (1 minus 119904) 119886119894 + V (120579 + 120573) + 119908119894(119887119894+ 120579)

2 (119887119894+ 120579)

+119888

2 (1 minus 120582120572)

(17)

For the hotel the premise to overbook rooms is that themarket demand is greater than the supply When the hotelfaces the risk of overbooking the equilibrium prices in bothcentralized and decentralized decision-making supply chainwill improve In the busy season in order to reduce the riskof overbooking the hotel would increase the prices and theincrement will increase as the transfer cost increases From(16) and (17) we can know that the increment in centralizeddecision-making model is the greatest and that in Bertrandgame is the smallest

7 Numerical Analysis

In this section we do some numerical experiment to gainmore insights According to the China Hotel Sales Chan-nel Report by I-Research (httpreportiresearchcnreport2013031892shtml) there are 381 of the hotels that aresuitable for high-end travelers and 619 of the hotels thatare suitable for low-end travelersTherefore this part assumesthat the proportion of the economical rooms and the luxuryrooms is 4 6 that is 119886

119871= 06119886 119886

119867= 04119886 Other parameter

settings are made as follows 119886 = 600 119904 = 05 and 119887119871= 06

119887119867= 02 120573 = 120579 = 05 120578 = 004 120572 = 08 120582 = 01 119908

119894= 05119901

119894

1

(119894 = 119871119867) In the following we investigate the impact of V onthe optimal prices and profits

When V = 0 that is the OTA does not offer any servicethen the optimal prices of HA are equal to the prices ofOTA Since 119887

119871gt 120573 gt 119887

119867 then the market of economy

rooms is service-oriented while the market of luxury roomsis price-oriented FromFigure 2 we can know that whenOTAoffers more services OTArsquos optimal price will be increasedaccordingly It is reasonable that if V increases the cost ofOTAwill also definitely increase With the increase of V 119901119871lowast

1will

decline slowly while 119901119867lowast1

will increaseThe OTArsquos profit status becomes better with the improve-

ment of its price But as the V increases the cost of OTA willalso definitely increase When V is equal to 27 then the profitof OTA is the highest If V is larger then the high costs willreduce the profits of OTAWhen V is equal to 34 the profit ofthewhole supply chain is the highest So from the perspectiveof the supply chain V is expected to be 34 rather than 27Similarly for the integrated system the profit of the OTAalso rises first and then declines with the increase of V Aftercalculationwe can get thatwhen V = 27 both120587119861lowast

2and120587119878lowast2will

be the highest From Figures 3 and 4 we know that the OTAwould tend to offer service that valued 27 so as to maximizeits own profit

After calculation we can conclude that when V = 34 then120587119861lowast is highest when V = 35 then 120587

119878lowast is highest (Figure 5)

10 Discrete Dynamics in Nature and Society

0 10 20 30 40 50 60 70 80100

150

200

250

300

350

400

450

Pric

e

pLlowast

1

pLlowast

2

pHlowast

1

pHlowast

2

Value added by OTArsquos services ()

Figure 2 Equilibrium prices in the integrated system

0 10 20 30 40 50 60 70 800

1

2

3

4

5

6

7

Profi

t

times104

120587lowast

1

120587lowast

2

120587lowast

Value added by OTArsquos services ()

Figure 3 Profits in the integrated system

From the perspective of the supply chain theOTA is expectedto offer more services Despite the rising cost of OTA willlower its profit the hotel can lower the wholesale prices tocoordinate the distribution of profits so as to achieve a win-win situation

In the following we focus on the comparison of differentchannelrsquos profit in each model Figure 6 depicts the curves ofthe total profits of the HAOTA channels in the integratedsystem with respect to V Figure 7 draws the curves of the dif-ferent channelsrsquo profits under both Bertrand and Stackelberggame The profit of the HA channel refers to the profit thatthe hotel derived from the HA channelThe profit of the OTA

0 10 20 30 40 50 60125

13

135

14

145

15

155

16

165

Profi

t

times104

120587Blowast

2

120587Slowast

2

Value added by OTArsquos services ()

Figure 4 OTArsquos profits under two games

0 10 20 30 40 50 60 70 8052

53

54

55

56

57

58

59

6

61

62

Profi

t

times104

120587Blowast

2

120587Slowast

2120587lowast

Value added by OTArsquos services ()

Figure 5 The profit comparison

channel involves the OTArsquos profit and the hotelrsquos profit gainedfrom the OTA channel

As shown in Figures 6 and 7 with the increase of V theprofit of the OTA channel will increase first and will thendecrease This indicates that a high level of service by OTAwill be detrimental to the channel profit That is because ahigh level of service will bring a high cost undoubtedly Forthe integrated model and Bertrand game model this disad-vantage is more evident The OTArsquos service can motivate theactual purchase behavior of customers in the OTA channelWhen V is relatively lower the additional profits from OTArsquos

Discrete Dynamics in Nature and Society 11

0 10 20 30 40 50 60 70 8018

2

22

24

26

28

3

32

34

36

38

4

Profi

t

HA channelOTA channel

times104

Value added by OTArsquos services ()

Figure 6 Channel profits in the integrated system

0 10 20 30 40 50 60 70 8005

1

15

2

25

3

35

4

45

Profi

t

HA channel in Bertrand gameOTA channel in Bertrand gameHA channel in Stackelberg gameOTA channel in Stackelberg game

times104

Value added by OTArsquos services ()

Figure 7 Channel profits in two games

service are enough to compensate for the cost In this casethe hotel and the OTA can get more profit from providing theservice However when V is high the additional profits fromOTArsquos service cannot make up for the high cost In such phe-nomenon the OTA should not increase investment in ser-vice

For both integrated model and Bertrand game modelwith the increase of V the profit of the HA channel willdecrease first and will then increase while in the Stackelberggamemodel the profit of theHA channel will always increase

with V With Figure 2 we can know that when OTA providesmore additional services it tends to increase its price Someof the customers will turn to reserve rooms from the HAbecause of the excessively high price in OTA As a result thehotel can gain more profits from the HA channel

8 Conclusion

With the development of e-commerce the providers oftourism products are more inclined to build dual-channelsIn this paper we consider the direct selling channel of HAand the traditional retail channel ofOTA from the perspectiveof tourism supply chain We develop a two-echelon tourismsupply chain model involving one hotel and one OTA wheretheOTAprovides related service Customers will be refundedpartially in case of cancelation or no-show We investigatethe optimal pricing strategies under several common casesThe integrated operation and the decentralized operationbased on Bertrand and Stackelberg games are studied andcorresponding equilibrium pricing policies are obtained

Our findings demonstrate that the hotel plays a crucialrole in optimizing the benefits of supply chain Consideringthe overall profit of the supply chain the hotel should act as aleader in dual-channel supply chain and formulate reasonablewholesale prices to improve the cooperative enthusiasm ofOTA so as to achieve optimization of the whole supplychain A lower wholesale price can help reduce OTArsquos loss ofprofit because of the opening of HA channel In addition weconsider the overbooking of the hotel and obtain the optimaloverbooking quantity We conclude that the hotel can alwaysobtain higher profits when the overbooking proportion iscontrolledwithin a certain range Otherwise if the overbook-ing proportion is too high the hotel can get extra profits onlywhen the overbooking cost is lower than a certain value

The contribution of this paper is that we extend tourismsupply chain to the dual-channel structure in which the hotelopens its direct channel to sell tourism products And theextant literature only refers to the single channel In additionwe realize that customer cancellations andno-showoccur fre-quently in hotel industry Thus we develop the game modelsbased on such phenomenon At last we derive the conditionsunder which the hotel dominant case is profitable for boththe supply chain members Our results can provide hotelsand OTAs with some new managerial insights under thedual-channel environment

This research can be extended in several directions infuture work For example in this paper we assume that allinformation is known to the hotel and OTA However someinformation could be asymmetric (eg see Chen [37]) Thuswe can explore the Bayesian equilibrium under asymmetricinformation settings Secondly the assumption of lineardemand is a limitation of this paperWe can further study thedynamic pricing in tourism dual-channel supply chain

Appendix

A Proof of Corollary 8

First we set (1199011198711)119861lowast

gt (119901119871

1)119878lowast which can be expressed as

12 Discrete Dynamics in Nature and Society

(1 minus 120582120572) (120579119886119871 + 120579119904119886119871+ 2119887119871119904119886119871+ 120579V120573 + 3119908

1198711205792+ 3119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

gt(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(A1)

The above equation can be simplified as

119908119871gt120579 [(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)]

4119887119871 (1 minus 120582120572) (119887119871 + 120579) (119887

119871+ 2120579)

(A2)

So we can get Corollary 8 B Proof of Corollary 9

If (1199011198941)119878lowast

gt (119901119894

1)119861lowast then

(1 minus 120582120572) (120579119886119894 + 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 2119908

1198941205792+ 2119908119894119887119894120579 minus 1205792V minus 2120579119887

119894V) + 119888120579 (119887

119894+ 120579)

minus (1 minus 120582120572) ((119901119894

1)119878lowast

+ (119901119894

1)119861lowast

) [2 (119887119894+ 120579)2minus 1205792] gt 0

120587119878lowast

1minus 120587119861lowast

1=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

2 (119887119871+ 120579)

((119901119871

1)119878lowast

minus (119901119871

1)119861lowast

)

+(1 minus 120582120572) (120579119886119867 + 120579119904119886

119867+ 2119887119867119904119886119867+ 120579V120573 + 2119908

1198671205792+ 2119908119867119887119867120579 minus 1205792V minus 2120579119887

119867V) + 119888120579 (119887

119867+ 120579)

2 (119887119867+ 120579)

((119901119867

1)119878lowast

minus (119901119867

1)119861lowast

)

minus (1 minus 120582120572)2 (119887119871+ 120579)2minus 1205792

2 (119887119871+ 120579)

[((119901119871

1)119878lowast

)2

minus ((119901119871

1)119861lowast

)2

] minus (1 minus 120582120572)2 (119887119867+ 120579)2minus 1205792

2 (119887119867+ 120579)

[((119901119867

1)119878lowast

)2

minus ((119901119867

1)119861lowast

)2

] gt 0

(B1)

If (1199011198711)119878lowast

lt (119901119871

1)119861lowast and (119901

119867

1)119878lowast

lt (119901119867

1)119861lowast we can prove

120587119878lowast

1gt 120587119861lowast

1similarly

From Propositions 3 and 7 with (3) we obtain that

120587119861lowast

2minus 120587119878lowast

2=

120579

4 (119887119871+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119871 + V (120573 + 120579) minus 119908119871(119887119871+ 120579)]

minus 2119888 (119887119871+ 120579) + 120579 (1 minus 120582120572) ((119901

119871

1)119861lowast

+ (119901119871

1)119878lowast

)

sdot ((119901119871

1)119861lowast

minus (119901119871

1)119878lowast

) +120579

4 (119887119867+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119867 + V (120573 + 120579) minus 119908 (119887119867+ 120579)]

minus 2119888 (119887119867+ 120579) + 120579 (1 minus 120582120572) ((119901

119867

1)119861lowast

+ (119901119867

1)119878lowast

)

sdot ((119901119867

1)119861lowast

minus (119901119867

1)119878lowast

)

(B2)

Note that

119863119894

2= [(1 minus 119904) 119886119894 minus 119887

119894119901119894

2] + 120573V + 120579 (119901

119894

1+ V minus 119901

119894

2) gt 0 (B3)

so we show that

2 (1 minus 120582120572) [(1 minus 119904) 119886119894 + V (120573 + 120579) minus 119908119894(119887119894+ 120579)]

minus 2119888 (119887119894+ 120579) + 120579 (1 minus 120582120572) ((119901

119894

1)119861lowast

+ (119901119894

1)119878lowast

)

gt 0

(B4)

Thus we have the following

(1) 120587119861lowast2

gt 120587119878lowast

2 if (1199011198711)119861lowast

gt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

gt (119901119867

1)119878lowast

(2) 120587119861lowast2

= 120587119878lowast

2 if (1199011198711)119861lowast

= (119901119871

1)119878lowast and (119901

119867

1)119861lowast

= (119901119867

1)119878lowast

(3) 120587119861lowast2

lt 120587119878lowast

2 if (1199011198711)119861lowast

lt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

lt (119901119867

1)119878lowast

Combined with Corollary 8 the proposition is proved

Discrete Dynamics in Nature and Society 13

C Proof of Corollary 10

The profit of hotel from the economy rooms is as follows

120587119871

= [(1 minus 120582120572) (119904119886119871 minus 120579V) minus 119888120579] 119901119871

1

+ [(1 minus 120582120572) (119886119871 minus 119904119886119871+ 120573V + 120579V) + 119888 (119887

119871+ 120579)] 119901

119871

2

+ 2120579 (1 minus 120582120572) 119901119871

1119901119871

2minus (1 minus 120582120572) (119887119871 + 120579) (119901

119871

1)2

minus (1 minus 120582120572) (119887119871 + 120579) (119901119871

2)2

minus (119886119871minus 119904119886119871+ 120573V + 120579V) 119888

(C1)

Define (119901119871

1)119861(119878)

= (119860119871

1)119861(119878)

+ (119861119871

1)119861(119878)

119908119871 (1199011198712)119861(119878)

=

(119860119871

2)119861(119878)

+ (119861119871

2)119861(119878)

119908119871 where

(119861119871

1)119861

=3120579 (119887119871+ 120579)

4 (119887119871+ 120579)2minus 1205792

(119861119871

1)119878

=120579 (119887119871+ 120579)

2 (119887119871+ 120579)2minus 1205792

(119861119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119861119871

1)119861(119878)

+1

2

(119860119871

1)119861

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

(119860119871

1)119878

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(119860119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119860119871

1)119861(119878)

+(1 minus 120582120572) [(1 minus 119904) 119886119871 + V (120579 + 120573)] + 119888 (119887

119871+ 120579)

2 (1 minus 120582120572) (119887119871 + 120579)

(C2)

Let 120597120587119871120597119908 = 0 then we get119908lowast

119871 Similarly we can get119908lowast

119867

D Proof of Proposition 12

Let 120587119889minus 120587119903gt 0 then we can get 119904

0 where the profits of hotel

from HA and OTA are as follows

120587119889= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1)

120587119903= (1 minus 120582120572) (119908119871119863

119871

2+ 119908119867119863119867

2)

(D1)

E Proof of Corollary 11

If Δ119862119871le 120582(1 minus 120582)119876

119871 then the profit of hotel is 120587119871

11 The

derivative of 12058711987111(Δ119862119871) is 120597120587119871

11120597Δ119862119871= (1 minus 120582120572)119901

119871

1gt 0 So

with the increase of Δ119862119871 12058711987111

will increase When Δ119862119871

=

120582(1 minus 120582)119876119871 12058711987111

is maximized If Δ119862119871

ge 120582(1 minus 120582)119876119871

then the profit of hotel is 12058711987112 The derivative of 120587119871

12(Δ119862119871) is

120597120587119871

12120597Δ119862119871= (1 minus 120582120572)119901

119871

1minus (1 minus 120582)(119901

119871

1+ 119888119871) lt 0 So with the

increase of Δ119862119871 12058711987111will decline When Δ119862

119871= 120582(1 minus 120582)119876

119871

120587119871

11is maximizedSimilarly we can get Δ119862lowast

119867

F Proof of Proposition 13

Assume that the overbooking proportion is 120574119871and 120574119867

(1) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) le 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

That is

120574119867lt

120582

1 minus 120582lt 120574119871

le120582119876119871+ 119876119867[1 minus (1 minus 120582) (1 + 120574

119867)]

(1 minus 120582)119876119871

(F1)

Thus the hotel would like to overbook to get more profitrather than room vacancy

(2) Consider (1198631198711+119863119871

2)(1minus120582) lt 119876

119871and (119863119867

1+119863119867

2)(1minus120582) gt

119876119867That is 120574

119871lt 120582(1 minus 120582) lt 120574

119867 Then the profit of hotel is

120587112

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F2)

Thenwhen 119888119867119906

lt (1minus120582120572)119901119867

1(1minus120582) that is120587

112minus120587111

gt 0the hotel would carry out overbooking

(3) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

14 Discrete Dynamics in Nature and Society

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867lt 120582(1 minus 120582) Then the profit of hotel is

120587113

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2+ 119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876]

(F3)

Then when 119888119871

119906lt (1 minus 120582120572)119901

119871

1(1 minus 120582) 120587

113minus120587111

gt 0 thusthe hotel would carry out overbooking

(4) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) gt 119876

119867

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867gt (120582119876

119867+ 119876119871[1 minus (1 minus 120582)(1 + 120574

119871)])(1 minus 120582)119876

119867

Then the profit of hotel is as follows

120587114

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2) (1 minus 120582) minus 119876

119871]

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F4)

Then when 119888119871119906lt (1minus120582120572)119901

119871

1(1minus120582) and 119888119867

119906lt (1minus120582120572)119901

119867

1

(1 minus 120582) 120587114

minus 120587111

gt 0 overbooking is preferred

G Threshold Values

Threshold values are as follows

1198711= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 3119908

1198941205792+ 3119908119894119887119894120579

minus 1205792V minus 2120579119887

119894V

1198712= 2119886119894(119887119894+ 120579) minus 119904119886

119894(2119887119894+ 120579) + 120579

2119908119894+ 2 (120579 + 120573) (119887

119894

+ 120579) V + 2119908119894(119887119894+ 120579)2minus 1205792V

1198713= 4120579V119887

119894120573 minus 120579119904119886

119894119887119894+ 2V1205731198872

119894+ 31198861198941205792+ 4119886119894119887119894120579

minus 21198861198941198872

119894119904 + 3120579

2V120573 + 1205792V119887119894+ 2120579V1198872

119894+ 21198861198941198872

119894

1198714= 3119886119894119887119894120579 + 3120579

2V120573 minus 2120579V1198872119894minus 1205792V119887119894+ 31198861198941205792

+ 21198861198941198872

119894119904 + 119886119887

119894119904120579 + 3119887

119894120573V120579

1198715= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 minus 120579

2V minus 2120579119887119894V

1198661= [(1 minus 120582120572) (119904119886119894 minus 120579V) minus 119888120579] (119861

119894

1)119861(119878)

+ [(1 minus 120582120572) (119886119894 minus 119904119886119894+ 120573V + 120579V) + 119888 (119887

119894+ 120579)]

sdot (119861119894

1)119861(119878)

+ 2120579 (1 minus 120582120572) [(119860119894

1)119861(119878)

(119861119894

2)119861(119878)

+ (119861119894

1)119861(119878)

(119860119894

2)119861(119878)

] minus 2 (1 minus 120582120572) (119887119894 + 120579)

sdot [(119860119894

1)119861(119878)

(119861119894

1)119861(119878)

+ (119860119894

2)119861(119878)

(119861119894

2)119861(119878)

]

1198662= 2 (1 minus 120582120572)

sdot (119887119894+ 120579) [((119861

119894

1)119861(119878)

)

2

+ ((119861119894

2)119861(119878)

)

2

]

minus 2120579 (119861119894

1)119861(119878)

(119861119894

2)119861(119878)

1199040= ((119887119871+ 120579) (119901

119871

1)2

+ (119887119867+ 120579) (119901

119867

1)2

+ 120579119908119871(119901119871

1minus 119901119871

2) + 120579119908

119867(119901119867

1minus 119901119867

2)

+ 120579V (1199011198711+ 119901119867

1) + (119908

119871+ 119908119867) (120573 + 120579) V

+ 119908119871(119886119871minus 119887119871119901119871

2) + 119908119867(119886119867minus 119887119867119901119867

2)

minus 120579 (119901119871

1119901119871

2+ 119901119867

1119901119867

2)) (119886119871(119901119871

1+ 119908119871)

+ 119886119867(119901119867

1+ 119908119867))minus1

(G1)

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The authors thank associate editor and anonymous refereesfor their numerous constructive comments and encourage-ment that have improved their paper greatly The work waspartly supported by (i) the National Natural Science Founda-tion ofChina (71201083 71572058 and 71571100) (ii) the Fun-damental Research Funds for the Central Universities SCUT(2015ZZ057) (iii) Jiangsu Province Science Foundation forYouths (BK2012379) and (iv) the Fundamental ResearchFunds for the Central Universities (NS2015076)

References

[1] J Li W N Zhang H Xu and J Jiang ldquoDynamic competitionand cooperation of road infrastructure investment of multipletourism destinations a case Study of Xidi and Hongcun WorldCulturalHeritagerdquoDiscreteDynamics inNature and Society vol2015 Article ID 962028 10 pages 2015

[2] T Paksoy EOzceylan andG-WWeber ldquoProfit oriented supplychain network optimizationrdquoCentral European Journal of Oper-ations Research vol 21 no 2 pp 455ndash478 2013

[3] X Zhang H Song and G Q Huang ldquoTourism supply chainmanagement a new research agendardquo Tourism Managementvol 30 no 3 pp 345ndash358 2009

[4] Z Yang and J Cai ldquoDo regional factors matter Determinantsof hotel industry performance in Chinardquo TourismManagementvol 52 pp 242ndash253 2016

[5] B Pan L Zhang and R Law ldquoThe complex matter of onlinehotel choicerdquoCornell Hospitality Quarterly vol 54 no 1 pp 74ndash83 2013

[6] L Ling X Guo and C Yang ldquoOpening the online marketplacean examination of hotel pricing and travel agency on-line

Discrete Dynamics in Nature and Society 15

distribution of roomsrdquo Tourism Management vol 45 pp 234ndash243 2014

[7] L Ling Y Dong X Guo and L Liang ldquoAvailability man-agement of hotel rooms under cooperation with online travelagenciesrdquo International Journal of Hospitality Management vol50 pp 145ndash152 2015

[8] J N K Liu andE Y Zhang ldquoAn investigation of factors affectingcustomer selection of online hotel booking channelsrdquo Interna-tional Journal of Hospitality Management vol 39 pp 71ndash832014

[9] L Fox ldquoFour Seasons Unveils $18 Million Website as LuxuryTravel Growsrdquo 2012 httpwwwtnoozcomarticlefour-sea-sons-unveils-18-million-dollar-website-as-luxury-travel-grows

[10] C-M Chen and Y-C Lin ldquoThe influence of uncertain demandon hotel capacityrdquo International Journal of Hospitality Manage-ment vol 34 no 1 pp 462ndash465 2013

[11] S Yang G Q Huang H Song and L Liang ldquoGame-theoreticapproach to competition dynamics in tourism supply chainsrdquoJournal of Travel Research vol 47 no 4 pp 425ndash439 2009

[12] G Q Huang H Song and X Zhang ldquoA comparative analysis ofquantity and price competitions in tourism supply chain net-works for package holidaysrdquo Service Industries Journal vol 30no 10 pp 1593ndash1606 2010

[13] Y Huang H Song G Q Huang and J Lou ldquoA comparativestudy of tourism supply chains with quantity competitionrdquoJournal of Travel Research vol 51 no 6 pp 717ndash729 2012

[14] H K Lee and Y Fernando ldquoThe antecedents and outcomes ofthe medical tourism supply chainrdquo Tourism Management vol46 pp 148ndash157 2015

[15] W-Y K Chiang D Chhajed and J D Hess ldquoDirect marketingindirect profits a strategic analysis of dual-channel supply-chain designrdquoManagement Science vol 49 no 1 pp 1ndash20 2003

[16] A A Tsay and N Agrawal ldquoChannel conflict and coordinationin the E-commerce agerdquo Production and Operations Manage-ment vol 13 no 1 pp 93ndash110 2004

[17] Q-H Li and B Li ldquoDual-channel supply chain equilibriumproblems regarding retail services and fairness concernsrdquoApplied Mathematical Modelling 2016

[18] S Panda N M Modak S S Sana and M Basu ldquoPricingand replenishment policies in dual-channel supply chain undercontinuous unit cost decreaserdquo Applied Mathematics and Com-putation vol 256 pp 913ndash929 2015

[19] Y Liu C Ding C Fan and X Chen ldquoPricing decision underdual-channel structure considering fairness and free-ridingbehaviorrdquo Discrete Dynamics in Nature and Society vol 2014Article ID 536576 10 pages 2014

[20] J Chen H Zhang and Y Sun ldquoImplementing coordinationcontracts in a manufacturer Stackelberg dual-channel supplychainrdquo Omega vol 40 no 5 pp 571ndash583 2012

[21] Q Ding C Dong and Z Pan ldquoA hierarchical pricing decisionprocess on a dual-channel problem with one manufacturer andone retailerrdquo International Journal of Production Economics vol175 pp 197ndash212 2016

[22] B Rodriguez and G Aydin ldquoPricing and assortment decisionsfor a manufacturer selling through dual channelsrdquo EuropeanJournal of Operational Research vol 242 no 3 pp 901ndash9092015

[23] T Lockyer ldquoThe perceived importance of price as one hotelselection dimensionrdquo Tourism Management vol 26 no 4 pp529ndash537 2005

[24] C-M Chen H-W Yang E Y Li and C-C Liu ldquoHow doeshotel pricing influence guest satisfaction by the moderatinginfluence of room occupancyrdquo International Journal of Hospi-tality Management vol 49 pp 136ndash138 2015

[25] J-M Espinet M Fluvia R Rigall-I-Torrent and A Salo ldquoHotelcharacteristics and seasonality in prices an analysis usingSpanish tour operatorsrsquo brochuresrdquo Tourism Economics vol 18no 4 pp 749ndash767 2012

[26] C Juaneda J M Raya and F Sastre ldquoPricing the time and loca-tion of a stay at a hotel or apartmentrdquo Tourism Economics vol17 no 2 pp 321ndash338 2011

[27] G Abrate G Fraquelli and G Viglia ldquoDynamic pricing strate-gies evidence from European hotelsrdquo International Journal ofHospitality Management vol 31 no 1 pp 160ndash168 2012

[28] D Q Yao and J J Liu ldquoCompetitive pricing of mixed retail ande-tail distribution channelsrdquo Omega vol 33 no 3 pp 235ndash2472005

[29] J Zhao and L Wang ldquoPricing and retail service decisionsin fuzzy uncertainty environmentsrdquo Applied Mathematics andComputation vol 250 pp 580ndash592 2015

[30] A A Tsay and N Agrawal ldquoChannel dynamics under priceand service competitionrdquo Manufacturing amp Service OperationsManagement vol 2 no 4 pp 372ndash391 2000

[31] S C Choi ldquoPrice competition in a duopoly common retailerchannelrdquo Journal of Retailing vol 72 no 2 pp 117ndash134 1996

[32] Y Bakos andE Brynjolfsson ldquoBundling and competition on theinternetrdquoMarketing Science vol 19 no 1 pp 63ndash82 2000

[33] H Song J H Kim and S Yang ldquoConfidence intervals fortourism demand elasticityrdquo Annals of Tourism Research vol 37no 2 pp 377ndash396 2010

[34] DMHanssens L J Parsons andR L SchultzMarket ResponseModels Econometric and Time Series Analysis Kluwer Aca-demic Publishers Boston Mass USA 2nd edition 2001

[35] H Kurata D-Q Yao and J J Liu ldquoPricing policies under directvs indirect channel competition and national vs store brandcompetitionrdquo European Journal of Operational Research vol180 no 1 pp 262ndash281 2007

[36] R Law and C Cheung ldquoA study of the perceived importance ofthe overall website quality of different classes of hotelsrdquo Inter-national Journal of Hospitality Management vol 25 no 3 pp525ndash531 2006

[37] K B Chen ldquoProcurement strategies and coordination mecha-nism of the supply chain with one manufacturer and multiplesuppliersrdquo International Journal of Production Economics vol138 no 1 pp 125ndash135 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Discrete Dynamics in Nature and Society

From Proposition 3 in the Bertrand model the equilib-rium prices for hotel and OTA are both affected by 120572 and 120582With the increase of 120572 or 120582 both (119901

119894

1)119861lowast and (119901

119894

2)119861lowast will be

higher In otherwords with higher uncertainty of roomoccu-pancy the hotel and OTA tend to increase prices to protecttheir own profits

Denote 1198881= (1 minus 120582120572)(2119887

119871+ 120579 minus 120573)(119887

119871+ 120579) and 119888

2= (1 minus

120582120572)(2119887119867+ 120579 minus 120573)(119887

119867+ 120579) then 119888

1gt 1198882

Corollary 4 (1199011198712)119861lowast and (119901

119867

2)119861lowast are increasing in V (119901119871

1)119861lowast

and (119901119867

1)119861lowast have the following relationships with respect to

OTArsquos service

(1) if 1198881015840(V) gt 1198881 then 120597(119901

119871

1)119861lowast120597V gt 0 120597(119901119867

1)119861lowast120597V gt 0

(2) if 1198881gt 1198881015840(V) gt 119888

2 then 120597(119901

119871

1)119861lowast120597V lt 0 120597(119901119867

1)119861lowast120597V gt

0(3) if 1198881015840(V) lt 119888

2 then 120597(119901

119871

1)119861lowast120597V lt 0 120597(119901119867

1)119861lowast120597V lt 0

From Corollary 4 when OTA offers more effective ser-vices its optimal prices will increase due to the incrementin the cost Marginal cost measures the input costs and theoutput value per unit If the marginal cost is greater than1198881 then the costs of OTA to provide additional services are

higher So the equilibrium prices of HA will increase as thevalue added by OTArsquos services increases When the marginalcost is between 119888

1and 1198882 HArsquos equilibrium price of economy

rooms and the value added by OTArsquos service have a negativecorrelation but HArsquos equilibrium price of luxury roomswould increase with the increment of V In addition when themarginal cost is less than 119888

2 the costs of OTA to provide addi-

tional service are lower And the equilibriumprices ofHAwilldecrease when V increases

Corollary 5 There exist threshold unit wholesale prices 1199080119894

1199081

119894(119894 = 119871119867) such that

(1) (1199011198941)lowastlt (119901119894

1)119861lowast if 119908

119894gt 1199080

119894 (1199011198941)lowast= (119901119894

1)119861lowast if 119908

119894= 1199080

119894

(119901119894

1)lowastgt (119901119894

1)119861lowast if 119908

119894lt 1199080

119894

(2) (1199011198942)lowastlt (119901119894

2)119861lowast if 119908

119894gt 1199081

119894 (1199011198942)lowast= (119901119894

2)119861lowast if 119908

119894= 1199081

119894

(119901119894

2)lowastgt (119901119894

2)119861lowast if 119908

119894lt 1199081

119894

where

1199080

119894=

1198713

6119887119894(119887119894+ 120579) (119887

119894+ 2120579)

minus119888

3 (1 minus 120582120572)

1199081

119894=

120579 [(1 minus 120582120572) 1198714 minus 119888119887119894120579 (119887119894+ 2120579)]

2119887119894 (1 minus 120582120572) (119887119894 + 2120579) (31205792 + 21198872

119894+ 2119887119894120579)

(7)

FromProposition 1 it is easy to know that the equilibriumprices in the integrated system are not affected by the whole-sale prices However from Proposition 3 in the Bertrandmodel there is a positive correlation between the equilibriumprices and the wholesale prices Corollary 5 shows that theequilibrium price of HA in the Bertrand game is higherthan that in the integrated system if the wholesale price isgreater than a certain critical point (1199080

119894) Additionally if the

wholesale price is greater than1199081119894 then the equilibrium price

of OTA in Bertrand model will be higher than that in theintegrated model

Corollary 6 There exists a threshold unit wholesale price1199082

119894(119894 = 119871119867) such that if119908

119894gt 1199082

119894 then119863lowast

119894gt 119863119861lowast

119894(119894 = 119871119867)

where

1199082

119894=120579 [(1 minus 120582120572) (V120573 + 119886

119894) minus 119887119894119888]

2119887119894 (1 minus 120582120572) (119887119894 + 2120579)

(8)

Corollary 6 shows that when thewholesale price is greaterthan 119908

2

119894 the high price will lead to a lower demand in the

Bertrand game That is the reservation amount of Bertrandmodel is less than that in the integrated model The highersale price in OTA results from the higher wholesale priceThus the above result is reasonable because travelers are pricesensitive especially for leisure travelers the increase of pricewill bring the decline of reservation amount When the rela-tionship between the hotel and OTA is modeled as a Stackel-berg game the hotel canmotivate customers to reserve roomsthrough a reasonable wholesale price If the wholesale price isgreater than the threshold the sales volume in the centralizedcase is lower than that in the Bertrand case

52 Stackelberg Game In a Stackelberg game the procedureis as follows keeping thewholesale price unchanged the hotel(as the leader) announces HArsquos prices 119901119871

1and 119901119867

1of two types

of rooms respectively in order to maximize its profit 1205871 In

response to HArsquos prices OTA (as the follower) determinesprices 119901

119871

2and 119901

119867

2to maximize its profit 120587

2 Let (119901

119894

1)119878

(119901119894

2)119878(119894 = 119871119867) denote respectively HArsquos and OTArsquos prices

under a Stackelberg game

Proposition 7 The optimal prices are (119901119894

1)119878lowast (119901119894

2)119878lowast

(119894 =

119871119867) and there exists a threshold unit wholesale price 1199083119894(119894 =

119871119867) such that if 119908119894gt 1199083

119894 then (119901

119894

1)lowastlt (119901119894

1)119878lowast where

(119901119894

1)119878lowast

=(1 minus 120582120572) (1198711 minus 119908

1198941205792minus 119908119894119887119894120579) + 119888120579 (119887

119894+ 120579)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 21205792]

(119901119894

2)119878lowast

=120579 (119901119894

1)119878lowast

+ (1 minus 119904) 119886119894 + V (120579 + 120573) + 119908119894(119887119894+ 120579)

2 (119887119894+ 120579)

+119888

2 (1 minus 120582120572)

1199083

119894

=119887119894V120573 + 119886119887

119894+ 120579V119887119894+ 119886119894120579 + 120579V120573 minus 119886

119894119887119894119904

2119887119894(119887119894+ 2120579)

minus119888

2 (1 minus 120582120572)

(9)

Similar to the Bertrand competition the equilibriumprices in Stackelberg game will increase with the increase of

Discrete Dynamics in Nature and Society 7

the return expense proportion (120572) or the cancellations andno-show proportion (120582)

From Proposition 7 we can see that the Stackelbergmodel is similar to the Bertrand model that the equilibriumprices would increase with the increase of wholesale pricesFurthermore when thewholesale price is greater than1199083

119894 the

equilibrium price of HA in Stackelberg model will be higherthan that in the integrated model

In the Stackelberg game if OTA offers more effective ser-vices the equilibrium prices of OTA would increase accord-ingly The relationship between the Stackelberg equilibriumprices and V is similar to that in the Bertrand model

53 Contrastive Analysis of Bertrand and Stackelberg GamesBased on the equilibrium prices obtained in the previoussection we in this section compare the equilibriumprices andoptimal profit under Bertrand and Stackelberg games

Corollary 8 There exists a threshold unit wholesale price1199084

119894(119894 = 119871119867) such that

(1) (1199011198941)119861lowast

gt (119901119894

1)119878lowast and (119901119894

2)119861lowast

gt (119901119894

2)119878lowast if 119908

119894gt 1199084

119894

(2) (1199011198941)119861lowast

= (119901119894

1)119878lowast and (119901119894

2)119861lowast

= (119901119894

2)119878lowast if 119908

119894= 1199084

119894

(3) (1199011198941)119861lowast

lt (119901119894

1)119878lowast and (119901119894

2)119861lowast

lt (119901119894

2)119878lowast if 119908

119894lt 1199084

119894

where

1199084

119894=

120579 [(1 minus 120582120572) 1198715 + 119888120579 (119887119894+ 120579)]

4119887119894 (1 minus 120582120572) (119887119894 + 120579) (119887

119894+ 2120579)

(10)

Corollary 8 compares the equilibrium prices under theBertrand and Stackelberg game with respect to the wholesaleprice It shows that if the wholesale price is greater than1199084

119894 the pricing equilibrium under the Bertrand is higher

than that under the Stackelberg game Conversely the pricingequilibrium is lower if the wholesale price is less than 119908

4

119894

In the decentralized case both the manufacturer and theretailer want to maximize their profit A high wholesale pricecould be passed on to customersTherefore the above resultsexist In addition how to share the profit between the manu-facturer and the retailer depends on their bargaining powers

Corollary 9 If 119908119894

= 1199084

119894(119894 = 119871119867) then 120587

119878lowast

1gt 120587119861lowast

1 OTArsquos

profit has the following relationship with respect to 1199084119894

(1) 120587119861lowast2

gt 120587119878lowast

2if 119908119871gt 1199084

119871and 119908

119867gt 1199084

119867

(2) 120587119861lowast2

= 120587119878lowast

2if 119908119871= 1199084

119871and 119908

119867= 1199084

119867

(3) 120587119861lowast2

lt 120587119878lowast

2if 119908119871lt 1199084

119871and 119908

119867lt 1199084

119867

Thehotel is the leader in Stackelberg game and can alwaysbenefit from it except for the critical point1199084

119894 Comparedwith

the Bertrand game the hotel can get higher profits in Stackel-berg gamewhen the wholesale price is not equal to1199084

119894There-

fore in decentralized decision-making model the hotel willbe more inclined to be the price leader in order to ensure thatit can achieve higher profits

Corollary 9 indicates that the Stackelberg model is supe-rior to the Bertrand model when the wholesale price is less

than the critical point1199084119894 Not only the hotel but alsoOTA can

gain more profit from the Stackelberg game Though OTA isa follower in Stackelberg game the profit will not be reducedbecause the lower wholesale prices can compensate for theloss of profit caused by the opening of HA channel Conse-quently the hotel should play the role of the price leader inthe supply chain and develop reasonable wholesale prices toachieve optimization of the whole supply chain profit whileoptimizing its own profit

Corollary 10 Under either Bertrand or Stackelberg equi-librium channel prices there exists optimal wholesale price119908lowast

119894(119894 = 119871119867) that maximizes the total equilibrium channel

profit where 119908lowast119894= 11986611198662

According to Corollary 10 there exists optimal wholesaleprice 119908

lowast

119894(119894 = 119871119867) that maximizes the total equilibrium

channel profit under either Bertrand or Stackelberg gameThe optimal wholesale price will optimize the decentralizeddecision-making supply chainMeanwhile both the hotel andtheOTA can benefit from the optimal wholesale priceThere-fore the reasonable wholesale price can help promotemutualcooperation and communication between the supply chainmembers

54 Contrastive Analysis of Two Channels in the Supply Chain

Corollary 11 There exists a threshold unit market share of HAin the tourism dual-channel supply chain (119904

0) such that when

119904 gt 1199040 the hotelrsquos profit from HA is higher than that from OTA

Keeping the wholesale prices and sales prices unchangedwhen the market share of HA in the tourism dual-channelsupply chain exceeds a certain value 119904

0 the hotelrsquos profit from

HA is higher than that from OTA The result is suitable forthe integrated system Bertrand and Stackelberg games Fromthe perspective of hotelrsquos revenue the hotel should explorethe channel for direct selling actively Also the hotel canstrengthen the promotion of HA channel to improve thecustomerrsquos understanding and preference for theHA channelBut the premise is that the profit growth from the promotioncan compensate for the cost According to the statistical datafrom the hotel price competitiveness analysis report in thefirst half of 2012 we know that the booking cost from directselling channel is about 1 dollar per night but that fromOTAis about 10 dollars per night Booking cost can be reducedby 46 if the direct selling level is doubled Then improvingthe market share of direct selling will greatly reduce the costMore comparisons of different channelrsquos profits in eachmodelcan be found in part of numerical analysis

6 Overbooking

This section extends to consider the overbooking caseRegarding overbooking in the hospitality industry the com-mon practice is that the hotel upgrades the room type ortransfers customers to other hotels nearby that have the samelevel and same type In airline industry if customers aredenied boarding after arriving at the airport the airline will

8 Discrete Dynamics in Nature and Society

provide a free upgrade endorse the ticket or provide com-pensation for the customers according to specific situationCompared to the hotels the airlines cannot transfer cus-tomers to other companies The air ticket alteration will usu-ally disrupt customersrsquo traveling schedule Though the over-booking by airlines has been well studied in the literature ourresearch is new in the hospitality industry by considering theoverbooking withwithout room transfer with the hope thatcertain implications can be enlightened to the hotel man-agers

The hotel wants to increase the occupancy rates toincrease the profits through overbooking However over-booking will lead to the risk that the actual occupancyamount is greater than the number of hotel roomsThereforethe hotel has to provide compensation to travelers who can-not check in that is overbooking cost The greater the num-bers of overbooking the less the probability of room vacancybut at the same time travelers are more likely to be refusedby the hotel Therefore the hotel must balance between thevacancy lost and the overbooking costs We develop a modelto analyze the overbooking choice

In reality the OTA is always a crucial partner of hotelsfor it can attract a large number of customers for hotelsand improve their occupancy rates [36] Spontaneously theOTA plays an increasingly significant role in the distributionsystems of hotels [5 7] By contrast the HA mainly providesa platform for individual guest Compared with individualcustomers hotel pays more attention to the long-term coop-eration relationship with the OTA Therefore in our modelwe assume that when the market demand is greater than thesupply and the hotel does not carry out overbooking the hotelwould give priority to customers who are booking fromOTA

61 Without Room Transfer Here we consider the casewith no room transfer When the actual occupancy amountexceeds the total quantity of rooms the hotel does not arrangeother alternative accommodation for the customers who can-not check in But the hotel must pay the loss of goodwill costSuppose that the overbooking quantity of economy and lux-ury rooms isΔ119862

119871andΔ119862

119867and the overbooking cost is 119888

119871and

119888119867 respectivelyWe discuss economy roomsrsquo overbooking The actual

occupancy can be either of the following two cases (1) when119876119871

lt 119863119871

1+ 119863119871

2le 119876119871+ Δ119862

119871 the reservation amount of

rooms is 1198631198711+ 119863119871

2 so the actual occupancy amount is (119863119871

1+

119863119871

2)(1 minus 120582) (2) when119863

119871

1+ 119863119871

2gt 119876119871+ Δ119862

119871 the reservation

amount is 119876119871+ Δ119862119871 then the actual occupancy amount is

(119876119871+Δ119862119871)(1 minus 120582) Therefore if (119876

119871+Δ119862119871)(1 minus 120582) le 119876

119871 that

is Δ119862119871le 120582119876119871(1 minus 120582) the profit of hotel is

120587119871

11= (1 minus 120582120572) [119901

119871

1(119876119871+ Δ119862119871minus 119863119871

2) + 119908119871119863119871

2] (11)

If (119876119871+ Δ119862119871)(1 minus 120582) ge 119876

119871 that is Δ119862

119871ge 120582119876119871(1 minus 120582)

the economy roomsrsquo actual occupancy amount exceeds theeconomy roomsrsquo number in the hotel so the hotel must paythe overbooking cost then the profit of hotel is

120587119871

12= (1 minus 120582120572) [119901

119871

1(119876119871+ Δ119862119871minus 119863119871

2) + 119908119871119863119871

2]

minus (119901119871

1+ 119888119871) [(119876119871+ Δ119862119871) (1 minus 120582) minus 119876

119871]

(12)

Proposition 12 Without considering roomsrsquo transfer the opti-mal overbooking quantity of economy rooms and luxury roomsis

Δ119862lowast

119894=

120582

1 minus 120582119876119894 119894 = 119871119867 (13)

FromProposition 12 we know that the higher the propor-tion of customer cancellations and no-show is the larger theoptimal overbooking quantity of the hotel will be With theincrease of 120572 the penalty that customers need to pay for theircancellation or no-show decreases Two following extremesituations are considered When 120572 = 1 the hotel will returnall the guarantee fee in case of customersrsquo cancellation or no-showThat is the same as the hotel does not charge customersany guarantee fee when customers book the rooms Undersuch circumstances customers can book rooms for severaldays firstly after they identify a specific itinerary they cancancel the extra rooms for they do not suffer any loss It is nodoubt that such regulation will increase the cancellation andno-show rate On the other hand if 120572 = 1 all the guaranteefee will not be returned after cancellation or no-show In thiscase customers need to reserve a room cautiously If it is notnecessary customers will not choose cancellation or no-showbecause the penalty cost is too high Such policy will reducethe cancellation and no-show rate Spontaneously to someextent 120572 and 120582 are positive correlation When the hotelincreases proportion 120572 it would like to increase the over-booking quantity so as to increase the actual occupancy rateNowadays the time-limited orders are widely used amonghotels Such regulation cannot only reduce customersrsquo lossfor the change of schedule but also help the hotel confirmthe orders so as to handle the overbooking phenomenon inadvance

In addition the risk of overbooking the economy roomsis relatively lower than the luxury rooms Compared toeconomic rooms it is more difficult for the hotel to findalternative luxury rooms to satisfy the customers Naturallyoverbooking cost of luxury room is higher For instance ifeconomy rooms are overbooked the hotel can transfer thecustomers to luxury rooms and the customers are willingto accept By contrast if luxury rooms are overbooked cus-tomers are not willing to accept the adjustment from luxuryrooms to economic rooms This implies that the hotel has topay a higher default costTherefore the hotel should be morecareful to choose the overbooking quantity of luxury rooms

62 With Room Transfer The following discusses the casewith room transfer Firstly when the economy rooms areinsufficient and luxury rooms have a surplus customers cancheck in the hotelrsquos luxury rooms with the price of economyrooms Customers spend the same money and can enjoybetter service so they are willing to accept this adjustmentSecondly when the luxury roomsrsquo actual occupancy amountexceeds the number of luxury rooms in the hotel the hotelusually transfers customers to other hotels nearby that havethe same level and same type because the customers whobook luxury room have a high requirement Customers canenjoy the same service so they are willing to accept this trans-fer However the hotelrsquos credibility in customersrsquo mind will be

Discrete Dynamics in Nature and Society 9

damaged and it must pay the additional costsThirdly if boththe economy rooms and luxury rooms are unable to meetthe demand the hotel usually transfers the customers whocannot check in to other hotels Note that when119863119894

1+119863119894

2gt 119876119894

119894 = 119871119867 if the hotel does not overbook its profit is

120587111

= (1 minus 120582120572) [119901119871

1(119876119871minus 119863119871

2) + 119901119867

1(119876119867minus 119863119867

2)

+ 119908119871119863119871

2+ 119908119867119863119867

2]

(14)

Proposition 13 With room transfer there exists threshold unitoverbooking cost 119888

1198940 such that if 119888

119894lt 1198881198940 then overbooking is

profitable for the hotel where

1198881198940=(1 minus 120582120572) 119901

119894

1

1 minus 120582 119894 = 119871119867 (15)

From Propositions 12 and 13 we conclude that the hotelshould control the overbooking quantity in a certain rangeto prevent lacking of rooms If the overbooking proportionis too large then the hotel may face a loss Only when theoverbooking cost is low the hotel can obtain additional profitOtherwise if the overbooking cost exceeds a certain valuethe hotelrsquos profit would be lower when it carries out over-booking As the market demand increases the supply is closeto saturation and then the overbooking costs will be higherTherefore when the market demand is excessive the hotelshould strictly control the proportion of overbooking Inaddition if the number of hotels that have the same level andtype in the same region is little that is the possibility to trans-fer customer is small then the hotel should lower the propor-tion of overbooking

The proportion of overbooking depends on the propor-tion of customer cancellations andno-showaswell as the totalnumber of hotel rooms so the hotel can analyze the historicaldata to develop an appropriate overbooking proportion so asto maximize the hotelrsquos expected profit

Proposition 14 When the economy rooms and luxury roomsare both overbooked the optimal centralized prices are asfollows 119894 = 119871119867

119901119894lowast

14= 119901119894lowast

1+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

119901119894lowast

24= 119901119894lowast

2+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

(16)

Bertrand and Stackelberg prices are as follows

(119901119894

14)119861lowast

= (119901119894

1)119861lowast

+2119888119894

119906119887119894(119887119894+ 120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

24)119861lowast

= (119901119894

2)119861lowast

+120579119888119894

119906119887119894 (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

14)119878lowast

= (119901119894

1)119878lowast

+119888119894

119906119887119894(2119887119894+ 3120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 21205792]

(119901119894

24)119878lowast

=120579 (119901119894

14)119878lowast

+ (1 minus 119904) 119886119894 + V (120579 + 120573) + 119908119894(119887119894+ 120579)

2 (119887119894+ 120579)

+119888

2 (1 minus 120582120572)

(17)

For the hotel the premise to overbook rooms is that themarket demand is greater than the supply When the hotelfaces the risk of overbooking the equilibrium prices in bothcentralized and decentralized decision-making supply chainwill improve In the busy season in order to reduce the riskof overbooking the hotel would increase the prices and theincrement will increase as the transfer cost increases From(16) and (17) we can know that the increment in centralizeddecision-making model is the greatest and that in Bertrandgame is the smallest

7 Numerical Analysis

In this section we do some numerical experiment to gainmore insights According to the China Hotel Sales Chan-nel Report by I-Research (httpreportiresearchcnreport2013031892shtml) there are 381 of the hotels that aresuitable for high-end travelers and 619 of the hotels thatare suitable for low-end travelersTherefore this part assumesthat the proportion of the economical rooms and the luxuryrooms is 4 6 that is 119886

119871= 06119886 119886

119867= 04119886 Other parameter

settings are made as follows 119886 = 600 119904 = 05 and 119887119871= 06

119887119867= 02 120573 = 120579 = 05 120578 = 004 120572 = 08 120582 = 01 119908

119894= 05119901

119894

1

(119894 = 119871119867) In the following we investigate the impact of V onthe optimal prices and profits

When V = 0 that is the OTA does not offer any servicethen the optimal prices of HA are equal to the prices ofOTA Since 119887

119871gt 120573 gt 119887

119867 then the market of economy

rooms is service-oriented while the market of luxury roomsis price-oriented FromFigure 2 we can know that whenOTAoffers more services OTArsquos optimal price will be increasedaccordingly It is reasonable that if V increases the cost ofOTAwill also definitely increase With the increase of V 119901119871lowast

1will

decline slowly while 119901119867lowast1

will increaseThe OTArsquos profit status becomes better with the improve-

ment of its price But as the V increases the cost of OTA willalso definitely increase When V is equal to 27 then the profitof OTA is the highest If V is larger then the high costs willreduce the profits of OTAWhen V is equal to 34 the profit ofthewhole supply chain is the highest So from the perspectiveof the supply chain V is expected to be 34 rather than 27Similarly for the integrated system the profit of the OTAalso rises first and then declines with the increase of V Aftercalculationwe can get thatwhen V = 27 both120587119861lowast

2and120587119878lowast2will

be the highest From Figures 3 and 4 we know that the OTAwould tend to offer service that valued 27 so as to maximizeits own profit

After calculation we can conclude that when V = 34 then120587119861lowast is highest when V = 35 then 120587

119878lowast is highest (Figure 5)

10 Discrete Dynamics in Nature and Society

0 10 20 30 40 50 60 70 80100

150

200

250

300

350

400

450

Pric

e

pLlowast

1

pLlowast

2

pHlowast

1

pHlowast

2

Value added by OTArsquos services ()

Figure 2 Equilibrium prices in the integrated system

0 10 20 30 40 50 60 70 800

1

2

3

4

5

6

7

Profi

t

times104

120587lowast

1

120587lowast

2

120587lowast

Value added by OTArsquos services ()

Figure 3 Profits in the integrated system

From the perspective of the supply chain theOTA is expectedto offer more services Despite the rising cost of OTA willlower its profit the hotel can lower the wholesale prices tocoordinate the distribution of profits so as to achieve a win-win situation

In the following we focus on the comparison of differentchannelrsquos profit in each model Figure 6 depicts the curves ofthe total profits of the HAOTA channels in the integratedsystem with respect to V Figure 7 draws the curves of the dif-ferent channelsrsquo profits under both Bertrand and Stackelberggame The profit of the HA channel refers to the profit thatthe hotel derived from the HA channelThe profit of the OTA

0 10 20 30 40 50 60125

13

135

14

145

15

155

16

165

Profi

t

times104

120587Blowast

2

120587Slowast

2

Value added by OTArsquos services ()

Figure 4 OTArsquos profits under two games

0 10 20 30 40 50 60 70 8052

53

54

55

56

57

58

59

6

61

62

Profi

t

times104

120587Blowast

2

120587Slowast

2120587lowast

Value added by OTArsquos services ()

Figure 5 The profit comparison

channel involves the OTArsquos profit and the hotelrsquos profit gainedfrom the OTA channel

As shown in Figures 6 and 7 with the increase of V theprofit of the OTA channel will increase first and will thendecrease This indicates that a high level of service by OTAwill be detrimental to the channel profit That is because ahigh level of service will bring a high cost undoubtedly Forthe integrated model and Bertrand game model this disad-vantage is more evident The OTArsquos service can motivate theactual purchase behavior of customers in the OTA channelWhen V is relatively lower the additional profits from OTArsquos

Discrete Dynamics in Nature and Society 11

0 10 20 30 40 50 60 70 8018

2

22

24

26

28

3

32

34

36

38

4

Profi

t

HA channelOTA channel

times104

Value added by OTArsquos services ()

Figure 6 Channel profits in the integrated system

0 10 20 30 40 50 60 70 8005

1

15

2

25

3

35

4

45

Profi

t

HA channel in Bertrand gameOTA channel in Bertrand gameHA channel in Stackelberg gameOTA channel in Stackelberg game

times104

Value added by OTArsquos services ()

Figure 7 Channel profits in two games

service are enough to compensate for the cost In this casethe hotel and the OTA can get more profit from providing theservice However when V is high the additional profits fromOTArsquos service cannot make up for the high cost In such phe-nomenon the OTA should not increase investment in ser-vice

For both integrated model and Bertrand game modelwith the increase of V the profit of the HA channel willdecrease first and will then increase while in the Stackelberggamemodel the profit of theHA channel will always increase

with V With Figure 2 we can know that when OTA providesmore additional services it tends to increase its price Someof the customers will turn to reserve rooms from the HAbecause of the excessively high price in OTA As a result thehotel can gain more profits from the HA channel

8 Conclusion

With the development of e-commerce the providers oftourism products are more inclined to build dual-channelsIn this paper we consider the direct selling channel of HAand the traditional retail channel ofOTA from the perspectiveof tourism supply chain We develop a two-echelon tourismsupply chain model involving one hotel and one OTA wheretheOTAprovides related service Customers will be refundedpartially in case of cancelation or no-show We investigatethe optimal pricing strategies under several common casesThe integrated operation and the decentralized operationbased on Bertrand and Stackelberg games are studied andcorresponding equilibrium pricing policies are obtained

Our findings demonstrate that the hotel plays a crucialrole in optimizing the benefits of supply chain Consideringthe overall profit of the supply chain the hotel should act as aleader in dual-channel supply chain and formulate reasonablewholesale prices to improve the cooperative enthusiasm ofOTA so as to achieve optimization of the whole supplychain A lower wholesale price can help reduce OTArsquos loss ofprofit because of the opening of HA channel In addition weconsider the overbooking of the hotel and obtain the optimaloverbooking quantity We conclude that the hotel can alwaysobtain higher profits when the overbooking proportion iscontrolledwithin a certain range Otherwise if the overbook-ing proportion is too high the hotel can get extra profits onlywhen the overbooking cost is lower than a certain value

The contribution of this paper is that we extend tourismsupply chain to the dual-channel structure in which the hotelopens its direct channel to sell tourism products And theextant literature only refers to the single channel In additionwe realize that customer cancellations andno-showoccur fre-quently in hotel industry Thus we develop the game modelsbased on such phenomenon At last we derive the conditionsunder which the hotel dominant case is profitable for boththe supply chain members Our results can provide hotelsand OTAs with some new managerial insights under thedual-channel environment

This research can be extended in several directions infuture work For example in this paper we assume that allinformation is known to the hotel and OTA However someinformation could be asymmetric (eg see Chen [37]) Thuswe can explore the Bayesian equilibrium under asymmetricinformation settings Secondly the assumption of lineardemand is a limitation of this paperWe can further study thedynamic pricing in tourism dual-channel supply chain

Appendix

A Proof of Corollary 8

First we set (1199011198711)119861lowast

gt (119901119871

1)119878lowast which can be expressed as

12 Discrete Dynamics in Nature and Society

(1 minus 120582120572) (120579119886119871 + 120579119904119886119871+ 2119887119871119904119886119871+ 120579V120573 + 3119908

1198711205792+ 3119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

gt(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(A1)

The above equation can be simplified as

119908119871gt120579 [(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)]

4119887119871 (1 minus 120582120572) (119887119871 + 120579) (119887

119871+ 2120579)

(A2)

So we can get Corollary 8 B Proof of Corollary 9

If (1199011198941)119878lowast

gt (119901119894

1)119861lowast then

(1 minus 120582120572) (120579119886119894 + 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 2119908

1198941205792+ 2119908119894119887119894120579 minus 1205792V minus 2120579119887

119894V) + 119888120579 (119887

119894+ 120579)

minus (1 minus 120582120572) ((119901119894

1)119878lowast

+ (119901119894

1)119861lowast

) [2 (119887119894+ 120579)2minus 1205792] gt 0

120587119878lowast

1minus 120587119861lowast

1=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

2 (119887119871+ 120579)

((119901119871

1)119878lowast

minus (119901119871

1)119861lowast

)

+(1 minus 120582120572) (120579119886119867 + 120579119904119886

119867+ 2119887119867119904119886119867+ 120579V120573 + 2119908

1198671205792+ 2119908119867119887119867120579 minus 1205792V minus 2120579119887

119867V) + 119888120579 (119887

119867+ 120579)

2 (119887119867+ 120579)

((119901119867

1)119878lowast

minus (119901119867

1)119861lowast

)

minus (1 minus 120582120572)2 (119887119871+ 120579)2minus 1205792

2 (119887119871+ 120579)

[((119901119871

1)119878lowast

)2

minus ((119901119871

1)119861lowast

)2

] minus (1 minus 120582120572)2 (119887119867+ 120579)2minus 1205792

2 (119887119867+ 120579)

[((119901119867

1)119878lowast

)2

minus ((119901119867

1)119861lowast

)2

] gt 0

(B1)

If (1199011198711)119878lowast

lt (119901119871

1)119861lowast and (119901

119867

1)119878lowast

lt (119901119867

1)119861lowast we can prove

120587119878lowast

1gt 120587119861lowast

1similarly

From Propositions 3 and 7 with (3) we obtain that

120587119861lowast

2minus 120587119878lowast

2=

120579

4 (119887119871+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119871 + V (120573 + 120579) minus 119908119871(119887119871+ 120579)]

minus 2119888 (119887119871+ 120579) + 120579 (1 minus 120582120572) ((119901

119871

1)119861lowast

+ (119901119871

1)119878lowast

)

sdot ((119901119871

1)119861lowast

minus (119901119871

1)119878lowast

) +120579

4 (119887119867+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119867 + V (120573 + 120579) minus 119908 (119887119867+ 120579)]

minus 2119888 (119887119867+ 120579) + 120579 (1 minus 120582120572) ((119901

119867

1)119861lowast

+ (119901119867

1)119878lowast

)

sdot ((119901119867

1)119861lowast

minus (119901119867

1)119878lowast

)

(B2)

Note that

119863119894

2= [(1 minus 119904) 119886119894 minus 119887

119894119901119894

2] + 120573V + 120579 (119901

119894

1+ V minus 119901

119894

2) gt 0 (B3)

so we show that

2 (1 minus 120582120572) [(1 minus 119904) 119886119894 + V (120573 + 120579) minus 119908119894(119887119894+ 120579)]

minus 2119888 (119887119894+ 120579) + 120579 (1 minus 120582120572) ((119901

119894

1)119861lowast

+ (119901119894

1)119878lowast

)

gt 0

(B4)

Thus we have the following

(1) 120587119861lowast2

gt 120587119878lowast

2 if (1199011198711)119861lowast

gt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

gt (119901119867

1)119878lowast

(2) 120587119861lowast2

= 120587119878lowast

2 if (1199011198711)119861lowast

= (119901119871

1)119878lowast and (119901

119867

1)119861lowast

= (119901119867

1)119878lowast

(3) 120587119861lowast2

lt 120587119878lowast

2 if (1199011198711)119861lowast

lt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

lt (119901119867

1)119878lowast

Combined with Corollary 8 the proposition is proved

Discrete Dynamics in Nature and Society 13

C Proof of Corollary 10

The profit of hotel from the economy rooms is as follows

120587119871

= [(1 minus 120582120572) (119904119886119871 minus 120579V) minus 119888120579] 119901119871

1

+ [(1 minus 120582120572) (119886119871 minus 119904119886119871+ 120573V + 120579V) + 119888 (119887

119871+ 120579)] 119901

119871

2

+ 2120579 (1 minus 120582120572) 119901119871

1119901119871

2minus (1 minus 120582120572) (119887119871 + 120579) (119901

119871

1)2

minus (1 minus 120582120572) (119887119871 + 120579) (119901119871

2)2

minus (119886119871minus 119904119886119871+ 120573V + 120579V) 119888

(C1)

Define (119901119871

1)119861(119878)

= (119860119871

1)119861(119878)

+ (119861119871

1)119861(119878)

119908119871 (1199011198712)119861(119878)

=

(119860119871

2)119861(119878)

+ (119861119871

2)119861(119878)

119908119871 where

(119861119871

1)119861

=3120579 (119887119871+ 120579)

4 (119887119871+ 120579)2minus 1205792

(119861119871

1)119878

=120579 (119887119871+ 120579)

2 (119887119871+ 120579)2minus 1205792

(119861119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119861119871

1)119861(119878)

+1

2

(119860119871

1)119861

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

(119860119871

1)119878

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(119860119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119860119871

1)119861(119878)

+(1 minus 120582120572) [(1 minus 119904) 119886119871 + V (120579 + 120573)] + 119888 (119887

119871+ 120579)

2 (1 minus 120582120572) (119887119871 + 120579)

(C2)

Let 120597120587119871120597119908 = 0 then we get119908lowast

119871 Similarly we can get119908lowast

119867

D Proof of Proposition 12

Let 120587119889minus 120587119903gt 0 then we can get 119904

0 where the profits of hotel

from HA and OTA are as follows

120587119889= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1)

120587119903= (1 minus 120582120572) (119908119871119863

119871

2+ 119908119867119863119867

2)

(D1)

E Proof of Corollary 11

If Δ119862119871le 120582(1 minus 120582)119876

119871 then the profit of hotel is 120587119871

11 The

derivative of 12058711987111(Δ119862119871) is 120597120587119871

11120597Δ119862119871= (1 minus 120582120572)119901

119871

1gt 0 So

with the increase of Δ119862119871 12058711987111

will increase When Δ119862119871

=

120582(1 minus 120582)119876119871 12058711987111

is maximized If Δ119862119871

ge 120582(1 minus 120582)119876119871

then the profit of hotel is 12058711987112 The derivative of 120587119871

12(Δ119862119871) is

120597120587119871

12120597Δ119862119871= (1 minus 120582120572)119901

119871

1minus (1 minus 120582)(119901

119871

1+ 119888119871) lt 0 So with the

increase of Δ119862119871 12058711987111will decline When Δ119862

119871= 120582(1 minus 120582)119876

119871

120587119871

11is maximizedSimilarly we can get Δ119862lowast

119867

F Proof of Proposition 13

Assume that the overbooking proportion is 120574119871and 120574119867

(1) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) le 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

That is

120574119867lt

120582

1 minus 120582lt 120574119871

le120582119876119871+ 119876119867[1 minus (1 minus 120582) (1 + 120574

119867)]

(1 minus 120582)119876119871

(F1)

Thus the hotel would like to overbook to get more profitrather than room vacancy

(2) Consider (1198631198711+119863119871

2)(1minus120582) lt 119876

119871and (119863119867

1+119863119867

2)(1minus120582) gt

119876119867That is 120574

119871lt 120582(1 minus 120582) lt 120574

119867 Then the profit of hotel is

120587112

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F2)

Thenwhen 119888119867119906

lt (1minus120582120572)119901119867

1(1minus120582) that is120587

112minus120587111

gt 0the hotel would carry out overbooking

(3) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

14 Discrete Dynamics in Nature and Society

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867lt 120582(1 minus 120582) Then the profit of hotel is

120587113

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2+ 119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876]

(F3)

Then when 119888119871

119906lt (1 minus 120582120572)119901

119871

1(1 minus 120582) 120587

113minus120587111

gt 0 thusthe hotel would carry out overbooking

(4) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) gt 119876

119867

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867gt (120582119876

119867+ 119876119871[1 minus (1 minus 120582)(1 + 120574

119871)])(1 minus 120582)119876

119867

Then the profit of hotel is as follows

120587114

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2) (1 minus 120582) minus 119876

119871]

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F4)

Then when 119888119871119906lt (1minus120582120572)119901

119871

1(1minus120582) and 119888119867

119906lt (1minus120582120572)119901

119867

1

(1 minus 120582) 120587114

minus 120587111

gt 0 overbooking is preferred

G Threshold Values

Threshold values are as follows

1198711= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 3119908

1198941205792+ 3119908119894119887119894120579

minus 1205792V minus 2120579119887

119894V

1198712= 2119886119894(119887119894+ 120579) minus 119904119886

119894(2119887119894+ 120579) + 120579

2119908119894+ 2 (120579 + 120573) (119887

119894

+ 120579) V + 2119908119894(119887119894+ 120579)2minus 1205792V

1198713= 4120579V119887

119894120573 minus 120579119904119886

119894119887119894+ 2V1205731198872

119894+ 31198861198941205792+ 4119886119894119887119894120579

minus 21198861198941198872

119894119904 + 3120579

2V120573 + 1205792V119887119894+ 2120579V1198872

119894+ 21198861198941198872

119894

1198714= 3119886119894119887119894120579 + 3120579

2V120573 minus 2120579V1198872119894minus 1205792V119887119894+ 31198861198941205792

+ 21198861198941198872

119894119904 + 119886119887

119894119904120579 + 3119887

119894120573V120579

1198715= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 minus 120579

2V minus 2120579119887119894V

1198661= [(1 minus 120582120572) (119904119886119894 minus 120579V) minus 119888120579] (119861

119894

1)119861(119878)

+ [(1 minus 120582120572) (119886119894 minus 119904119886119894+ 120573V + 120579V) + 119888 (119887

119894+ 120579)]

sdot (119861119894

1)119861(119878)

+ 2120579 (1 minus 120582120572) [(119860119894

1)119861(119878)

(119861119894

2)119861(119878)

+ (119861119894

1)119861(119878)

(119860119894

2)119861(119878)

] minus 2 (1 minus 120582120572) (119887119894 + 120579)

sdot [(119860119894

1)119861(119878)

(119861119894

1)119861(119878)

+ (119860119894

2)119861(119878)

(119861119894

2)119861(119878)

]

1198662= 2 (1 minus 120582120572)

sdot (119887119894+ 120579) [((119861

119894

1)119861(119878)

)

2

+ ((119861119894

2)119861(119878)

)

2

]

minus 2120579 (119861119894

1)119861(119878)

(119861119894

2)119861(119878)

1199040= ((119887119871+ 120579) (119901

119871

1)2

+ (119887119867+ 120579) (119901

119867

1)2

+ 120579119908119871(119901119871

1minus 119901119871

2) + 120579119908

119867(119901119867

1minus 119901119867

2)

+ 120579V (1199011198711+ 119901119867

1) + (119908

119871+ 119908119867) (120573 + 120579) V

+ 119908119871(119886119871minus 119887119871119901119871

2) + 119908119867(119886119867minus 119887119867119901119867

2)

minus 120579 (119901119871

1119901119871

2+ 119901119867

1119901119867

2)) (119886119871(119901119871

1+ 119908119871)

+ 119886119867(119901119867

1+ 119908119867))minus1

(G1)

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The authors thank associate editor and anonymous refereesfor their numerous constructive comments and encourage-ment that have improved their paper greatly The work waspartly supported by (i) the National Natural Science Founda-tion ofChina (71201083 71572058 and 71571100) (ii) the Fun-damental Research Funds for the Central Universities SCUT(2015ZZ057) (iii) Jiangsu Province Science Foundation forYouths (BK2012379) and (iv) the Fundamental ResearchFunds for the Central Universities (NS2015076)

References

[1] J Li W N Zhang H Xu and J Jiang ldquoDynamic competitionand cooperation of road infrastructure investment of multipletourism destinations a case Study of Xidi and Hongcun WorldCulturalHeritagerdquoDiscreteDynamics inNature and Society vol2015 Article ID 962028 10 pages 2015

[2] T Paksoy EOzceylan andG-WWeber ldquoProfit oriented supplychain network optimizationrdquoCentral European Journal of Oper-ations Research vol 21 no 2 pp 455ndash478 2013

[3] X Zhang H Song and G Q Huang ldquoTourism supply chainmanagement a new research agendardquo Tourism Managementvol 30 no 3 pp 345ndash358 2009

[4] Z Yang and J Cai ldquoDo regional factors matter Determinantsof hotel industry performance in Chinardquo TourismManagementvol 52 pp 242ndash253 2016

[5] B Pan L Zhang and R Law ldquoThe complex matter of onlinehotel choicerdquoCornell Hospitality Quarterly vol 54 no 1 pp 74ndash83 2013

[6] L Ling X Guo and C Yang ldquoOpening the online marketplacean examination of hotel pricing and travel agency on-line

Discrete Dynamics in Nature and Society 15

distribution of roomsrdquo Tourism Management vol 45 pp 234ndash243 2014

[7] L Ling Y Dong X Guo and L Liang ldquoAvailability man-agement of hotel rooms under cooperation with online travelagenciesrdquo International Journal of Hospitality Management vol50 pp 145ndash152 2015

[8] J N K Liu andE Y Zhang ldquoAn investigation of factors affectingcustomer selection of online hotel booking channelsrdquo Interna-tional Journal of Hospitality Management vol 39 pp 71ndash832014

[9] L Fox ldquoFour Seasons Unveils $18 Million Website as LuxuryTravel Growsrdquo 2012 httpwwwtnoozcomarticlefour-sea-sons-unveils-18-million-dollar-website-as-luxury-travel-grows

[10] C-M Chen and Y-C Lin ldquoThe influence of uncertain demandon hotel capacityrdquo International Journal of Hospitality Manage-ment vol 34 no 1 pp 462ndash465 2013

[11] S Yang G Q Huang H Song and L Liang ldquoGame-theoreticapproach to competition dynamics in tourism supply chainsrdquoJournal of Travel Research vol 47 no 4 pp 425ndash439 2009

[12] G Q Huang H Song and X Zhang ldquoA comparative analysis ofquantity and price competitions in tourism supply chain net-works for package holidaysrdquo Service Industries Journal vol 30no 10 pp 1593ndash1606 2010

[13] Y Huang H Song G Q Huang and J Lou ldquoA comparativestudy of tourism supply chains with quantity competitionrdquoJournal of Travel Research vol 51 no 6 pp 717ndash729 2012

[14] H K Lee and Y Fernando ldquoThe antecedents and outcomes ofthe medical tourism supply chainrdquo Tourism Management vol46 pp 148ndash157 2015

[15] W-Y K Chiang D Chhajed and J D Hess ldquoDirect marketingindirect profits a strategic analysis of dual-channel supply-chain designrdquoManagement Science vol 49 no 1 pp 1ndash20 2003

[16] A A Tsay and N Agrawal ldquoChannel conflict and coordinationin the E-commerce agerdquo Production and Operations Manage-ment vol 13 no 1 pp 93ndash110 2004

[17] Q-H Li and B Li ldquoDual-channel supply chain equilibriumproblems regarding retail services and fairness concernsrdquoApplied Mathematical Modelling 2016

[18] S Panda N M Modak S S Sana and M Basu ldquoPricingand replenishment policies in dual-channel supply chain undercontinuous unit cost decreaserdquo Applied Mathematics and Com-putation vol 256 pp 913ndash929 2015

[19] Y Liu C Ding C Fan and X Chen ldquoPricing decision underdual-channel structure considering fairness and free-ridingbehaviorrdquo Discrete Dynamics in Nature and Society vol 2014Article ID 536576 10 pages 2014

[20] J Chen H Zhang and Y Sun ldquoImplementing coordinationcontracts in a manufacturer Stackelberg dual-channel supplychainrdquo Omega vol 40 no 5 pp 571ndash583 2012

[21] Q Ding C Dong and Z Pan ldquoA hierarchical pricing decisionprocess on a dual-channel problem with one manufacturer andone retailerrdquo International Journal of Production Economics vol175 pp 197ndash212 2016

[22] B Rodriguez and G Aydin ldquoPricing and assortment decisionsfor a manufacturer selling through dual channelsrdquo EuropeanJournal of Operational Research vol 242 no 3 pp 901ndash9092015

[23] T Lockyer ldquoThe perceived importance of price as one hotelselection dimensionrdquo Tourism Management vol 26 no 4 pp529ndash537 2005

[24] C-M Chen H-W Yang E Y Li and C-C Liu ldquoHow doeshotel pricing influence guest satisfaction by the moderatinginfluence of room occupancyrdquo International Journal of Hospi-tality Management vol 49 pp 136ndash138 2015

[25] J-M Espinet M Fluvia R Rigall-I-Torrent and A Salo ldquoHotelcharacteristics and seasonality in prices an analysis usingSpanish tour operatorsrsquo brochuresrdquo Tourism Economics vol 18no 4 pp 749ndash767 2012

[26] C Juaneda J M Raya and F Sastre ldquoPricing the time and loca-tion of a stay at a hotel or apartmentrdquo Tourism Economics vol17 no 2 pp 321ndash338 2011

[27] G Abrate G Fraquelli and G Viglia ldquoDynamic pricing strate-gies evidence from European hotelsrdquo International Journal ofHospitality Management vol 31 no 1 pp 160ndash168 2012

[28] D Q Yao and J J Liu ldquoCompetitive pricing of mixed retail ande-tail distribution channelsrdquo Omega vol 33 no 3 pp 235ndash2472005

[29] J Zhao and L Wang ldquoPricing and retail service decisionsin fuzzy uncertainty environmentsrdquo Applied Mathematics andComputation vol 250 pp 580ndash592 2015

[30] A A Tsay and N Agrawal ldquoChannel dynamics under priceand service competitionrdquo Manufacturing amp Service OperationsManagement vol 2 no 4 pp 372ndash391 2000

[31] S C Choi ldquoPrice competition in a duopoly common retailerchannelrdquo Journal of Retailing vol 72 no 2 pp 117ndash134 1996

[32] Y Bakos andE Brynjolfsson ldquoBundling and competition on theinternetrdquoMarketing Science vol 19 no 1 pp 63ndash82 2000

[33] H Song J H Kim and S Yang ldquoConfidence intervals fortourism demand elasticityrdquo Annals of Tourism Research vol 37no 2 pp 377ndash396 2010

[34] DMHanssens L J Parsons andR L SchultzMarket ResponseModels Econometric and Time Series Analysis Kluwer Aca-demic Publishers Boston Mass USA 2nd edition 2001

[35] H Kurata D-Q Yao and J J Liu ldquoPricing policies under directvs indirect channel competition and national vs store brandcompetitionrdquo European Journal of Operational Research vol180 no 1 pp 262ndash281 2007

[36] R Law and C Cheung ldquoA study of the perceived importance ofthe overall website quality of different classes of hotelsrdquo Inter-national Journal of Hospitality Management vol 25 no 3 pp525ndash531 2006

[37] K B Chen ldquoProcurement strategies and coordination mecha-nism of the supply chain with one manufacturer and multiplesuppliersrdquo International Journal of Production Economics vol138 no 1 pp 125ndash135 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Discrete Dynamics in Nature and Society 7

the return expense proportion (120572) or the cancellations andno-show proportion (120582)

From Proposition 7 we can see that the Stackelbergmodel is similar to the Bertrand model that the equilibriumprices would increase with the increase of wholesale pricesFurthermore when thewholesale price is greater than1199083

119894 the

equilibrium price of HA in Stackelberg model will be higherthan that in the integrated model

In the Stackelberg game if OTA offers more effective ser-vices the equilibrium prices of OTA would increase accord-ingly The relationship between the Stackelberg equilibriumprices and V is similar to that in the Bertrand model

53 Contrastive Analysis of Bertrand and Stackelberg GamesBased on the equilibrium prices obtained in the previoussection we in this section compare the equilibriumprices andoptimal profit under Bertrand and Stackelberg games

Corollary 8 There exists a threshold unit wholesale price1199084

119894(119894 = 119871119867) such that

(1) (1199011198941)119861lowast

gt (119901119894

1)119878lowast and (119901119894

2)119861lowast

gt (119901119894

2)119878lowast if 119908

119894gt 1199084

119894

(2) (1199011198941)119861lowast

= (119901119894

1)119878lowast and (119901119894

2)119861lowast

= (119901119894

2)119878lowast if 119908

119894= 1199084

119894

(3) (1199011198941)119861lowast

lt (119901119894

1)119878lowast and (119901119894

2)119861lowast

lt (119901119894

2)119878lowast if 119908

119894lt 1199084

119894

where

1199084

119894=

120579 [(1 minus 120582120572) 1198715 + 119888120579 (119887119894+ 120579)]

4119887119894 (1 minus 120582120572) (119887119894 + 120579) (119887

119894+ 2120579)

(10)

Corollary 8 compares the equilibrium prices under theBertrand and Stackelberg game with respect to the wholesaleprice It shows that if the wholesale price is greater than1199084

119894 the pricing equilibrium under the Bertrand is higher

than that under the Stackelberg game Conversely the pricingequilibrium is lower if the wholesale price is less than 119908

4

119894

In the decentralized case both the manufacturer and theretailer want to maximize their profit A high wholesale pricecould be passed on to customersTherefore the above resultsexist In addition how to share the profit between the manu-facturer and the retailer depends on their bargaining powers

Corollary 9 If 119908119894

= 1199084

119894(119894 = 119871119867) then 120587

119878lowast

1gt 120587119861lowast

1 OTArsquos

profit has the following relationship with respect to 1199084119894

(1) 120587119861lowast2

gt 120587119878lowast

2if 119908119871gt 1199084

119871and 119908

119867gt 1199084

119867

(2) 120587119861lowast2

= 120587119878lowast

2if 119908119871= 1199084

119871and 119908

119867= 1199084

119867

(3) 120587119861lowast2

lt 120587119878lowast

2if 119908119871lt 1199084

119871and 119908

119867lt 1199084

119867

Thehotel is the leader in Stackelberg game and can alwaysbenefit from it except for the critical point1199084

119894 Comparedwith

the Bertrand game the hotel can get higher profits in Stackel-berg gamewhen the wholesale price is not equal to1199084

119894There-

fore in decentralized decision-making model the hotel willbe more inclined to be the price leader in order to ensure thatit can achieve higher profits

Corollary 9 indicates that the Stackelberg model is supe-rior to the Bertrand model when the wholesale price is less

than the critical point1199084119894 Not only the hotel but alsoOTA can

gain more profit from the Stackelberg game Though OTA isa follower in Stackelberg game the profit will not be reducedbecause the lower wholesale prices can compensate for theloss of profit caused by the opening of HA channel Conse-quently the hotel should play the role of the price leader inthe supply chain and develop reasonable wholesale prices toachieve optimization of the whole supply chain profit whileoptimizing its own profit

Corollary 10 Under either Bertrand or Stackelberg equi-librium channel prices there exists optimal wholesale price119908lowast

119894(119894 = 119871119867) that maximizes the total equilibrium channel

profit where 119908lowast119894= 11986611198662

According to Corollary 10 there exists optimal wholesaleprice 119908

lowast

119894(119894 = 119871119867) that maximizes the total equilibrium

channel profit under either Bertrand or Stackelberg gameThe optimal wholesale price will optimize the decentralizeddecision-making supply chainMeanwhile both the hotel andtheOTA can benefit from the optimal wholesale priceThere-fore the reasonable wholesale price can help promotemutualcooperation and communication between the supply chainmembers

54 Contrastive Analysis of Two Channels in the Supply Chain

Corollary 11 There exists a threshold unit market share of HAin the tourism dual-channel supply chain (119904

0) such that when

119904 gt 1199040 the hotelrsquos profit from HA is higher than that from OTA

Keeping the wholesale prices and sales prices unchangedwhen the market share of HA in the tourism dual-channelsupply chain exceeds a certain value 119904

0 the hotelrsquos profit from

HA is higher than that from OTA The result is suitable forthe integrated system Bertrand and Stackelberg games Fromthe perspective of hotelrsquos revenue the hotel should explorethe channel for direct selling actively Also the hotel canstrengthen the promotion of HA channel to improve thecustomerrsquos understanding and preference for theHA channelBut the premise is that the profit growth from the promotioncan compensate for the cost According to the statistical datafrom the hotel price competitiveness analysis report in thefirst half of 2012 we know that the booking cost from directselling channel is about 1 dollar per night but that fromOTAis about 10 dollars per night Booking cost can be reducedby 46 if the direct selling level is doubled Then improvingthe market share of direct selling will greatly reduce the costMore comparisons of different channelrsquos profits in eachmodelcan be found in part of numerical analysis

6 Overbooking

This section extends to consider the overbooking caseRegarding overbooking in the hospitality industry the com-mon practice is that the hotel upgrades the room type ortransfers customers to other hotels nearby that have the samelevel and same type In airline industry if customers aredenied boarding after arriving at the airport the airline will

8 Discrete Dynamics in Nature and Society

provide a free upgrade endorse the ticket or provide com-pensation for the customers according to specific situationCompared to the hotels the airlines cannot transfer cus-tomers to other companies The air ticket alteration will usu-ally disrupt customersrsquo traveling schedule Though the over-booking by airlines has been well studied in the literature ourresearch is new in the hospitality industry by considering theoverbooking withwithout room transfer with the hope thatcertain implications can be enlightened to the hotel man-agers

The hotel wants to increase the occupancy rates toincrease the profits through overbooking However over-booking will lead to the risk that the actual occupancyamount is greater than the number of hotel roomsThereforethe hotel has to provide compensation to travelers who can-not check in that is overbooking cost The greater the num-bers of overbooking the less the probability of room vacancybut at the same time travelers are more likely to be refusedby the hotel Therefore the hotel must balance between thevacancy lost and the overbooking costs We develop a modelto analyze the overbooking choice

In reality the OTA is always a crucial partner of hotelsfor it can attract a large number of customers for hotelsand improve their occupancy rates [36] Spontaneously theOTA plays an increasingly significant role in the distributionsystems of hotels [5 7] By contrast the HA mainly providesa platform for individual guest Compared with individualcustomers hotel pays more attention to the long-term coop-eration relationship with the OTA Therefore in our modelwe assume that when the market demand is greater than thesupply and the hotel does not carry out overbooking the hotelwould give priority to customers who are booking fromOTA

61 Without Room Transfer Here we consider the casewith no room transfer When the actual occupancy amountexceeds the total quantity of rooms the hotel does not arrangeother alternative accommodation for the customers who can-not check in But the hotel must pay the loss of goodwill costSuppose that the overbooking quantity of economy and lux-ury rooms isΔ119862

119871andΔ119862

119867and the overbooking cost is 119888

119871and

119888119867 respectivelyWe discuss economy roomsrsquo overbooking The actual

occupancy can be either of the following two cases (1) when119876119871

lt 119863119871

1+ 119863119871

2le 119876119871+ Δ119862

119871 the reservation amount of

rooms is 1198631198711+ 119863119871

2 so the actual occupancy amount is (119863119871

1+

119863119871

2)(1 minus 120582) (2) when119863

119871

1+ 119863119871

2gt 119876119871+ Δ119862

119871 the reservation

amount is 119876119871+ Δ119862119871 then the actual occupancy amount is

(119876119871+Δ119862119871)(1 minus 120582) Therefore if (119876

119871+Δ119862119871)(1 minus 120582) le 119876

119871 that

is Δ119862119871le 120582119876119871(1 minus 120582) the profit of hotel is

120587119871

11= (1 minus 120582120572) [119901

119871

1(119876119871+ Δ119862119871minus 119863119871

2) + 119908119871119863119871

2] (11)

If (119876119871+ Δ119862119871)(1 minus 120582) ge 119876

119871 that is Δ119862

119871ge 120582119876119871(1 minus 120582)

the economy roomsrsquo actual occupancy amount exceeds theeconomy roomsrsquo number in the hotel so the hotel must paythe overbooking cost then the profit of hotel is

120587119871

12= (1 minus 120582120572) [119901

119871

1(119876119871+ Δ119862119871minus 119863119871

2) + 119908119871119863119871

2]

minus (119901119871

1+ 119888119871) [(119876119871+ Δ119862119871) (1 minus 120582) minus 119876

119871]

(12)

Proposition 12 Without considering roomsrsquo transfer the opti-mal overbooking quantity of economy rooms and luxury roomsis

Δ119862lowast

119894=

120582

1 minus 120582119876119894 119894 = 119871119867 (13)

FromProposition 12 we know that the higher the propor-tion of customer cancellations and no-show is the larger theoptimal overbooking quantity of the hotel will be With theincrease of 120572 the penalty that customers need to pay for theircancellation or no-show decreases Two following extremesituations are considered When 120572 = 1 the hotel will returnall the guarantee fee in case of customersrsquo cancellation or no-showThat is the same as the hotel does not charge customersany guarantee fee when customers book the rooms Undersuch circumstances customers can book rooms for severaldays firstly after they identify a specific itinerary they cancancel the extra rooms for they do not suffer any loss It is nodoubt that such regulation will increase the cancellation andno-show rate On the other hand if 120572 = 1 all the guaranteefee will not be returned after cancellation or no-show In thiscase customers need to reserve a room cautiously If it is notnecessary customers will not choose cancellation or no-showbecause the penalty cost is too high Such policy will reducethe cancellation and no-show rate Spontaneously to someextent 120572 and 120582 are positive correlation When the hotelincreases proportion 120572 it would like to increase the over-booking quantity so as to increase the actual occupancy rateNowadays the time-limited orders are widely used amonghotels Such regulation cannot only reduce customersrsquo lossfor the change of schedule but also help the hotel confirmthe orders so as to handle the overbooking phenomenon inadvance

In addition the risk of overbooking the economy roomsis relatively lower than the luxury rooms Compared toeconomic rooms it is more difficult for the hotel to findalternative luxury rooms to satisfy the customers Naturallyoverbooking cost of luxury room is higher For instance ifeconomy rooms are overbooked the hotel can transfer thecustomers to luxury rooms and the customers are willingto accept By contrast if luxury rooms are overbooked cus-tomers are not willing to accept the adjustment from luxuryrooms to economic rooms This implies that the hotel has topay a higher default costTherefore the hotel should be morecareful to choose the overbooking quantity of luxury rooms

62 With Room Transfer The following discusses the casewith room transfer Firstly when the economy rooms areinsufficient and luxury rooms have a surplus customers cancheck in the hotelrsquos luxury rooms with the price of economyrooms Customers spend the same money and can enjoybetter service so they are willing to accept this adjustmentSecondly when the luxury roomsrsquo actual occupancy amountexceeds the number of luxury rooms in the hotel the hotelusually transfers customers to other hotels nearby that havethe same level and same type because the customers whobook luxury room have a high requirement Customers canenjoy the same service so they are willing to accept this trans-fer However the hotelrsquos credibility in customersrsquo mind will be

Discrete Dynamics in Nature and Society 9

damaged and it must pay the additional costsThirdly if boththe economy rooms and luxury rooms are unable to meetthe demand the hotel usually transfers the customers whocannot check in to other hotels Note that when119863119894

1+119863119894

2gt 119876119894

119894 = 119871119867 if the hotel does not overbook its profit is

120587111

= (1 minus 120582120572) [119901119871

1(119876119871minus 119863119871

2) + 119901119867

1(119876119867minus 119863119867

2)

+ 119908119871119863119871

2+ 119908119867119863119867

2]

(14)

Proposition 13 With room transfer there exists threshold unitoverbooking cost 119888

1198940 such that if 119888

119894lt 1198881198940 then overbooking is

profitable for the hotel where

1198881198940=(1 minus 120582120572) 119901

119894

1

1 minus 120582 119894 = 119871119867 (15)

From Propositions 12 and 13 we conclude that the hotelshould control the overbooking quantity in a certain rangeto prevent lacking of rooms If the overbooking proportionis too large then the hotel may face a loss Only when theoverbooking cost is low the hotel can obtain additional profitOtherwise if the overbooking cost exceeds a certain valuethe hotelrsquos profit would be lower when it carries out over-booking As the market demand increases the supply is closeto saturation and then the overbooking costs will be higherTherefore when the market demand is excessive the hotelshould strictly control the proportion of overbooking Inaddition if the number of hotels that have the same level andtype in the same region is little that is the possibility to trans-fer customer is small then the hotel should lower the propor-tion of overbooking

The proportion of overbooking depends on the propor-tion of customer cancellations andno-showaswell as the totalnumber of hotel rooms so the hotel can analyze the historicaldata to develop an appropriate overbooking proportion so asto maximize the hotelrsquos expected profit

Proposition 14 When the economy rooms and luxury roomsare both overbooked the optimal centralized prices are asfollows 119894 = 119871119867

119901119894lowast

14= 119901119894lowast

1+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

119901119894lowast

24= 119901119894lowast

2+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

(16)

Bertrand and Stackelberg prices are as follows

(119901119894

14)119861lowast

= (119901119894

1)119861lowast

+2119888119894

119906119887119894(119887119894+ 120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

24)119861lowast

= (119901119894

2)119861lowast

+120579119888119894

119906119887119894 (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

14)119878lowast

= (119901119894

1)119878lowast

+119888119894

119906119887119894(2119887119894+ 3120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 21205792]

(119901119894

24)119878lowast

=120579 (119901119894

14)119878lowast

+ (1 minus 119904) 119886119894 + V (120579 + 120573) + 119908119894(119887119894+ 120579)

2 (119887119894+ 120579)

+119888

2 (1 minus 120582120572)

(17)

For the hotel the premise to overbook rooms is that themarket demand is greater than the supply When the hotelfaces the risk of overbooking the equilibrium prices in bothcentralized and decentralized decision-making supply chainwill improve In the busy season in order to reduce the riskof overbooking the hotel would increase the prices and theincrement will increase as the transfer cost increases From(16) and (17) we can know that the increment in centralizeddecision-making model is the greatest and that in Bertrandgame is the smallest

7 Numerical Analysis

In this section we do some numerical experiment to gainmore insights According to the China Hotel Sales Chan-nel Report by I-Research (httpreportiresearchcnreport2013031892shtml) there are 381 of the hotels that aresuitable for high-end travelers and 619 of the hotels thatare suitable for low-end travelersTherefore this part assumesthat the proportion of the economical rooms and the luxuryrooms is 4 6 that is 119886

119871= 06119886 119886

119867= 04119886 Other parameter

settings are made as follows 119886 = 600 119904 = 05 and 119887119871= 06

119887119867= 02 120573 = 120579 = 05 120578 = 004 120572 = 08 120582 = 01 119908

119894= 05119901

119894

1

(119894 = 119871119867) In the following we investigate the impact of V onthe optimal prices and profits

When V = 0 that is the OTA does not offer any servicethen the optimal prices of HA are equal to the prices ofOTA Since 119887

119871gt 120573 gt 119887

119867 then the market of economy

rooms is service-oriented while the market of luxury roomsis price-oriented FromFigure 2 we can know that whenOTAoffers more services OTArsquos optimal price will be increasedaccordingly It is reasonable that if V increases the cost ofOTAwill also definitely increase With the increase of V 119901119871lowast

1will

decline slowly while 119901119867lowast1

will increaseThe OTArsquos profit status becomes better with the improve-

ment of its price But as the V increases the cost of OTA willalso definitely increase When V is equal to 27 then the profitof OTA is the highest If V is larger then the high costs willreduce the profits of OTAWhen V is equal to 34 the profit ofthewhole supply chain is the highest So from the perspectiveof the supply chain V is expected to be 34 rather than 27Similarly for the integrated system the profit of the OTAalso rises first and then declines with the increase of V Aftercalculationwe can get thatwhen V = 27 both120587119861lowast

2and120587119878lowast2will

be the highest From Figures 3 and 4 we know that the OTAwould tend to offer service that valued 27 so as to maximizeits own profit

After calculation we can conclude that when V = 34 then120587119861lowast is highest when V = 35 then 120587

119878lowast is highest (Figure 5)

10 Discrete Dynamics in Nature and Society

0 10 20 30 40 50 60 70 80100

150

200

250

300

350

400

450

Pric

e

pLlowast

1

pLlowast

2

pHlowast

1

pHlowast

2

Value added by OTArsquos services ()

Figure 2 Equilibrium prices in the integrated system

0 10 20 30 40 50 60 70 800

1

2

3

4

5

6

7

Profi

t

times104

120587lowast

1

120587lowast

2

120587lowast

Value added by OTArsquos services ()

Figure 3 Profits in the integrated system

From the perspective of the supply chain theOTA is expectedto offer more services Despite the rising cost of OTA willlower its profit the hotel can lower the wholesale prices tocoordinate the distribution of profits so as to achieve a win-win situation

In the following we focus on the comparison of differentchannelrsquos profit in each model Figure 6 depicts the curves ofthe total profits of the HAOTA channels in the integratedsystem with respect to V Figure 7 draws the curves of the dif-ferent channelsrsquo profits under both Bertrand and Stackelberggame The profit of the HA channel refers to the profit thatthe hotel derived from the HA channelThe profit of the OTA

0 10 20 30 40 50 60125

13

135

14

145

15

155

16

165

Profi

t

times104

120587Blowast

2

120587Slowast

2

Value added by OTArsquos services ()

Figure 4 OTArsquos profits under two games

0 10 20 30 40 50 60 70 8052

53

54

55

56

57

58

59

6

61

62

Profi

t

times104

120587Blowast

2

120587Slowast

2120587lowast

Value added by OTArsquos services ()

Figure 5 The profit comparison

channel involves the OTArsquos profit and the hotelrsquos profit gainedfrom the OTA channel

As shown in Figures 6 and 7 with the increase of V theprofit of the OTA channel will increase first and will thendecrease This indicates that a high level of service by OTAwill be detrimental to the channel profit That is because ahigh level of service will bring a high cost undoubtedly Forthe integrated model and Bertrand game model this disad-vantage is more evident The OTArsquos service can motivate theactual purchase behavior of customers in the OTA channelWhen V is relatively lower the additional profits from OTArsquos

Discrete Dynamics in Nature and Society 11

0 10 20 30 40 50 60 70 8018

2

22

24

26

28

3

32

34

36

38

4

Profi

t

HA channelOTA channel

times104

Value added by OTArsquos services ()

Figure 6 Channel profits in the integrated system

0 10 20 30 40 50 60 70 8005

1

15

2

25

3

35

4

45

Profi

t

HA channel in Bertrand gameOTA channel in Bertrand gameHA channel in Stackelberg gameOTA channel in Stackelberg game

times104

Value added by OTArsquos services ()

Figure 7 Channel profits in two games

service are enough to compensate for the cost In this casethe hotel and the OTA can get more profit from providing theservice However when V is high the additional profits fromOTArsquos service cannot make up for the high cost In such phe-nomenon the OTA should not increase investment in ser-vice

For both integrated model and Bertrand game modelwith the increase of V the profit of the HA channel willdecrease first and will then increase while in the Stackelberggamemodel the profit of theHA channel will always increase

with V With Figure 2 we can know that when OTA providesmore additional services it tends to increase its price Someof the customers will turn to reserve rooms from the HAbecause of the excessively high price in OTA As a result thehotel can gain more profits from the HA channel

8 Conclusion

With the development of e-commerce the providers oftourism products are more inclined to build dual-channelsIn this paper we consider the direct selling channel of HAand the traditional retail channel ofOTA from the perspectiveof tourism supply chain We develop a two-echelon tourismsupply chain model involving one hotel and one OTA wheretheOTAprovides related service Customers will be refundedpartially in case of cancelation or no-show We investigatethe optimal pricing strategies under several common casesThe integrated operation and the decentralized operationbased on Bertrand and Stackelberg games are studied andcorresponding equilibrium pricing policies are obtained

Our findings demonstrate that the hotel plays a crucialrole in optimizing the benefits of supply chain Consideringthe overall profit of the supply chain the hotel should act as aleader in dual-channel supply chain and formulate reasonablewholesale prices to improve the cooperative enthusiasm ofOTA so as to achieve optimization of the whole supplychain A lower wholesale price can help reduce OTArsquos loss ofprofit because of the opening of HA channel In addition weconsider the overbooking of the hotel and obtain the optimaloverbooking quantity We conclude that the hotel can alwaysobtain higher profits when the overbooking proportion iscontrolledwithin a certain range Otherwise if the overbook-ing proportion is too high the hotel can get extra profits onlywhen the overbooking cost is lower than a certain value

The contribution of this paper is that we extend tourismsupply chain to the dual-channel structure in which the hotelopens its direct channel to sell tourism products And theextant literature only refers to the single channel In additionwe realize that customer cancellations andno-showoccur fre-quently in hotel industry Thus we develop the game modelsbased on such phenomenon At last we derive the conditionsunder which the hotel dominant case is profitable for boththe supply chain members Our results can provide hotelsand OTAs with some new managerial insights under thedual-channel environment

This research can be extended in several directions infuture work For example in this paper we assume that allinformation is known to the hotel and OTA However someinformation could be asymmetric (eg see Chen [37]) Thuswe can explore the Bayesian equilibrium under asymmetricinformation settings Secondly the assumption of lineardemand is a limitation of this paperWe can further study thedynamic pricing in tourism dual-channel supply chain

Appendix

A Proof of Corollary 8

First we set (1199011198711)119861lowast

gt (119901119871

1)119878lowast which can be expressed as

12 Discrete Dynamics in Nature and Society

(1 minus 120582120572) (120579119886119871 + 120579119904119886119871+ 2119887119871119904119886119871+ 120579V120573 + 3119908

1198711205792+ 3119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

gt(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(A1)

The above equation can be simplified as

119908119871gt120579 [(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)]

4119887119871 (1 minus 120582120572) (119887119871 + 120579) (119887

119871+ 2120579)

(A2)

So we can get Corollary 8 B Proof of Corollary 9

If (1199011198941)119878lowast

gt (119901119894

1)119861lowast then

(1 minus 120582120572) (120579119886119894 + 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 2119908

1198941205792+ 2119908119894119887119894120579 minus 1205792V minus 2120579119887

119894V) + 119888120579 (119887

119894+ 120579)

minus (1 minus 120582120572) ((119901119894

1)119878lowast

+ (119901119894

1)119861lowast

) [2 (119887119894+ 120579)2minus 1205792] gt 0

120587119878lowast

1minus 120587119861lowast

1=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

2 (119887119871+ 120579)

((119901119871

1)119878lowast

minus (119901119871

1)119861lowast

)

+(1 minus 120582120572) (120579119886119867 + 120579119904119886

119867+ 2119887119867119904119886119867+ 120579V120573 + 2119908

1198671205792+ 2119908119867119887119867120579 minus 1205792V minus 2120579119887

119867V) + 119888120579 (119887

119867+ 120579)

2 (119887119867+ 120579)

((119901119867

1)119878lowast

minus (119901119867

1)119861lowast

)

minus (1 minus 120582120572)2 (119887119871+ 120579)2minus 1205792

2 (119887119871+ 120579)

[((119901119871

1)119878lowast

)2

minus ((119901119871

1)119861lowast

)2

] minus (1 minus 120582120572)2 (119887119867+ 120579)2minus 1205792

2 (119887119867+ 120579)

[((119901119867

1)119878lowast

)2

minus ((119901119867

1)119861lowast

)2

] gt 0

(B1)

If (1199011198711)119878lowast

lt (119901119871

1)119861lowast and (119901

119867

1)119878lowast

lt (119901119867

1)119861lowast we can prove

120587119878lowast

1gt 120587119861lowast

1similarly

From Propositions 3 and 7 with (3) we obtain that

120587119861lowast

2minus 120587119878lowast

2=

120579

4 (119887119871+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119871 + V (120573 + 120579) minus 119908119871(119887119871+ 120579)]

minus 2119888 (119887119871+ 120579) + 120579 (1 minus 120582120572) ((119901

119871

1)119861lowast

+ (119901119871

1)119878lowast

)

sdot ((119901119871

1)119861lowast

minus (119901119871

1)119878lowast

) +120579

4 (119887119867+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119867 + V (120573 + 120579) minus 119908 (119887119867+ 120579)]

minus 2119888 (119887119867+ 120579) + 120579 (1 minus 120582120572) ((119901

119867

1)119861lowast

+ (119901119867

1)119878lowast

)

sdot ((119901119867

1)119861lowast

minus (119901119867

1)119878lowast

)

(B2)

Note that

119863119894

2= [(1 minus 119904) 119886119894 minus 119887

119894119901119894

2] + 120573V + 120579 (119901

119894

1+ V minus 119901

119894

2) gt 0 (B3)

so we show that

2 (1 minus 120582120572) [(1 minus 119904) 119886119894 + V (120573 + 120579) minus 119908119894(119887119894+ 120579)]

minus 2119888 (119887119894+ 120579) + 120579 (1 minus 120582120572) ((119901

119894

1)119861lowast

+ (119901119894

1)119878lowast

)

gt 0

(B4)

Thus we have the following

(1) 120587119861lowast2

gt 120587119878lowast

2 if (1199011198711)119861lowast

gt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

gt (119901119867

1)119878lowast

(2) 120587119861lowast2

= 120587119878lowast

2 if (1199011198711)119861lowast

= (119901119871

1)119878lowast and (119901

119867

1)119861lowast

= (119901119867

1)119878lowast

(3) 120587119861lowast2

lt 120587119878lowast

2 if (1199011198711)119861lowast

lt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

lt (119901119867

1)119878lowast

Combined with Corollary 8 the proposition is proved

Discrete Dynamics in Nature and Society 13

C Proof of Corollary 10

The profit of hotel from the economy rooms is as follows

120587119871

= [(1 minus 120582120572) (119904119886119871 minus 120579V) minus 119888120579] 119901119871

1

+ [(1 minus 120582120572) (119886119871 minus 119904119886119871+ 120573V + 120579V) + 119888 (119887

119871+ 120579)] 119901

119871

2

+ 2120579 (1 minus 120582120572) 119901119871

1119901119871

2minus (1 minus 120582120572) (119887119871 + 120579) (119901

119871

1)2

minus (1 minus 120582120572) (119887119871 + 120579) (119901119871

2)2

minus (119886119871minus 119904119886119871+ 120573V + 120579V) 119888

(C1)

Define (119901119871

1)119861(119878)

= (119860119871

1)119861(119878)

+ (119861119871

1)119861(119878)

119908119871 (1199011198712)119861(119878)

=

(119860119871

2)119861(119878)

+ (119861119871

2)119861(119878)

119908119871 where

(119861119871

1)119861

=3120579 (119887119871+ 120579)

4 (119887119871+ 120579)2minus 1205792

(119861119871

1)119878

=120579 (119887119871+ 120579)

2 (119887119871+ 120579)2minus 1205792

(119861119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119861119871

1)119861(119878)

+1

2

(119860119871

1)119861

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

(119860119871

1)119878

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(119860119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119860119871

1)119861(119878)

+(1 minus 120582120572) [(1 minus 119904) 119886119871 + V (120579 + 120573)] + 119888 (119887

119871+ 120579)

2 (1 minus 120582120572) (119887119871 + 120579)

(C2)

Let 120597120587119871120597119908 = 0 then we get119908lowast

119871 Similarly we can get119908lowast

119867

D Proof of Proposition 12

Let 120587119889minus 120587119903gt 0 then we can get 119904

0 where the profits of hotel

from HA and OTA are as follows

120587119889= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1)

120587119903= (1 minus 120582120572) (119908119871119863

119871

2+ 119908119867119863119867

2)

(D1)

E Proof of Corollary 11

If Δ119862119871le 120582(1 minus 120582)119876

119871 then the profit of hotel is 120587119871

11 The

derivative of 12058711987111(Δ119862119871) is 120597120587119871

11120597Δ119862119871= (1 minus 120582120572)119901

119871

1gt 0 So

with the increase of Δ119862119871 12058711987111

will increase When Δ119862119871

=

120582(1 minus 120582)119876119871 12058711987111

is maximized If Δ119862119871

ge 120582(1 minus 120582)119876119871

then the profit of hotel is 12058711987112 The derivative of 120587119871

12(Δ119862119871) is

120597120587119871

12120597Δ119862119871= (1 minus 120582120572)119901

119871

1minus (1 minus 120582)(119901

119871

1+ 119888119871) lt 0 So with the

increase of Δ119862119871 12058711987111will decline When Δ119862

119871= 120582(1 minus 120582)119876

119871

120587119871

11is maximizedSimilarly we can get Δ119862lowast

119867

F Proof of Proposition 13

Assume that the overbooking proportion is 120574119871and 120574119867

(1) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) le 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

That is

120574119867lt

120582

1 minus 120582lt 120574119871

le120582119876119871+ 119876119867[1 minus (1 minus 120582) (1 + 120574

119867)]

(1 minus 120582)119876119871

(F1)

Thus the hotel would like to overbook to get more profitrather than room vacancy

(2) Consider (1198631198711+119863119871

2)(1minus120582) lt 119876

119871and (119863119867

1+119863119867

2)(1minus120582) gt

119876119867That is 120574

119871lt 120582(1 minus 120582) lt 120574

119867 Then the profit of hotel is

120587112

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F2)

Thenwhen 119888119867119906

lt (1minus120582120572)119901119867

1(1minus120582) that is120587

112minus120587111

gt 0the hotel would carry out overbooking

(3) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

14 Discrete Dynamics in Nature and Society

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867lt 120582(1 minus 120582) Then the profit of hotel is

120587113

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2+ 119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876]

(F3)

Then when 119888119871

119906lt (1 minus 120582120572)119901

119871

1(1 minus 120582) 120587

113minus120587111

gt 0 thusthe hotel would carry out overbooking

(4) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) gt 119876

119867

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867gt (120582119876

119867+ 119876119871[1 minus (1 minus 120582)(1 + 120574

119871)])(1 minus 120582)119876

119867

Then the profit of hotel is as follows

120587114

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2) (1 minus 120582) minus 119876

119871]

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F4)

Then when 119888119871119906lt (1minus120582120572)119901

119871

1(1minus120582) and 119888119867

119906lt (1minus120582120572)119901

119867

1

(1 minus 120582) 120587114

minus 120587111

gt 0 overbooking is preferred

G Threshold Values

Threshold values are as follows

1198711= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 3119908

1198941205792+ 3119908119894119887119894120579

minus 1205792V minus 2120579119887

119894V

1198712= 2119886119894(119887119894+ 120579) minus 119904119886

119894(2119887119894+ 120579) + 120579

2119908119894+ 2 (120579 + 120573) (119887

119894

+ 120579) V + 2119908119894(119887119894+ 120579)2minus 1205792V

1198713= 4120579V119887

119894120573 minus 120579119904119886

119894119887119894+ 2V1205731198872

119894+ 31198861198941205792+ 4119886119894119887119894120579

minus 21198861198941198872

119894119904 + 3120579

2V120573 + 1205792V119887119894+ 2120579V1198872

119894+ 21198861198941198872

119894

1198714= 3119886119894119887119894120579 + 3120579

2V120573 minus 2120579V1198872119894minus 1205792V119887119894+ 31198861198941205792

+ 21198861198941198872

119894119904 + 119886119887

119894119904120579 + 3119887

119894120573V120579

1198715= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 minus 120579

2V minus 2120579119887119894V

1198661= [(1 minus 120582120572) (119904119886119894 minus 120579V) minus 119888120579] (119861

119894

1)119861(119878)

+ [(1 minus 120582120572) (119886119894 minus 119904119886119894+ 120573V + 120579V) + 119888 (119887

119894+ 120579)]

sdot (119861119894

1)119861(119878)

+ 2120579 (1 minus 120582120572) [(119860119894

1)119861(119878)

(119861119894

2)119861(119878)

+ (119861119894

1)119861(119878)

(119860119894

2)119861(119878)

] minus 2 (1 minus 120582120572) (119887119894 + 120579)

sdot [(119860119894

1)119861(119878)

(119861119894

1)119861(119878)

+ (119860119894

2)119861(119878)

(119861119894

2)119861(119878)

]

1198662= 2 (1 minus 120582120572)

sdot (119887119894+ 120579) [((119861

119894

1)119861(119878)

)

2

+ ((119861119894

2)119861(119878)

)

2

]

minus 2120579 (119861119894

1)119861(119878)

(119861119894

2)119861(119878)

1199040= ((119887119871+ 120579) (119901

119871

1)2

+ (119887119867+ 120579) (119901

119867

1)2

+ 120579119908119871(119901119871

1minus 119901119871

2) + 120579119908

119867(119901119867

1minus 119901119867

2)

+ 120579V (1199011198711+ 119901119867

1) + (119908

119871+ 119908119867) (120573 + 120579) V

+ 119908119871(119886119871minus 119887119871119901119871

2) + 119908119867(119886119867minus 119887119867119901119867

2)

minus 120579 (119901119871

1119901119871

2+ 119901119867

1119901119867

2)) (119886119871(119901119871

1+ 119908119871)

+ 119886119867(119901119867

1+ 119908119867))minus1

(G1)

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The authors thank associate editor and anonymous refereesfor their numerous constructive comments and encourage-ment that have improved their paper greatly The work waspartly supported by (i) the National Natural Science Founda-tion ofChina (71201083 71572058 and 71571100) (ii) the Fun-damental Research Funds for the Central Universities SCUT(2015ZZ057) (iii) Jiangsu Province Science Foundation forYouths (BK2012379) and (iv) the Fundamental ResearchFunds for the Central Universities (NS2015076)

References

[1] J Li W N Zhang H Xu and J Jiang ldquoDynamic competitionand cooperation of road infrastructure investment of multipletourism destinations a case Study of Xidi and Hongcun WorldCulturalHeritagerdquoDiscreteDynamics inNature and Society vol2015 Article ID 962028 10 pages 2015

[2] T Paksoy EOzceylan andG-WWeber ldquoProfit oriented supplychain network optimizationrdquoCentral European Journal of Oper-ations Research vol 21 no 2 pp 455ndash478 2013

[3] X Zhang H Song and G Q Huang ldquoTourism supply chainmanagement a new research agendardquo Tourism Managementvol 30 no 3 pp 345ndash358 2009

[4] Z Yang and J Cai ldquoDo regional factors matter Determinantsof hotel industry performance in Chinardquo TourismManagementvol 52 pp 242ndash253 2016

[5] B Pan L Zhang and R Law ldquoThe complex matter of onlinehotel choicerdquoCornell Hospitality Quarterly vol 54 no 1 pp 74ndash83 2013

[6] L Ling X Guo and C Yang ldquoOpening the online marketplacean examination of hotel pricing and travel agency on-line

Discrete Dynamics in Nature and Society 15

distribution of roomsrdquo Tourism Management vol 45 pp 234ndash243 2014

[7] L Ling Y Dong X Guo and L Liang ldquoAvailability man-agement of hotel rooms under cooperation with online travelagenciesrdquo International Journal of Hospitality Management vol50 pp 145ndash152 2015

[8] J N K Liu andE Y Zhang ldquoAn investigation of factors affectingcustomer selection of online hotel booking channelsrdquo Interna-tional Journal of Hospitality Management vol 39 pp 71ndash832014

[9] L Fox ldquoFour Seasons Unveils $18 Million Website as LuxuryTravel Growsrdquo 2012 httpwwwtnoozcomarticlefour-sea-sons-unveils-18-million-dollar-website-as-luxury-travel-grows

[10] C-M Chen and Y-C Lin ldquoThe influence of uncertain demandon hotel capacityrdquo International Journal of Hospitality Manage-ment vol 34 no 1 pp 462ndash465 2013

[11] S Yang G Q Huang H Song and L Liang ldquoGame-theoreticapproach to competition dynamics in tourism supply chainsrdquoJournal of Travel Research vol 47 no 4 pp 425ndash439 2009

[12] G Q Huang H Song and X Zhang ldquoA comparative analysis ofquantity and price competitions in tourism supply chain net-works for package holidaysrdquo Service Industries Journal vol 30no 10 pp 1593ndash1606 2010

[13] Y Huang H Song G Q Huang and J Lou ldquoA comparativestudy of tourism supply chains with quantity competitionrdquoJournal of Travel Research vol 51 no 6 pp 717ndash729 2012

[14] H K Lee and Y Fernando ldquoThe antecedents and outcomes ofthe medical tourism supply chainrdquo Tourism Management vol46 pp 148ndash157 2015

[15] W-Y K Chiang D Chhajed and J D Hess ldquoDirect marketingindirect profits a strategic analysis of dual-channel supply-chain designrdquoManagement Science vol 49 no 1 pp 1ndash20 2003

[16] A A Tsay and N Agrawal ldquoChannel conflict and coordinationin the E-commerce agerdquo Production and Operations Manage-ment vol 13 no 1 pp 93ndash110 2004

[17] Q-H Li and B Li ldquoDual-channel supply chain equilibriumproblems regarding retail services and fairness concernsrdquoApplied Mathematical Modelling 2016

[18] S Panda N M Modak S S Sana and M Basu ldquoPricingand replenishment policies in dual-channel supply chain undercontinuous unit cost decreaserdquo Applied Mathematics and Com-putation vol 256 pp 913ndash929 2015

[19] Y Liu C Ding C Fan and X Chen ldquoPricing decision underdual-channel structure considering fairness and free-ridingbehaviorrdquo Discrete Dynamics in Nature and Society vol 2014Article ID 536576 10 pages 2014

[20] J Chen H Zhang and Y Sun ldquoImplementing coordinationcontracts in a manufacturer Stackelberg dual-channel supplychainrdquo Omega vol 40 no 5 pp 571ndash583 2012

[21] Q Ding C Dong and Z Pan ldquoA hierarchical pricing decisionprocess on a dual-channel problem with one manufacturer andone retailerrdquo International Journal of Production Economics vol175 pp 197ndash212 2016

[22] B Rodriguez and G Aydin ldquoPricing and assortment decisionsfor a manufacturer selling through dual channelsrdquo EuropeanJournal of Operational Research vol 242 no 3 pp 901ndash9092015

[23] T Lockyer ldquoThe perceived importance of price as one hotelselection dimensionrdquo Tourism Management vol 26 no 4 pp529ndash537 2005

[24] C-M Chen H-W Yang E Y Li and C-C Liu ldquoHow doeshotel pricing influence guest satisfaction by the moderatinginfluence of room occupancyrdquo International Journal of Hospi-tality Management vol 49 pp 136ndash138 2015

[25] J-M Espinet M Fluvia R Rigall-I-Torrent and A Salo ldquoHotelcharacteristics and seasonality in prices an analysis usingSpanish tour operatorsrsquo brochuresrdquo Tourism Economics vol 18no 4 pp 749ndash767 2012

[26] C Juaneda J M Raya and F Sastre ldquoPricing the time and loca-tion of a stay at a hotel or apartmentrdquo Tourism Economics vol17 no 2 pp 321ndash338 2011

[27] G Abrate G Fraquelli and G Viglia ldquoDynamic pricing strate-gies evidence from European hotelsrdquo International Journal ofHospitality Management vol 31 no 1 pp 160ndash168 2012

[28] D Q Yao and J J Liu ldquoCompetitive pricing of mixed retail ande-tail distribution channelsrdquo Omega vol 33 no 3 pp 235ndash2472005

[29] J Zhao and L Wang ldquoPricing and retail service decisionsin fuzzy uncertainty environmentsrdquo Applied Mathematics andComputation vol 250 pp 580ndash592 2015

[30] A A Tsay and N Agrawal ldquoChannel dynamics under priceand service competitionrdquo Manufacturing amp Service OperationsManagement vol 2 no 4 pp 372ndash391 2000

[31] S C Choi ldquoPrice competition in a duopoly common retailerchannelrdquo Journal of Retailing vol 72 no 2 pp 117ndash134 1996

[32] Y Bakos andE Brynjolfsson ldquoBundling and competition on theinternetrdquoMarketing Science vol 19 no 1 pp 63ndash82 2000

[33] H Song J H Kim and S Yang ldquoConfidence intervals fortourism demand elasticityrdquo Annals of Tourism Research vol 37no 2 pp 377ndash396 2010

[34] DMHanssens L J Parsons andR L SchultzMarket ResponseModels Econometric and Time Series Analysis Kluwer Aca-demic Publishers Boston Mass USA 2nd edition 2001

[35] H Kurata D-Q Yao and J J Liu ldquoPricing policies under directvs indirect channel competition and national vs store brandcompetitionrdquo European Journal of Operational Research vol180 no 1 pp 262ndash281 2007

[36] R Law and C Cheung ldquoA study of the perceived importance ofthe overall website quality of different classes of hotelsrdquo Inter-national Journal of Hospitality Management vol 25 no 3 pp525ndash531 2006

[37] K B Chen ldquoProcurement strategies and coordination mecha-nism of the supply chain with one manufacturer and multiplesuppliersrdquo International Journal of Production Economics vol138 no 1 pp 125ndash135 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Discrete Dynamics in Nature and Society

provide a free upgrade endorse the ticket or provide com-pensation for the customers according to specific situationCompared to the hotels the airlines cannot transfer cus-tomers to other companies The air ticket alteration will usu-ally disrupt customersrsquo traveling schedule Though the over-booking by airlines has been well studied in the literature ourresearch is new in the hospitality industry by considering theoverbooking withwithout room transfer with the hope thatcertain implications can be enlightened to the hotel man-agers

The hotel wants to increase the occupancy rates toincrease the profits through overbooking However over-booking will lead to the risk that the actual occupancyamount is greater than the number of hotel roomsThereforethe hotel has to provide compensation to travelers who can-not check in that is overbooking cost The greater the num-bers of overbooking the less the probability of room vacancybut at the same time travelers are more likely to be refusedby the hotel Therefore the hotel must balance between thevacancy lost and the overbooking costs We develop a modelto analyze the overbooking choice

In reality the OTA is always a crucial partner of hotelsfor it can attract a large number of customers for hotelsand improve their occupancy rates [36] Spontaneously theOTA plays an increasingly significant role in the distributionsystems of hotels [5 7] By contrast the HA mainly providesa platform for individual guest Compared with individualcustomers hotel pays more attention to the long-term coop-eration relationship with the OTA Therefore in our modelwe assume that when the market demand is greater than thesupply and the hotel does not carry out overbooking the hotelwould give priority to customers who are booking fromOTA

61 Without Room Transfer Here we consider the casewith no room transfer When the actual occupancy amountexceeds the total quantity of rooms the hotel does not arrangeother alternative accommodation for the customers who can-not check in But the hotel must pay the loss of goodwill costSuppose that the overbooking quantity of economy and lux-ury rooms isΔ119862

119871andΔ119862

119867and the overbooking cost is 119888

119871and

119888119867 respectivelyWe discuss economy roomsrsquo overbooking The actual

occupancy can be either of the following two cases (1) when119876119871

lt 119863119871

1+ 119863119871

2le 119876119871+ Δ119862

119871 the reservation amount of

rooms is 1198631198711+ 119863119871

2 so the actual occupancy amount is (119863119871

1+

119863119871

2)(1 minus 120582) (2) when119863

119871

1+ 119863119871

2gt 119876119871+ Δ119862

119871 the reservation

amount is 119876119871+ Δ119862119871 then the actual occupancy amount is

(119876119871+Δ119862119871)(1 minus 120582) Therefore if (119876

119871+Δ119862119871)(1 minus 120582) le 119876

119871 that

is Δ119862119871le 120582119876119871(1 minus 120582) the profit of hotel is

120587119871

11= (1 minus 120582120572) [119901

119871

1(119876119871+ Δ119862119871minus 119863119871

2) + 119908119871119863119871

2] (11)

If (119876119871+ Δ119862119871)(1 minus 120582) ge 119876

119871 that is Δ119862

119871ge 120582119876119871(1 minus 120582)

the economy roomsrsquo actual occupancy amount exceeds theeconomy roomsrsquo number in the hotel so the hotel must paythe overbooking cost then the profit of hotel is

120587119871

12= (1 minus 120582120572) [119901

119871

1(119876119871+ Δ119862119871minus 119863119871

2) + 119908119871119863119871

2]

minus (119901119871

1+ 119888119871) [(119876119871+ Δ119862119871) (1 minus 120582) minus 119876

119871]

(12)

Proposition 12 Without considering roomsrsquo transfer the opti-mal overbooking quantity of economy rooms and luxury roomsis

Δ119862lowast

119894=

120582

1 minus 120582119876119894 119894 = 119871119867 (13)

FromProposition 12 we know that the higher the propor-tion of customer cancellations and no-show is the larger theoptimal overbooking quantity of the hotel will be With theincrease of 120572 the penalty that customers need to pay for theircancellation or no-show decreases Two following extremesituations are considered When 120572 = 1 the hotel will returnall the guarantee fee in case of customersrsquo cancellation or no-showThat is the same as the hotel does not charge customersany guarantee fee when customers book the rooms Undersuch circumstances customers can book rooms for severaldays firstly after they identify a specific itinerary they cancancel the extra rooms for they do not suffer any loss It is nodoubt that such regulation will increase the cancellation andno-show rate On the other hand if 120572 = 1 all the guaranteefee will not be returned after cancellation or no-show In thiscase customers need to reserve a room cautiously If it is notnecessary customers will not choose cancellation or no-showbecause the penalty cost is too high Such policy will reducethe cancellation and no-show rate Spontaneously to someextent 120572 and 120582 are positive correlation When the hotelincreases proportion 120572 it would like to increase the over-booking quantity so as to increase the actual occupancy rateNowadays the time-limited orders are widely used amonghotels Such regulation cannot only reduce customersrsquo lossfor the change of schedule but also help the hotel confirmthe orders so as to handle the overbooking phenomenon inadvance

In addition the risk of overbooking the economy roomsis relatively lower than the luxury rooms Compared toeconomic rooms it is more difficult for the hotel to findalternative luxury rooms to satisfy the customers Naturallyoverbooking cost of luxury room is higher For instance ifeconomy rooms are overbooked the hotel can transfer thecustomers to luxury rooms and the customers are willingto accept By contrast if luxury rooms are overbooked cus-tomers are not willing to accept the adjustment from luxuryrooms to economic rooms This implies that the hotel has topay a higher default costTherefore the hotel should be morecareful to choose the overbooking quantity of luxury rooms

62 With Room Transfer The following discusses the casewith room transfer Firstly when the economy rooms areinsufficient and luxury rooms have a surplus customers cancheck in the hotelrsquos luxury rooms with the price of economyrooms Customers spend the same money and can enjoybetter service so they are willing to accept this adjustmentSecondly when the luxury roomsrsquo actual occupancy amountexceeds the number of luxury rooms in the hotel the hotelusually transfers customers to other hotels nearby that havethe same level and same type because the customers whobook luxury room have a high requirement Customers canenjoy the same service so they are willing to accept this trans-fer However the hotelrsquos credibility in customersrsquo mind will be

Discrete Dynamics in Nature and Society 9

damaged and it must pay the additional costsThirdly if boththe economy rooms and luxury rooms are unable to meetthe demand the hotel usually transfers the customers whocannot check in to other hotels Note that when119863119894

1+119863119894

2gt 119876119894

119894 = 119871119867 if the hotel does not overbook its profit is

120587111

= (1 minus 120582120572) [119901119871

1(119876119871minus 119863119871

2) + 119901119867

1(119876119867minus 119863119867

2)

+ 119908119871119863119871

2+ 119908119867119863119867

2]

(14)

Proposition 13 With room transfer there exists threshold unitoverbooking cost 119888

1198940 such that if 119888

119894lt 1198881198940 then overbooking is

profitable for the hotel where

1198881198940=(1 minus 120582120572) 119901

119894

1

1 minus 120582 119894 = 119871119867 (15)

From Propositions 12 and 13 we conclude that the hotelshould control the overbooking quantity in a certain rangeto prevent lacking of rooms If the overbooking proportionis too large then the hotel may face a loss Only when theoverbooking cost is low the hotel can obtain additional profitOtherwise if the overbooking cost exceeds a certain valuethe hotelrsquos profit would be lower when it carries out over-booking As the market demand increases the supply is closeto saturation and then the overbooking costs will be higherTherefore when the market demand is excessive the hotelshould strictly control the proportion of overbooking Inaddition if the number of hotels that have the same level andtype in the same region is little that is the possibility to trans-fer customer is small then the hotel should lower the propor-tion of overbooking

The proportion of overbooking depends on the propor-tion of customer cancellations andno-showaswell as the totalnumber of hotel rooms so the hotel can analyze the historicaldata to develop an appropriate overbooking proportion so asto maximize the hotelrsquos expected profit

Proposition 14 When the economy rooms and luxury roomsare both overbooked the optimal centralized prices are asfollows 119894 = 119871119867

119901119894lowast

14= 119901119894lowast

1+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

119901119894lowast

24= 119901119894lowast

2+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

(16)

Bertrand and Stackelberg prices are as follows

(119901119894

14)119861lowast

= (119901119894

1)119861lowast

+2119888119894

119906119887119894(119887119894+ 120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

24)119861lowast

= (119901119894

2)119861lowast

+120579119888119894

119906119887119894 (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

14)119878lowast

= (119901119894

1)119878lowast

+119888119894

119906119887119894(2119887119894+ 3120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 21205792]

(119901119894

24)119878lowast

=120579 (119901119894

14)119878lowast

+ (1 minus 119904) 119886119894 + V (120579 + 120573) + 119908119894(119887119894+ 120579)

2 (119887119894+ 120579)

+119888

2 (1 minus 120582120572)

(17)

For the hotel the premise to overbook rooms is that themarket demand is greater than the supply When the hotelfaces the risk of overbooking the equilibrium prices in bothcentralized and decentralized decision-making supply chainwill improve In the busy season in order to reduce the riskof overbooking the hotel would increase the prices and theincrement will increase as the transfer cost increases From(16) and (17) we can know that the increment in centralizeddecision-making model is the greatest and that in Bertrandgame is the smallest

7 Numerical Analysis

In this section we do some numerical experiment to gainmore insights According to the China Hotel Sales Chan-nel Report by I-Research (httpreportiresearchcnreport2013031892shtml) there are 381 of the hotels that aresuitable for high-end travelers and 619 of the hotels thatare suitable for low-end travelersTherefore this part assumesthat the proportion of the economical rooms and the luxuryrooms is 4 6 that is 119886

119871= 06119886 119886

119867= 04119886 Other parameter

settings are made as follows 119886 = 600 119904 = 05 and 119887119871= 06

119887119867= 02 120573 = 120579 = 05 120578 = 004 120572 = 08 120582 = 01 119908

119894= 05119901

119894

1

(119894 = 119871119867) In the following we investigate the impact of V onthe optimal prices and profits

When V = 0 that is the OTA does not offer any servicethen the optimal prices of HA are equal to the prices ofOTA Since 119887

119871gt 120573 gt 119887

119867 then the market of economy

rooms is service-oriented while the market of luxury roomsis price-oriented FromFigure 2 we can know that whenOTAoffers more services OTArsquos optimal price will be increasedaccordingly It is reasonable that if V increases the cost ofOTAwill also definitely increase With the increase of V 119901119871lowast

1will

decline slowly while 119901119867lowast1

will increaseThe OTArsquos profit status becomes better with the improve-

ment of its price But as the V increases the cost of OTA willalso definitely increase When V is equal to 27 then the profitof OTA is the highest If V is larger then the high costs willreduce the profits of OTAWhen V is equal to 34 the profit ofthewhole supply chain is the highest So from the perspectiveof the supply chain V is expected to be 34 rather than 27Similarly for the integrated system the profit of the OTAalso rises first and then declines with the increase of V Aftercalculationwe can get thatwhen V = 27 both120587119861lowast

2and120587119878lowast2will

be the highest From Figures 3 and 4 we know that the OTAwould tend to offer service that valued 27 so as to maximizeits own profit

After calculation we can conclude that when V = 34 then120587119861lowast is highest when V = 35 then 120587

119878lowast is highest (Figure 5)

10 Discrete Dynamics in Nature and Society

0 10 20 30 40 50 60 70 80100

150

200

250

300

350

400

450

Pric

e

pLlowast

1

pLlowast

2

pHlowast

1

pHlowast

2

Value added by OTArsquos services ()

Figure 2 Equilibrium prices in the integrated system

0 10 20 30 40 50 60 70 800

1

2

3

4

5

6

7

Profi

t

times104

120587lowast

1

120587lowast

2

120587lowast

Value added by OTArsquos services ()

Figure 3 Profits in the integrated system

From the perspective of the supply chain theOTA is expectedto offer more services Despite the rising cost of OTA willlower its profit the hotel can lower the wholesale prices tocoordinate the distribution of profits so as to achieve a win-win situation

In the following we focus on the comparison of differentchannelrsquos profit in each model Figure 6 depicts the curves ofthe total profits of the HAOTA channels in the integratedsystem with respect to V Figure 7 draws the curves of the dif-ferent channelsrsquo profits under both Bertrand and Stackelberggame The profit of the HA channel refers to the profit thatthe hotel derived from the HA channelThe profit of the OTA

0 10 20 30 40 50 60125

13

135

14

145

15

155

16

165

Profi

t

times104

120587Blowast

2

120587Slowast

2

Value added by OTArsquos services ()

Figure 4 OTArsquos profits under two games

0 10 20 30 40 50 60 70 8052

53

54

55

56

57

58

59

6

61

62

Profi

t

times104

120587Blowast

2

120587Slowast

2120587lowast

Value added by OTArsquos services ()

Figure 5 The profit comparison

channel involves the OTArsquos profit and the hotelrsquos profit gainedfrom the OTA channel

As shown in Figures 6 and 7 with the increase of V theprofit of the OTA channel will increase first and will thendecrease This indicates that a high level of service by OTAwill be detrimental to the channel profit That is because ahigh level of service will bring a high cost undoubtedly Forthe integrated model and Bertrand game model this disad-vantage is more evident The OTArsquos service can motivate theactual purchase behavior of customers in the OTA channelWhen V is relatively lower the additional profits from OTArsquos

Discrete Dynamics in Nature and Society 11

0 10 20 30 40 50 60 70 8018

2

22

24

26

28

3

32

34

36

38

4

Profi

t

HA channelOTA channel

times104

Value added by OTArsquos services ()

Figure 6 Channel profits in the integrated system

0 10 20 30 40 50 60 70 8005

1

15

2

25

3

35

4

45

Profi

t

HA channel in Bertrand gameOTA channel in Bertrand gameHA channel in Stackelberg gameOTA channel in Stackelberg game

times104

Value added by OTArsquos services ()

Figure 7 Channel profits in two games

service are enough to compensate for the cost In this casethe hotel and the OTA can get more profit from providing theservice However when V is high the additional profits fromOTArsquos service cannot make up for the high cost In such phe-nomenon the OTA should not increase investment in ser-vice

For both integrated model and Bertrand game modelwith the increase of V the profit of the HA channel willdecrease first and will then increase while in the Stackelberggamemodel the profit of theHA channel will always increase

with V With Figure 2 we can know that when OTA providesmore additional services it tends to increase its price Someof the customers will turn to reserve rooms from the HAbecause of the excessively high price in OTA As a result thehotel can gain more profits from the HA channel

8 Conclusion

With the development of e-commerce the providers oftourism products are more inclined to build dual-channelsIn this paper we consider the direct selling channel of HAand the traditional retail channel ofOTA from the perspectiveof tourism supply chain We develop a two-echelon tourismsupply chain model involving one hotel and one OTA wheretheOTAprovides related service Customers will be refundedpartially in case of cancelation or no-show We investigatethe optimal pricing strategies under several common casesThe integrated operation and the decentralized operationbased on Bertrand and Stackelberg games are studied andcorresponding equilibrium pricing policies are obtained

Our findings demonstrate that the hotel plays a crucialrole in optimizing the benefits of supply chain Consideringthe overall profit of the supply chain the hotel should act as aleader in dual-channel supply chain and formulate reasonablewholesale prices to improve the cooperative enthusiasm ofOTA so as to achieve optimization of the whole supplychain A lower wholesale price can help reduce OTArsquos loss ofprofit because of the opening of HA channel In addition weconsider the overbooking of the hotel and obtain the optimaloverbooking quantity We conclude that the hotel can alwaysobtain higher profits when the overbooking proportion iscontrolledwithin a certain range Otherwise if the overbook-ing proportion is too high the hotel can get extra profits onlywhen the overbooking cost is lower than a certain value

The contribution of this paper is that we extend tourismsupply chain to the dual-channel structure in which the hotelopens its direct channel to sell tourism products And theextant literature only refers to the single channel In additionwe realize that customer cancellations andno-showoccur fre-quently in hotel industry Thus we develop the game modelsbased on such phenomenon At last we derive the conditionsunder which the hotel dominant case is profitable for boththe supply chain members Our results can provide hotelsand OTAs with some new managerial insights under thedual-channel environment

This research can be extended in several directions infuture work For example in this paper we assume that allinformation is known to the hotel and OTA However someinformation could be asymmetric (eg see Chen [37]) Thuswe can explore the Bayesian equilibrium under asymmetricinformation settings Secondly the assumption of lineardemand is a limitation of this paperWe can further study thedynamic pricing in tourism dual-channel supply chain

Appendix

A Proof of Corollary 8

First we set (1199011198711)119861lowast

gt (119901119871

1)119878lowast which can be expressed as

12 Discrete Dynamics in Nature and Society

(1 minus 120582120572) (120579119886119871 + 120579119904119886119871+ 2119887119871119904119886119871+ 120579V120573 + 3119908

1198711205792+ 3119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

gt(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(A1)

The above equation can be simplified as

119908119871gt120579 [(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)]

4119887119871 (1 minus 120582120572) (119887119871 + 120579) (119887

119871+ 2120579)

(A2)

So we can get Corollary 8 B Proof of Corollary 9

If (1199011198941)119878lowast

gt (119901119894

1)119861lowast then

(1 minus 120582120572) (120579119886119894 + 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 2119908

1198941205792+ 2119908119894119887119894120579 minus 1205792V minus 2120579119887

119894V) + 119888120579 (119887

119894+ 120579)

minus (1 minus 120582120572) ((119901119894

1)119878lowast

+ (119901119894

1)119861lowast

) [2 (119887119894+ 120579)2minus 1205792] gt 0

120587119878lowast

1minus 120587119861lowast

1=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

2 (119887119871+ 120579)

((119901119871

1)119878lowast

minus (119901119871

1)119861lowast

)

+(1 minus 120582120572) (120579119886119867 + 120579119904119886

119867+ 2119887119867119904119886119867+ 120579V120573 + 2119908

1198671205792+ 2119908119867119887119867120579 minus 1205792V minus 2120579119887

119867V) + 119888120579 (119887

119867+ 120579)

2 (119887119867+ 120579)

((119901119867

1)119878lowast

minus (119901119867

1)119861lowast

)

minus (1 minus 120582120572)2 (119887119871+ 120579)2minus 1205792

2 (119887119871+ 120579)

[((119901119871

1)119878lowast

)2

minus ((119901119871

1)119861lowast

)2

] minus (1 minus 120582120572)2 (119887119867+ 120579)2minus 1205792

2 (119887119867+ 120579)

[((119901119867

1)119878lowast

)2

minus ((119901119867

1)119861lowast

)2

] gt 0

(B1)

If (1199011198711)119878lowast

lt (119901119871

1)119861lowast and (119901

119867

1)119878lowast

lt (119901119867

1)119861lowast we can prove

120587119878lowast

1gt 120587119861lowast

1similarly

From Propositions 3 and 7 with (3) we obtain that

120587119861lowast

2minus 120587119878lowast

2=

120579

4 (119887119871+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119871 + V (120573 + 120579) minus 119908119871(119887119871+ 120579)]

minus 2119888 (119887119871+ 120579) + 120579 (1 minus 120582120572) ((119901

119871

1)119861lowast

+ (119901119871

1)119878lowast

)

sdot ((119901119871

1)119861lowast

minus (119901119871

1)119878lowast

) +120579

4 (119887119867+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119867 + V (120573 + 120579) minus 119908 (119887119867+ 120579)]

minus 2119888 (119887119867+ 120579) + 120579 (1 minus 120582120572) ((119901

119867

1)119861lowast

+ (119901119867

1)119878lowast

)

sdot ((119901119867

1)119861lowast

minus (119901119867

1)119878lowast

)

(B2)

Note that

119863119894

2= [(1 minus 119904) 119886119894 minus 119887

119894119901119894

2] + 120573V + 120579 (119901

119894

1+ V minus 119901

119894

2) gt 0 (B3)

so we show that

2 (1 minus 120582120572) [(1 minus 119904) 119886119894 + V (120573 + 120579) minus 119908119894(119887119894+ 120579)]

minus 2119888 (119887119894+ 120579) + 120579 (1 minus 120582120572) ((119901

119894

1)119861lowast

+ (119901119894

1)119878lowast

)

gt 0

(B4)

Thus we have the following

(1) 120587119861lowast2

gt 120587119878lowast

2 if (1199011198711)119861lowast

gt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

gt (119901119867

1)119878lowast

(2) 120587119861lowast2

= 120587119878lowast

2 if (1199011198711)119861lowast

= (119901119871

1)119878lowast and (119901

119867

1)119861lowast

= (119901119867

1)119878lowast

(3) 120587119861lowast2

lt 120587119878lowast

2 if (1199011198711)119861lowast

lt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

lt (119901119867

1)119878lowast

Combined with Corollary 8 the proposition is proved

Discrete Dynamics in Nature and Society 13

C Proof of Corollary 10

The profit of hotel from the economy rooms is as follows

120587119871

= [(1 minus 120582120572) (119904119886119871 minus 120579V) minus 119888120579] 119901119871

1

+ [(1 minus 120582120572) (119886119871 minus 119904119886119871+ 120573V + 120579V) + 119888 (119887

119871+ 120579)] 119901

119871

2

+ 2120579 (1 minus 120582120572) 119901119871

1119901119871

2minus (1 minus 120582120572) (119887119871 + 120579) (119901

119871

1)2

minus (1 minus 120582120572) (119887119871 + 120579) (119901119871

2)2

minus (119886119871minus 119904119886119871+ 120573V + 120579V) 119888

(C1)

Define (119901119871

1)119861(119878)

= (119860119871

1)119861(119878)

+ (119861119871

1)119861(119878)

119908119871 (1199011198712)119861(119878)

=

(119860119871

2)119861(119878)

+ (119861119871

2)119861(119878)

119908119871 where

(119861119871

1)119861

=3120579 (119887119871+ 120579)

4 (119887119871+ 120579)2minus 1205792

(119861119871

1)119878

=120579 (119887119871+ 120579)

2 (119887119871+ 120579)2minus 1205792

(119861119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119861119871

1)119861(119878)

+1

2

(119860119871

1)119861

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

(119860119871

1)119878

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(119860119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119860119871

1)119861(119878)

+(1 minus 120582120572) [(1 minus 119904) 119886119871 + V (120579 + 120573)] + 119888 (119887

119871+ 120579)

2 (1 minus 120582120572) (119887119871 + 120579)

(C2)

Let 120597120587119871120597119908 = 0 then we get119908lowast

119871 Similarly we can get119908lowast

119867

D Proof of Proposition 12

Let 120587119889minus 120587119903gt 0 then we can get 119904

0 where the profits of hotel

from HA and OTA are as follows

120587119889= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1)

120587119903= (1 minus 120582120572) (119908119871119863

119871

2+ 119908119867119863119867

2)

(D1)

E Proof of Corollary 11

If Δ119862119871le 120582(1 minus 120582)119876

119871 then the profit of hotel is 120587119871

11 The

derivative of 12058711987111(Δ119862119871) is 120597120587119871

11120597Δ119862119871= (1 minus 120582120572)119901

119871

1gt 0 So

with the increase of Δ119862119871 12058711987111

will increase When Δ119862119871

=

120582(1 minus 120582)119876119871 12058711987111

is maximized If Δ119862119871

ge 120582(1 minus 120582)119876119871

then the profit of hotel is 12058711987112 The derivative of 120587119871

12(Δ119862119871) is

120597120587119871

12120597Δ119862119871= (1 minus 120582120572)119901

119871

1minus (1 minus 120582)(119901

119871

1+ 119888119871) lt 0 So with the

increase of Δ119862119871 12058711987111will decline When Δ119862

119871= 120582(1 minus 120582)119876

119871

120587119871

11is maximizedSimilarly we can get Δ119862lowast

119867

F Proof of Proposition 13

Assume that the overbooking proportion is 120574119871and 120574119867

(1) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) le 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

That is

120574119867lt

120582

1 minus 120582lt 120574119871

le120582119876119871+ 119876119867[1 minus (1 minus 120582) (1 + 120574

119867)]

(1 minus 120582)119876119871

(F1)

Thus the hotel would like to overbook to get more profitrather than room vacancy

(2) Consider (1198631198711+119863119871

2)(1minus120582) lt 119876

119871and (119863119867

1+119863119867

2)(1minus120582) gt

119876119867That is 120574

119871lt 120582(1 minus 120582) lt 120574

119867 Then the profit of hotel is

120587112

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F2)

Thenwhen 119888119867119906

lt (1minus120582120572)119901119867

1(1minus120582) that is120587

112minus120587111

gt 0the hotel would carry out overbooking

(3) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

14 Discrete Dynamics in Nature and Society

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867lt 120582(1 minus 120582) Then the profit of hotel is

120587113

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2+ 119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876]

(F3)

Then when 119888119871

119906lt (1 minus 120582120572)119901

119871

1(1 minus 120582) 120587

113minus120587111

gt 0 thusthe hotel would carry out overbooking

(4) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) gt 119876

119867

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867gt (120582119876

119867+ 119876119871[1 minus (1 minus 120582)(1 + 120574

119871)])(1 minus 120582)119876

119867

Then the profit of hotel is as follows

120587114

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2) (1 minus 120582) minus 119876

119871]

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F4)

Then when 119888119871119906lt (1minus120582120572)119901

119871

1(1minus120582) and 119888119867

119906lt (1minus120582120572)119901

119867

1

(1 minus 120582) 120587114

minus 120587111

gt 0 overbooking is preferred

G Threshold Values

Threshold values are as follows

1198711= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 3119908

1198941205792+ 3119908119894119887119894120579

minus 1205792V minus 2120579119887

119894V

1198712= 2119886119894(119887119894+ 120579) minus 119904119886

119894(2119887119894+ 120579) + 120579

2119908119894+ 2 (120579 + 120573) (119887

119894

+ 120579) V + 2119908119894(119887119894+ 120579)2minus 1205792V

1198713= 4120579V119887

119894120573 minus 120579119904119886

119894119887119894+ 2V1205731198872

119894+ 31198861198941205792+ 4119886119894119887119894120579

minus 21198861198941198872

119894119904 + 3120579

2V120573 + 1205792V119887119894+ 2120579V1198872

119894+ 21198861198941198872

119894

1198714= 3119886119894119887119894120579 + 3120579

2V120573 minus 2120579V1198872119894minus 1205792V119887119894+ 31198861198941205792

+ 21198861198941198872

119894119904 + 119886119887

119894119904120579 + 3119887

119894120573V120579

1198715= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 minus 120579

2V minus 2120579119887119894V

1198661= [(1 minus 120582120572) (119904119886119894 minus 120579V) minus 119888120579] (119861

119894

1)119861(119878)

+ [(1 minus 120582120572) (119886119894 minus 119904119886119894+ 120573V + 120579V) + 119888 (119887

119894+ 120579)]

sdot (119861119894

1)119861(119878)

+ 2120579 (1 minus 120582120572) [(119860119894

1)119861(119878)

(119861119894

2)119861(119878)

+ (119861119894

1)119861(119878)

(119860119894

2)119861(119878)

] minus 2 (1 minus 120582120572) (119887119894 + 120579)

sdot [(119860119894

1)119861(119878)

(119861119894

1)119861(119878)

+ (119860119894

2)119861(119878)

(119861119894

2)119861(119878)

]

1198662= 2 (1 minus 120582120572)

sdot (119887119894+ 120579) [((119861

119894

1)119861(119878)

)

2

+ ((119861119894

2)119861(119878)

)

2

]

minus 2120579 (119861119894

1)119861(119878)

(119861119894

2)119861(119878)

1199040= ((119887119871+ 120579) (119901

119871

1)2

+ (119887119867+ 120579) (119901

119867

1)2

+ 120579119908119871(119901119871

1minus 119901119871

2) + 120579119908

119867(119901119867

1minus 119901119867

2)

+ 120579V (1199011198711+ 119901119867

1) + (119908

119871+ 119908119867) (120573 + 120579) V

+ 119908119871(119886119871minus 119887119871119901119871

2) + 119908119867(119886119867minus 119887119867119901119867

2)

minus 120579 (119901119871

1119901119871

2+ 119901119867

1119901119867

2)) (119886119871(119901119871

1+ 119908119871)

+ 119886119867(119901119867

1+ 119908119867))minus1

(G1)

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The authors thank associate editor and anonymous refereesfor their numerous constructive comments and encourage-ment that have improved their paper greatly The work waspartly supported by (i) the National Natural Science Founda-tion ofChina (71201083 71572058 and 71571100) (ii) the Fun-damental Research Funds for the Central Universities SCUT(2015ZZ057) (iii) Jiangsu Province Science Foundation forYouths (BK2012379) and (iv) the Fundamental ResearchFunds for the Central Universities (NS2015076)

References

[1] J Li W N Zhang H Xu and J Jiang ldquoDynamic competitionand cooperation of road infrastructure investment of multipletourism destinations a case Study of Xidi and Hongcun WorldCulturalHeritagerdquoDiscreteDynamics inNature and Society vol2015 Article ID 962028 10 pages 2015

[2] T Paksoy EOzceylan andG-WWeber ldquoProfit oriented supplychain network optimizationrdquoCentral European Journal of Oper-ations Research vol 21 no 2 pp 455ndash478 2013

[3] X Zhang H Song and G Q Huang ldquoTourism supply chainmanagement a new research agendardquo Tourism Managementvol 30 no 3 pp 345ndash358 2009

[4] Z Yang and J Cai ldquoDo regional factors matter Determinantsof hotel industry performance in Chinardquo TourismManagementvol 52 pp 242ndash253 2016

[5] B Pan L Zhang and R Law ldquoThe complex matter of onlinehotel choicerdquoCornell Hospitality Quarterly vol 54 no 1 pp 74ndash83 2013

[6] L Ling X Guo and C Yang ldquoOpening the online marketplacean examination of hotel pricing and travel agency on-line

Discrete Dynamics in Nature and Society 15

distribution of roomsrdquo Tourism Management vol 45 pp 234ndash243 2014

[7] L Ling Y Dong X Guo and L Liang ldquoAvailability man-agement of hotel rooms under cooperation with online travelagenciesrdquo International Journal of Hospitality Management vol50 pp 145ndash152 2015

[8] J N K Liu andE Y Zhang ldquoAn investigation of factors affectingcustomer selection of online hotel booking channelsrdquo Interna-tional Journal of Hospitality Management vol 39 pp 71ndash832014

[9] L Fox ldquoFour Seasons Unveils $18 Million Website as LuxuryTravel Growsrdquo 2012 httpwwwtnoozcomarticlefour-sea-sons-unveils-18-million-dollar-website-as-luxury-travel-grows

[10] C-M Chen and Y-C Lin ldquoThe influence of uncertain demandon hotel capacityrdquo International Journal of Hospitality Manage-ment vol 34 no 1 pp 462ndash465 2013

[11] S Yang G Q Huang H Song and L Liang ldquoGame-theoreticapproach to competition dynamics in tourism supply chainsrdquoJournal of Travel Research vol 47 no 4 pp 425ndash439 2009

[12] G Q Huang H Song and X Zhang ldquoA comparative analysis ofquantity and price competitions in tourism supply chain net-works for package holidaysrdquo Service Industries Journal vol 30no 10 pp 1593ndash1606 2010

[13] Y Huang H Song G Q Huang and J Lou ldquoA comparativestudy of tourism supply chains with quantity competitionrdquoJournal of Travel Research vol 51 no 6 pp 717ndash729 2012

[14] H K Lee and Y Fernando ldquoThe antecedents and outcomes ofthe medical tourism supply chainrdquo Tourism Management vol46 pp 148ndash157 2015

[15] W-Y K Chiang D Chhajed and J D Hess ldquoDirect marketingindirect profits a strategic analysis of dual-channel supply-chain designrdquoManagement Science vol 49 no 1 pp 1ndash20 2003

[16] A A Tsay and N Agrawal ldquoChannel conflict and coordinationin the E-commerce agerdquo Production and Operations Manage-ment vol 13 no 1 pp 93ndash110 2004

[17] Q-H Li and B Li ldquoDual-channel supply chain equilibriumproblems regarding retail services and fairness concernsrdquoApplied Mathematical Modelling 2016

[18] S Panda N M Modak S S Sana and M Basu ldquoPricingand replenishment policies in dual-channel supply chain undercontinuous unit cost decreaserdquo Applied Mathematics and Com-putation vol 256 pp 913ndash929 2015

[19] Y Liu C Ding C Fan and X Chen ldquoPricing decision underdual-channel structure considering fairness and free-ridingbehaviorrdquo Discrete Dynamics in Nature and Society vol 2014Article ID 536576 10 pages 2014

[20] J Chen H Zhang and Y Sun ldquoImplementing coordinationcontracts in a manufacturer Stackelberg dual-channel supplychainrdquo Omega vol 40 no 5 pp 571ndash583 2012

[21] Q Ding C Dong and Z Pan ldquoA hierarchical pricing decisionprocess on a dual-channel problem with one manufacturer andone retailerrdquo International Journal of Production Economics vol175 pp 197ndash212 2016

[22] B Rodriguez and G Aydin ldquoPricing and assortment decisionsfor a manufacturer selling through dual channelsrdquo EuropeanJournal of Operational Research vol 242 no 3 pp 901ndash9092015

[23] T Lockyer ldquoThe perceived importance of price as one hotelselection dimensionrdquo Tourism Management vol 26 no 4 pp529ndash537 2005

[24] C-M Chen H-W Yang E Y Li and C-C Liu ldquoHow doeshotel pricing influence guest satisfaction by the moderatinginfluence of room occupancyrdquo International Journal of Hospi-tality Management vol 49 pp 136ndash138 2015

[25] J-M Espinet M Fluvia R Rigall-I-Torrent and A Salo ldquoHotelcharacteristics and seasonality in prices an analysis usingSpanish tour operatorsrsquo brochuresrdquo Tourism Economics vol 18no 4 pp 749ndash767 2012

[26] C Juaneda J M Raya and F Sastre ldquoPricing the time and loca-tion of a stay at a hotel or apartmentrdquo Tourism Economics vol17 no 2 pp 321ndash338 2011

[27] G Abrate G Fraquelli and G Viglia ldquoDynamic pricing strate-gies evidence from European hotelsrdquo International Journal ofHospitality Management vol 31 no 1 pp 160ndash168 2012

[28] D Q Yao and J J Liu ldquoCompetitive pricing of mixed retail ande-tail distribution channelsrdquo Omega vol 33 no 3 pp 235ndash2472005

[29] J Zhao and L Wang ldquoPricing and retail service decisionsin fuzzy uncertainty environmentsrdquo Applied Mathematics andComputation vol 250 pp 580ndash592 2015

[30] A A Tsay and N Agrawal ldquoChannel dynamics under priceand service competitionrdquo Manufacturing amp Service OperationsManagement vol 2 no 4 pp 372ndash391 2000

[31] S C Choi ldquoPrice competition in a duopoly common retailerchannelrdquo Journal of Retailing vol 72 no 2 pp 117ndash134 1996

[32] Y Bakos andE Brynjolfsson ldquoBundling and competition on theinternetrdquoMarketing Science vol 19 no 1 pp 63ndash82 2000

[33] H Song J H Kim and S Yang ldquoConfidence intervals fortourism demand elasticityrdquo Annals of Tourism Research vol 37no 2 pp 377ndash396 2010

[34] DMHanssens L J Parsons andR L SchultzMarket ResponseModels Econometric and Time Series Analysis Kluwer Aca-demic Publishers Boston Mass USA 2nd edition 2001

[35] H Kurata D-Q Yao and J J Liu ldquoPricing policies under directvs indirect channel competition and national vs store brandcompetitionrdquo European Journal of Operational Research vol180 no 1 pp 262ndash281 2007

[36] R Law and C Cheung ldquoA study of the perceived importance ofthe overall website quality of different classes of hotelsrdquo Inter-national Journal of Hospitality Management vol 25 no 3 pp525ndash531 2006

[37] K B Chen ldquoProcurement strategies and coordination mecha-nism of the supply chain with one manufacturer and multiplesuppliersrdquo International Journal of Production Economics vol138 no 1 pp 125ndash135 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Discrete Dynamics in Nature and Society 9

damaged and it must pay the additional costsThirdly if boththe economy rooms and luxury rooms are unable to meetthe demand the hotel usually transfers the customers whocannot check in to other hotels Note that when119863119894

1+119863119894

2gt 119876119894

119894 = 119871119867 if the hotel does not overbook its profit is

120587111

= (1 minus 120582120572) [119901119871

1(119876119871minus 119863119871

2) + 119901119867

1(119876119867minus 119863119867

2)

+ 119908119871119863119871

2+ 119908119867119863119867

2]

(14)

Proposition 13 With room transfer there exists threshold unitoverbooking cost 119888

1198940 such that if 119888

119894lt 1198881198940 then overbooking is

profitable for the hotel where

1198881198940=(1 minus 120582120572) 119901

119894

1

1 minus 120582 119894 = 119871119867 (15)

From Propositions 12 and 13 we conclude that the hotelshould control the overbooking quantity in a certain rangeto prevent lacking of rooms If the overbooking proportionis too large then the hotel may face a loss Only when theoverbooking cost is low the hotel can obtain additional profitOtherwise if the overbooking cost exceeds a certain valuethe hotelrsquos profit would be lower when it carries out over-booking As the market demand increases the supply is closeto saturation and then the overbooking costs will be higherTherefore when the market demand is excessive the hotelshould strictly control the proportion of overbooking Inaddition if the number of hotels that have the same level andtype in the same region is little that is the possibility to trans-fer customer is small then the hotel should lower the propor-tion of overbooking

The proportion of overbooking depends on the propor-tion of customer cancellations andno-showaswell as the totalnumber of hotel rooms so the hotel can analyze the historicaldata to develop an appropriate overbooking proportion so asto maximize the hotelrsquos expected profit

Proposition 14 When the economy rooms and luxury roomsare both overbooked the optimal centralized prices are asfollows 119894 = 119871119867

119901119894lowast

14= 119901119894lowast

1+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

119901119894lowast

24= 119901119894lowast

2+

119888119894

119906(1 minus 120582)

2 (1 minus 120582120572)

(16)

Bertrand and Stackelberg prices are as follows

(119901119894

14)119861lowast

= (119901119894

1)119861lowast

+2119888119894

119906119887119894(119887119894+ 120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

24)119861lowast

= (119901119894

2)119861lowast

+120579119888119894

119906119887119894 (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 1205792]

(119901119894

14)119878lowast

= (119901119894

1)119878lowast

+119888119894

119906119887119894(2119887119894+ 3120579) (1 minus 120582)

(1 minus 120582120572) [4 (119887119894 + 120579)2minus 21205792]

(119901119894

24)119878lowast

=120579 (119901119894

14)119878lowast

+ (1 minus 119904) 119886119894 + V (120579 + 120573) + 119908119894(119887119894+ 120579)

2 (119887119894+ 120579)

+119888

2 (1 minus 120582120572)

(17)

For the hotel the premise to overbook rooms is that themarket demand is greater than the supply When the hotelfaces the risk of overbooking the equilibrium prices in bothcentralized and decentralized decision-making supply chainwill improve In the busy season in order to reduce the riskof overbooking the hotel would increase the prices and theincrement will increase as the transfer cost increases From(16) and (17) we can know that the increment in centralizeddecision-making model is the greatest and that in Bertrandgame is the smallest

7 Numerical Analysis

In this section we do some numerical experiment to gainmore insights According to the China Hotel Sales Chan-nel Report by I-Research (httpreportiresearchcnreport2013031892shtml) there are 381 of the hotels that aresuitable for high-end travelers and 619 of the hotels thatare suitable for low-end travelersTherefore this part assumesthat the proportion of the economical rooms and the luxuryrooms is 4 6 that is 119886

119871= 06119886 119886

119867= 04119886 Other parameter

settings are made as follows 119886 = 600 119904 = 05 and 119887119871= 06

119887119867= 02 120573 = 120579 = 05 120578 = 004 120572 = 08 120582 = 01 119908

119894= 05119901

119894

1

(119894 = 119871119867) In the following we investigate the impact of V onthe optimal prices and profits

When V = 0 that is the OTA does not offer any servicethen the optimal prices of HA are equal to the prices ofOTA Since 119887

119871gt 120573 gt 119887

119867 then the market of economy

rooms is service-oriented while the market of luxury roomsis price-oriented FromFigure 2 we can know that whenOTAoffers more services OTArsquos optimal price will be increasedaccordingly It is reasonable that if V increases the cost ofOTAwill also definitely increase With the increase of V 119901119871lowast

1will

decline slowly while 119901119867lowast1

will increaseThe OTArsquos profit status becomes better with the improve-

ment of its price But as the V increases the cost of OTA willalso definitely increase When V is equal to 27 then the profitof OTA is the highest If V is larger then the high costs willreduce the profits of OTAWhen V is equal to 34 the profit ofthewhole supply chain is the highest So from the perspectiveof the supply chain V is expected to be 34 rather than 27Similarly for the integrated system the profit of the OTAalso rises first and then declines with the increase of V Aftercalculationwe can get thatwhen V = 27 both120587119861lowast

2and120587119878lowast2will

be the highest From Figures 3 and 4 we know that the OTAwould tend to offer service that valued 27 so as to maximizeits own profit

After calculation we can conclude that when V = 34 then120587119861lowast is highest when V = 35 then 120587

119878lowast is highest (Figure 5)

10 Discrete Dynamics in Nature and Society

0 10 20 30 40 50 60 70 80100

150

200

250

300

350

400

450

Pric

e

pLlowast

1

pLlowast

2

pHlowast

1

pHlowast

2

Value added by OTArsquos services ()

Figure 2 Equilibrium prices in the integrated system

0 10 20 30 40 50 60 70 800

1

2

3

4

5

6

7

Profi

t

times104

120587lowast

1

120587lowast

2

120587lowast

Value added by OTArsquos services ()

Figure 3 Profits in the integrated system

From the perspective of the supply chain theOTA is expectedto offer more services Despite the rising cost of OTA willlower its profit the hotel can lower the wholesale prices tocoordinate the distribution of profits so as to achieve a win-win situation

In the following we focus on the comparison of differentchannelrsquos profit in each model Figure 6 depicts the curves ofthe total profits of the HAOTA channels in the integratedsystem with respect to V Figure 7 draws the curves of the dif-ferent channelsrsquo profits under both Bertrand and Stackelberggame The profit of the HA channel refers to the profit thatthe hotel derived from the HA channelThe profit of the OTA

0 10 20 30 40 50 60125

13

135

14

145

15

155

16

165

Profi

t

times104

120587Blowast

2

120587Slowast

2

Value added by OTArsquos services ()

Figure 4 OTArsquos profits under two games

0 10 20 30 40 50 60 70 8052

53

54

55

56

57

58

59

6

61

62

Profi

t

times104

120587Blowast

2

120587Slowast

2120587lowast

Value added by OTArsquos services ()

Figure 5 The profit comparison

channel involves the OTArsquos profit and the hotelrsquos profit gainedfrom the OTA channel

As shown in Figures 6 and 7 with the increase of V theprofit of the OTA channel will increase first and will thendecrease This indicates that a high level of service by OTAwill be detrimental to the channel profit That is because ahigh level of service will bring a high cost undoubtedly Forthe integrated model and Bertrand game model this disad-vantage is more evident The OTArsquos service can motivate theactual purchase behavior of customers in the OTA channelWhen V is relatively lower the additional profits from OTArsquos

Discrete Dynamics in Nature and Society 11

0 10 20 30 40 50 60 70 8018

2

22

24

26

28

3

32

34

36

38

4

Profi

t

HA channelOTA channel

times104

Value added by OTArsquos services ()

Figure 6 Channel profits in the integrated system

0 10 20 30 40 50 60 70 8005

1

15

2

25

3

35

4

45

Profi

t

HA channel in Bertrand gameOTA channel in Bertrand gameHA channel in Stackelberg gameOTA channel in Stackelberg game

times104

Value added by OTArsquos services ()

Figure 7 Channel profits in two games

service are enough to compensate for the cost In this casethe hotel and the OTA can get more profit from providing theservice However when V is high the additional profits fromOTArsquos service cannot make up for the high cost In such phe-nomenon the OTA should not increase investment in ser-vice

For both integrated model and Bertrand game modelwith the increase of V the profit of the HA channel willdecrease first and will then increase while in the Stackelberggamemodel the profit of theHA channel will always increase

with V With Figure 2 we can know that when OTA providesmore additional services it tends to increase its price Someof the customers will turn to reserve rooms from the HAbecause of the excessively high price in OTA As a result thehotel can gain more profits from the HA channel

8 Conclusion

With the development of e-commerce the providers oftourism products are more inclined to build dual-channelsIn this paper we consider the direct selling channel of HAand the traditional retail channel ofOTA from the perspectiveof tourism supply chain We develop a two-echelon tourismsupply chain model involving one hotel and one OTA wheretheOTAprovides related service Customers will be refundedpartially in case of cancelation or no-show We investigatethe optimal pricing strategies under several common casesThe integrated operation and the decentralized operationbased on Bertrand and Stackelberg games are studied andcorresponding equilibrium pricing policies are obtained

Our findings demonstrate that the hotel plays a crucialrole in optimizing the benefits of supply chain Consideringthe overall profit of the supply chain the hotel should act as aleader in dual-channel supply chain and formulate reasonablewholesale prices to improve the cooperative enthusiasm ofOTA so as to achieve optimization of the whole supplychain A lower wholesale price can help reduce OTArsquos loss ofprofit because of the opening of HA channel In addition weconsider the overbooking of the hotel and obtain the optimaloverbooking quantity We conclude that the hotel can alwaysobtain higher profits when the overbooking proportion iscontrolledwithin a certain range Otherwise if the overbook-ing proportion is too high the hotel can get extra profits onlywhen the overbooking cost is lower than a certain value

The contribution of this paper is that we extend tourismsupply chain to the dual-channel structure in which the hotelopens its direct channel to sell tourism products And theextant literature only refers to the single channel In additionwe realize that customer cancellations andno-showoccur fre-quently in hotel industry Thus we develop the game modelsbased on such phenomenon At last we derive the conditionsunder which the hotel dominant case is profitable for boththe supply chain members Our results can provide hotelsand OTAs with some new managerial insights under thedual-channel environment

This research can be extended in several directions infuture work For example in this paper we assume that allinformation is known to the hotel and OTA However someinformation could be asymmetric (eg see Chen [37]) Thuswe can explore the Bayesian equilibrium under asymmetricinformation settings Secondly the assumption of lineardemand is a limitation of this paperWe can further study thedynamic pricing in tourism dual-channel supply chain

Appendix

A Proof of Corollary 8

First we set (1199011198711)119861lowast

gt (119901119871

1)119878lowast which can be expressed as

12 Discrete Dynamics in Nature and Society

(1 minus 120582120572) (120579119886119871 + 120579119904119886119871+ 2119887119871119904119886119871+ 120579V120573 + 3119908

1198711205792+ 3119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

gt(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(A1)

The above equation can be simplified as

119908119871gt120579 [(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)]

4119887119871 (1 minus 120582120572) (119887119871 + 120579) (119887

119871+ 2120579)

(A2)

So we can get Corollary 8 B Proof of Corollary 9

If (1199011198941)119878lowast

gt (119901119894

1)119861lowast then

(1 minus 120582120572) (120579119886119894 + 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 2119908

1198941205792+ 2119908119894119887119894120579 minus 1205792V minus 2120579119887

119894V) + 119888120579 (119887

119894+ 120579)

minus (1 minus 120582120572) ((119901119894

1)119878lowast

+ (119901119894

1)119861lowast

) [2 (119887119894+ 120579)2minus 1205792] gt 0

120587119878lowast

1minus 120587119861lowast

1=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

2 (119887119871+ 120579)

((119901119871

1)119878lowast

minus (119901119871

1)119861lowast

)

+(1 minus 120582120572) (120579119886119867 + 120579119904119886

119867+ 2119887119867119904119886119867+ 120579V120573 + 2119908

1198671205792+ 2119908119867119887119867120579 minus 1205792V minus 2120579119887

119867V) + 119888120579 (119887

119867+ 120579)

2 (119887119867+ 120579)

((119901119867

1)119878lowast

minus (119901119867

1)119861lowast

)

minus (1 minus 120582120572)2 (119887119871+ 120579)2minus 1205792

2 (119887119871+ 120579)

[((119901119871

1)119878lowast

)2

minus ((119901119871

1)119861lowast

)2

] minus (1 minus 120582120572)2 (119887119867+ 120579)2minus 1205792

2 (119887119867+ 120579)

[((119901119867

1)119878lowast

)2

minus ((119901119867

1)119861lowast

)2

] gt 0

(B1)

If (1199011198711)119878lowast

lt (119901119871

1)119861lowast and (119901

119867

1)119878lowast

lt (119901119867

1)119861lowast we can prove

120587119878lowast

1gt 120587119861lowast

1similarly

From Propositions 3 and 7 with (3) we obtain that

120587119861lowast

2minus 120587119878lowast

2=

120579

4 (119887119871+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119871 + V (120573 + 120579) minus 119908119871(119887119871+ 120579)]

minus 2119888 (119887119871+ 120579) + 120579 (1 minus 120582120572) ((119901

119871

1)119861lowast

+ (119901119871

1)119878lowast

)

sdot ((119901119871

1)119861lowast

minus (119901119871

1)119878lowast

) +120579

4 (119887119867+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119867 + V (120573 + 120579) minus 119908 (119887119867+ 120579)]

minus 2119888 (119887119867+ 120579) + 120579 (1 minus 120582120572) ((119901

119867

1)119861lowast

+ (119901119867

1)119878lowast

)

sdot ((119901119867

1)119861lowast

minus (119901119867

1)119878lowast

)

(B2)

Note that

119863119894

2= [(1 minus 119904) 119886119894 minus 119887

119894119901119894

2] + 120573V + 120579 (119901

119894

1+ V minus 119901

119894

2) gt 0 (B3)

so we show that

2 (1 minus 120582120572) [(1 minus 119904) 119886119894 + V (120573 + 120579) minus 119908119894(119887119894+ 120579)]

minus 2119888 (119887119894+ 120579) + 120579 (1 minus 120582120572) ((119901

119894

1)119861lowast

+ (119901119894

1)119878lowast

)

gt 0

(B4)

Thus we have the following

(1) 120587119861lowast2

gt 120587119878lowast

2 if (1199011198711)119861lowast

gt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

gt (119901119867

1)119878lowast

(2) 120587119861lowast2

= 120587119878lowast

2 if (1199011198711)119861lowast

= (119901119871

1)119878lowast and (119901

119867

1)119861lowast

= (119901119867

1)119878lowast

(3) 120587119861lowast2

lt 120587119878lowast

2 if (1199011198711)119861lowast

lt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

lt (119901119867

1)119878lowast

Combined with Corollary 8 the proposition is proved

Discrete Dynamics in Nature and Society 13

C Proof of Corollary 10

The profit of hotel from the economy rooms is as follows

120587119871

= [(1 minus 120582120572) (119904119886119871 minus 120579V) minus 119888120579] 119901119871

1

+ [(1 minus 120582120572) (119886119871 minus 119904119886119871+ 120573V + 120579V) + 119888 (119887

119871+ 120579)] 119901

119871

2

+ 2120579 (1 minus 120582120572) 119901119871

1119901119871

2minus (1 minus 120582120572) (119887119871 + 120579) (119901

119871

1)2

minus (1 minus 120582120572) (119887119871 + 120579) (119901119871

2)2

minus (119886119871minus 119904119886119871+ 120573V + 120579V) 119888

(C1)

Define (119901119871

1)119861(119878)

= (119860119871

1)119861(119878)

+ (119861119871

1)119861(119878)

119908119871 (1199011198712)119861(119878)

=

(119860119871

2)119861(119878)

+ (119861119871

2)119861(119878)

119908119871 where

(119861119871

1)119861

=3120579 (119887119871+ 120579)

4 (119887119871+ 120579)2minus 1205792

(119861119871

1)119878

=120579 (119887119871+ 120579)

2 (119887119871+ 120579)2minus 1205792

(119861119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119861119871

1)119861(119878)

+1

2

(119860119871

1)119861

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

(119860119871

1)119878

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(119860119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119860119871

1)119861(119878)

+(1 minus 120582120572) [(1 minus 119904) 119886119871 + V (120579 + 120573)] + 119888 (119887

119871+ 120579)

2 (1 minus 120582120572) (119887119871 + 120579)

(C2)

Let 120597120587119871120597119908 = 0 then we get119908lowast

119871 Similarly we can get119908lowast

119867

D Proof of Proposition 12

Let 120587119889minus 120587119903gt 0 then we can get 119904

0 where the profits of hotel

from HA and OTA are as follows

120587119889= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1)

120587119903= (1 minus 120582120572) (119908119871119863

119871

2+ 119908119867119863119867

2)

(D1)

E Proof of Corollary 11

If Δ119862119871le 120582(1 minus 120582)119876

119871 then the profit of hotel is 120587119871

11 The

derivative of 12058711987111(Δ119862119871) is 120597120587119871

11120597Δ119862119871= (1 minus 120582120572)119901

119871

1gt 0 So

with the increase of Δ119862119871 12058711987111

will increase When Δ119862119871

=

120582(1 minus 120582)119876119871 12058711987111

is maximized If Δ119862119871

ge 120582(1 minus 120582)119876119871

then the profit of hotel is 12058711987112 The derivative of 120587119871

12(Δ119862119871) is

120597120587119871

12120597Δ119862119871= (1 minus 120582120572)119901

119871

1minus (1 minus 120582)(119901

119871

1+ 119888119871) lt 0 So with the

increase of Δ119862119871 12058711987111will decline When Δ119862

119871= 120582(1 minus 120582)119876

119871

120587119871

11is maximizedSimilarly we can get Δ119862lowast

119867

F Proof of Proposition 13

Assume that the overbooking proportion is 120574119871and 120574119867

(1) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) le 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

That is

120574119867lt

120582

1 minus 120582lt 120574119871

le120582119876119871+ 119876119867[1 minus (1 minus 120582) (1 + 120574

119867)]

(1 minus 120582)119876119871

(F1)

Thus the hotel would like to overbook to get more profitrather than room vacancy

(2) Consider (1198631198711+119863119871

2)(1minus120582) lt 119876

119871and (119863119867

1+119863119867

2)(1minus120582) gt

119876119867That is 120574

119871lt 120582(1 minus 120582) lt 120574

119867 Then the profit of hotel is

120587112

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F2)

Thenwhen 119888119867119906

lt (1minus120582120572)119901119867

1(1minus120582) that is120587

112minus120587111

gt 0the hotel would carry out overbooking

(3) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

14 Discrete Dynamics in Nature and Society

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867lt 120582(1 minus 120582) Then the profit of hotel is

120587113

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2+ 119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876]

(F3)

Then when 119888119871

119906lt (1 minus 120582120572)119901

119871

1(1 minus 120582) 120587

113minus120587111

gt 0 thusthe hotel would carry out overbooking

(4) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) gt 119876

119867

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867gt (120582119876

119867+ 119876119871[1 minus (1 minus 120582)(1 + 120574

119871)])(1 minus 120582)119876

119867

Then the profit of hotel is as follows

120587114

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2) (1 minus 120582) minus 119876

119871]

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F4)

Then when 119888119871119906lt (1minus120582120572)119901

119871

1(1minus120582) and 119888119867

119906lt (1minus120582120572)119901

119867

1

(1 minus 120582) 120587114

minus 120587111

gt 0 overbooking is preferred

G Threshold Values

Threshold values are as follows

1198711= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 3119908

1198941205792+ 3119908119894119887119894120579

minus 1205792V minus 2120579119887

119894V

1198712= 2119886119894(119887119894+ 120579) minus 119904119886

119894(2119887119894+ 120579) + 120579

2119908119894+ 2 (120579 + 120573) (119887

119894

+ 120579) V + 2119908119894(119887119894+ 120579)2minus 1205792V

1198713= 4120579V119887

119894120573 minus 120579119904119886

119894119887119894+ 2V1205731198872

119894+ 31198861198941205792+ 4119886119894119887119894120579

minus 21198861198941198872

119894119904 + 3120579

2V120573 + 1205792V119887119894+ 2120579V1198872

119894+ 21198861198941198872

119894

1198714= 3119886119894119887119894120579 + 3120579

2V120573 minus 2120579V1198872119894minus 1205792V119887119894+ 31198861198941205792

+ 21198861198941198872

119894119904 + 119886119887

119894119904120579 + 3119887

119894120573V120579

1198715= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 minus 120579

2V minus 2120579119887119894V

1198661= [(1 minus 120582120572) (119904119886119894 minus 120579V) minus 119888120579] (119861

119894

1)119861(119878)

+ [(1 minus 120582120572) (119886119894 minus 119904119886119894+ 120573V + 120579V) + 119888 (119887

119894+ 120579)]

sdot (119861119894

1)119861(119878)

+ 2120579 (1 minus 120582120572) [(119860119894

1)119861(119878)

(119861119894

2)119861(119878)

+ (119861119894

1)119861(119878)

(119860119894

2)119861(119878)

] minus 2 (1 minus 120582120572) (119887119894 + 120579)

sdot [(119860119894

1)119861(119878)

(119861119894

1)119861(119878)

+ (119860119894

2)119861(119878)

(119861119894

2)119861(119878)

]

1198662= 2 (1 minus 120582120572)

sdot (119887119894+ 120579) [((119861

119894

1)119861(119878)

)

2

+ ((119861119894

2)119861(119878)

)

2

]

minus 2120579 (119861119894

1)119861(119878)

(119861119894

2)119861(119878)

1199040= ((119887119871+ 120579) (119901

119871

1)2

+ (119887119867+ 120579) (119901

119867

1)2

+ 120579119908119871(119901119871

1minus 119901119871

2) + 120579119908

119867(119901119867

1minus 119901119867

2)

+ 120579V (1199011198711+ 119901119867

1) + (119908

119871+ 119908119867) (120573 + 120579) V

+ 119908119871(119886119871minus 119887119871119901119871

2) + 119908119867(119886119867minus 119887119867119901119867

2)

minus 120579 (119901119871

1119901119871

2+ 119901119867

1119901119867

2)) (119886119871(119901119871

1+ 119908119871)

+ 119886119867(119901119867

1+ 119908119867))minus1

(G1)

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The authors thank associate editor and anonymous refereesfor their numerous constructive comments and encourage-ment that have improved their paper greatly The work waspartly supported by (i) the National Natural Science Founda-tion ofChina (71201083 71572058 and 71571100) (ii) the Fun-damental Research Funds for the Central Universities SCUT(2015ZZ057) (iii) Jiangsu Province Science Foundation forYouths (BK2012379) and (iv) the Fundamental ResearchFunds for the Central Universities (NS2015076)

References

[1] J Li W N Zhang H Xu and J Jiang ldquoDynamic competitionand cooperation of road infrastructure investment of multipletourism destinations a case Study of Xidi and Hongcun WorldCulturalHeritagerdquoDiscreteDynamics inNature and Society vol2015 Article ID 962028 10 pages 2015

[2] T Paksoy EOzceylan andG-WWeber ldquoProfit oriented supplychain network optimizationrdquoCentral European Journal of Oper-ations Research vol 21 no 2 pp 455ndash478 2013

[3] X Zhang H Song and G Q Huang ldquoTourism supply chainmanagement a new research agendardquo Tourism Managementvol 30 no 3 pp 345ndash358 2009

[4] Z Yang and J Cai ldquoDo regional factors matter Determinantsof hotel industry performance in Chinardquo TourismManagementvol 52 pp 242ndash253 2016

[5] B Pan L Zhang and R Law ldquoThe complex matter of onlinehotel choicerdquoCornell Hospitality Quarterly vol 54 no 1 pp 74ndash83 2013

[6] L Ling X Guo and C Yang ldquoOpening the online marketplacean examination of hotel pricing and travel agency on-line

Discrete Dynamics in Nature and Society 15

distribution of roomsrdquo Tourism Management vol 45 pp 234ndash243 2014

[7] L Ling Y Dong X Guo and L Liang ldquoAvailability man-agement of hotel rooms under cooperation with online travelagenciesrdquo International Journal of Hospitality Management vol50 pp 145ndash152 2015

[8] J N K Liu andE Y Zhang ldquoAn investigation of factors affectingcustomer selection of online hotel booking channelsrdquo Interna-tional Journal of Hospitality Management vol 39 pp 71ndash832014

[9] L Fox ldquoFour Seasons Unveils $18 Million Website as LuxuryTravel Growsrdquo 2012 httpwwwtnoozcomarticlefour-sea-sons-unveils-18-million-dollar-website-as-luxury-travel-grows

[10] C-M Chen and Y-C Lin ldquoThe influence of uncertain demandon hotel capacityrdquo International Journal of Hospitality Manage-ment vol 34 no 1 pp 462ndash465 2013

[11] S Yang G Q Huang H Song and L Liang ldquoGame-theoreticapproach to competition dynamics in tourism supply chainsrdquoJournal of Travel Research vol 47 no 4 pp 425ndash439 2009

[12] G Q Huang H Song and X Zhang ldquoA comparative analysis ofquantity and price competitions in tourism supply chain net-works for package holidaysrdquo Service Industries Journal vol 30no 10 pp 1593ndash1606 2010

[13] Y Huang H Song G Q Huang and J Lou ldquoA comparativestudy of tourism supply chains with quantity competitionrdquoJournal of Travel Research vol 51 no 6 pp 717ndash729 2012

[14] H K Lee and Y Fernando ldquoThe antecedents and outcomes ofthe medical tourism supply chainrdquo Tourism Management vol46 pp 148ndash157 2015

[15] W-Y K Chiang D Chhajed and J D Hess ldquoDirect marketingindirect profits a strategic analysis of dual-channel supply-chain designrdquoManagement Science vol 49 no 1 pp 1ndash20 2003

[16] A A Tsay and N Agrawal ldquoChannel conflict and coordinationin the E-commerce agerdquo Production and Operations Manage-ment vol 13 no 1 pp 93ndash110 2004

[17] Q-H Li and B Li ldquoDual-channel supply chain equilibriumproblems regarding retail services and fairness concernsrdquoApplied Mathematical Modelling 2016

[18] S Panda N M Modak S S Sana and M Basu ldquoPricingand replenishment policies in dual-channel supply chain undercontinuous unit cost decreaserdquo Applied Mathematics and Com-putation vol 256 pp 913ndash929 2015

[19] Y Liu C Ding C Fan and X Chen ldquoPricing decision underdual-channel structure considering fairness and free-ridingbehaviorrdquo Discrete Dynamics in Nature and Society vol 2014Article ID 536576 10 pages 2014

[20] J Chen H Zhang and Y Sun ldquoImplementing coordinationcontracts in a manufacturer Stackelberg dual-channel supplychainrdquo Omega vol 40 no 5 pp 571ndash583 2012

[21] Q Ding C Dong and Z Pan ldquoA hierarchical pricing decisionprocess on a dual-channel problem with one manufacturer andone retailerrdquo International Journal of Production Economics vol175 pp 197ndash212 2016

[22] B Rodriguez and G Aydin ldquoPricing and assortment decisionsfor a manufacturer selling through dual channelsrdquo EuropeanJournal of Operational Research vol 242 no 3 pp 901ndash9092015

[23] T Lockyer ldquoThe perceived importance of price as one hotelselection dimensionrdquo Tourism Management vol 26 no 4 pp529ndash537 2005

[24] C-M Chen H-W Yang E Y Li and C-C Liu ldquoHow doeshotel pricing influence guest satisfaction by the moderatinginfluence of room occupancyrdquo International Journal of Hospi-tality Management vol 49 pp 136ndash138 2015

[25] J-M Espinet M Fluvia R Rigall-I-Torrent and A Salo ldquoHotelcharacteristics and seasonality in prices an analysis usingSpanish tour operatorsrsquo brochuresrdquo Tourism Economics vol 18no 4 pp 749ndash767 2012

[26] C Juaneda J M Raya and F Sastre ldquoPricing the time and loca-tion of a stay at a hotel or apartmentrdquo Tourism Economics vol17 no 2 pp 321ndash338 2011

[27] G Abrate G Fraquelli and G Viglia ldquoDynamic pricing strate-gies evidence from European hotelsrdquo International Journal ofHospitality Management vol 31 no 1 pp 160ndash168 2012

[28] D Q Yao and J J Liu ldquoCompetitive pricing of mixed retail ande-tail distribution channelsrdquo Omega vol 33 no 3 pp 235ndash2472005

[29] J Zhao and L Wang ldquoPricing and retail service decisionsin fuzzy uncertainty environmentsrdquo Applied Mathematics andComputation vol 250 pp 580ndash592 2015

[30] A A Tsay and N Agrawal ldquoChannel dynamics under priceand service competitionrdquo Manufacturing amp Service OperationsManagement vol 2 no 4 pp 372ndash391 2000

[31] S C Choi ldquoPrice competition in a duopoly common retailerchannelrdquo Journal of Retailing vol 72 no 2 pp 117ndash134 1996

[32] Y Bakos andE Brynjolfsson ldquoBundling and competition on theinternetrdquoMarketing Science vol 19 no 1 pp 63ndash82 2000

[33] H Song J H Kim and S Yang ldquoConfidence intervals fortourism demand elasticityrdquo Annals of Tourism Research vol 37no 2 pp 377ndash396 2010

[34] DMHanssens L J Parsons andR L SchultzMarket ResponseModels Econometric and Time Series Analysis Kluwer Aca-demic Publishers Boston Mass USA 2nd edition 2001

[35] H Kurata D-Q Yao and J J Liu ldquoPricing policies under directvs indirect channel competition and national vs store brandcompetitionrdquo European Journal of Operational Research vol180 no 1 pp 262ndash281 2007

[36] R Law and C Cheung ldquoA study of the perceived importance ofthe overall website quality of different classes of hotelsrdquo Inter-national Journal of Hospitality Management vol 25 no 3 pp525ndash531 2006

[37] K B Chen ldquoProcurement strategies and coordination mecha-nism of the supply chain with one manufacturer and multiplesuppliersrdquo International Journal of Production Economics vol138 no 1 pp 125ndash135 2012

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Stochastic AnalysisInternational Journal of

10 Discrete Dynamics in Nature and Society

0 10 20 30 40 50 60 70 80100

150

200

250

300

350

400

450

Pric

e

pLlowast

1

pLlowast

2

pHlowast

1

pHlowast

2

Value added by OTArsquos services ()

Figure 2 Equilibrium prices in the integrated system

0 10 20 30 40 50 60 70 800

1

2

3

4

5

6

7

Profi

t

times104

120587lowast

1

120587lowast

2

120587lowast

Value added by OTArsquos services ()

Figure 3 Profits in the integrated system

From the perspective of the supply chain theOTA is expectedto offer more services Despite the rising cost of OTA willlower its profit the hotel can lower the wholesale prices tocoordinate the distribution of profits so as to achieve a win-win situation

In the following we focus on the comparison of differentchannelrsquos profit in each model Figure 6 depicts the curves ofthe total profits of the HAOTA channels in the integratedsystem with respect to V Figure 7 draws the curves of the dif-ferent channelsrsquo profits under both Bertrand and Stackelberggame The profit of the HA channel refers to the profit thatthe hotel derived from the HA channelThe profit of the OTA

0 10 20 30 40 50 60125

13

135

14

145

15

155

16

165

Profi

t

times104

120587Blowast

2

120587Slowast

2

Value added by OTArsquos services ()

Figure 4 OTArsquos profits under two games

0 10 20 30 40 50 60 70 8052

53

54

55

56

57

58

59

6

61

62

Profi

t

times104

120587Blowast

2

120587Slowast

2120587lowast

Value added by OTArsquos services ()

Figure 5 The profit comparison

channel involves the OTArsquos profit and the hotelrsquos profit gainedfrom the OTA channel

As shown in Figures 6 and 7 with the increase of V theprofit of the OTA channel will increase first and will thendecrease This indicates that a high level of service by OTAwill be detrimental to the channel profit That is because ahigh level of service will bring a high cost undoubtedly Forthe integrated model and Bertrand game model this disad-vantage is more evident The OTArsquos service can motivate theactual purchase behavior of customers in the OTA channelWhen V is relatively lower the additional profits from OTArsquos

Discrete Dynamics in Nature and Society 11

0 10 20 30 40 50 60 70 8018

2

22

24

26

28

3

32

34

36

38

4

Profi

t

HA channelOTA channel

times104

Value added by OTArsquos services ()

Figure 6 Channel profits in the integrated system

0 10 20 30 40 50 60 70 8005

1

15

2

25

3

35

4

45

Profi

t

HA channel in Bertrand gameOTA channel in Bertrand gameHA channel in Stackelberg gameOTA channel in Stackelberg game

times104

Value added by OTArsquos services ()

Figure 7 Channel profits in two games

service are enough to compensate for the cost In this casethe hotel and the OTA can get more profit from providing theservice However when V is high the additional profits fromOTArsquos service cannot make up for the high cost In such phe-nomenon the OTA should not increase investment in ser-vice

For both integrated model and Bertrand game modelwith the increase of V the profit of the HA channel willdecrease first and will then increase while in the Stackelberggamemodel the profit of theHA channel will always increase

with V With Figure 2 we can know that when OTA providesmore additional services it tends to increase its price Someof the customers will turn to reserve rooms from the HAbecause of the excessively high price in OTA As a result thehotel can gain more profits from the HA channel

8 Conclusion

With the development of e-commerce the providers oftourism products are more inclined to build dual-channelsIn this paper we consider the direct selling channel of HAand the traditional retail channel ofOTA from the perspectiveof tourism supply chain We develop a two-echelon tourismsupply chain model involving one hotel and one OTA wheretheOTAprovides related service Customers will be refundedpartially in case of cancelation or no-show We investigatethe optimal pricing strategies under several common casesThe integrated operation and the decentralized operationbased on Bertrand and Stackelberg games are studied andcorresponding equilibrium pricing policies are obtained

Our findings demonstrate that the hotel plays a crucialrole in optimizing the benefits of supply chain Consideringthe overall profit of the supply chain the hotel should act as aleader in dual-channel supply chain and formulate reasonablewholesale prices to improve the cooperative enthusiasm ofOTA so as to achieve optimization of the whole supplychain A lower wholesale price can help reduce OTArsquos loss ofprofit because of the opening of HA channel In addition weconsider the overbooking of the hotel and obtain the optimaloverbooking quantity We conclude that the hotel can alwaysobtain higher profits when the overbooking proportion iscontrolledwithin a certain range Otherwise if the overbook-ing proportion is too high the hotel can get extra profits onlywhen the overbooking cost is lower than a certain value

The contribution of this paper is that we extend tourismsupply chain to the dual-channel structure in which the hotelopens its direct channel to sell tourism products And theextant literature only refers to the single channel In additionwe realize that customer cancellations andno-showoccur fre-quently in hotel industry Thus we develop the game modelsbased on such phenomenon At last we derive the conditionsunder which the hotel dominant case is profitable for boththe supply chain members Our results can provide hotelsand OTAs with some new managerial insights under thedual-channel environment

This research can be extended in several directions infuture work For example in this paper we assume that allinformation is known to the hotel and OTA However someinformation could be asymmetric (eg see Chen [37]) Thuswe can explore the Bayesian equilibrium under asymmetricinformation settings Secondly the assumption of lineardemand is a limitation of this paperWe can further study thedynamic pricing in tourism dual-channel supply chain

Appendix

A Proof of Corollary 8

First we set (1199011198711)119861lowast

gt (119901119871

1)119878lowast which can be expressed as

12 Discrete Dynamics in Nature and Society

(1 minus 120582120572) (120579119886119871 + 120579119904119886119871+ 2119887119871119904119886119871+ 120579V120573 + 3119908

1198711205792+ 3119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

gt(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(A1)

The above equation can be simplified as

119908119871gt120579 [(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)]

4119887119871 (1 minus 120582120572) (119887119871 + 120579) (119887

119871+ 2120579)

(A2)

So we can get Corollary 8 B Proof of Corollary 9

If (1199011198941)119878lowast

gt (119901119894

1)119861lowast then

(1 minus 120582120572) (120579119886119894 + 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 2119908

1198941205792+ 2119908119894119887119894120579 minus 1205792V minus 2120579119887

119894V) + 119888120579 (119887

119894+ 120579)

minus (1 minus 120582120572) ((119901119894

1)119878lowast

+ (119901119894

1)119861lowast

) [2 (119887119894+ 120579)2minus 1205792] gt 0

120587119878lowast

1minus 120587119861lowast

1=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

2 (119887119871+ 120579)

((119901119871

1)119878lowast

minus (119901119871

1)119861lowast

)

+(1 minus 120582120572) (120579119886119867 + 120579119904119886

119867+ 2119887119867119904119886119867+ 120579V120573 + 2119908

1198671205792+ 2119908119867119887119867120579 minus 1205792V minus 2120579119887

119867V) + 119888120579 (119887

119867+ 120579)

2 (119887119867+ 120579)

((119901119867

1)119878lowast

minus (119901119867

1)119861lowast

)

minus (1 minus 120582120572)2 (119887119871+ 120579)2minus 1205792

2 (119887119871+ 120579)

[((119901119871

1)119878lowast

)2

minus ((119901119871

1)119861lowast

)2

] minus (1 minus 120582120572)2 (119887119867+ 120579)2minus 1205792

2 (119887119867+ 120579)

[((119901119867

1)119878lowast

)2

minus ((119901119867

1)119861lowast

)2

] gt 0

(B1)

If (1199011198711)119878lowast

lt (119901119871

1)119861lowast and (119901

119867

1)119878lowast

lt (119901119867

1)119861lowast we can prove

120587119878lowast

1gt 120587119861lowast

1similarly

From Propositions 3 and 7 with (3) we obtain that

120587119861lowast

2minus 120587119878lowast

2=

120579

4 (119887119871+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119871 + V (120573 + 120579) minus 119908119871(119887119871+ 120579)]

minus 2119888 (119887119871+ 120579) + 120579 (1 minus 120582120572) ((119901

119871

1)119861lowast

+ (119901119871

1)119878lowast

)

sdot ((119901119871

1)119861lowast

minus (119901119871

1)119878lowast

) +120579

4 (119887119867+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119867 + V (120573 + 120579) minus 119908 (119887119867+ 120579)]

minus 2119888 (119887119867+ 120579) + 120579 (1 minus 120582120572) ((119901

119867

1)119861lowast

+ (119901119867

1)119878lowast

)

sdot ((119901119867

1)119861lowast

minus (119901119867

1)119878lowast

)

(B2)

Note that

119863119894

2= [(1 minus 119904) 119886119894 minus 119887

119894119901119894

2] + 120573V + 120579 (119901

119894

1+ V minus 119901

119894

2) gt 0 (B3)

so we show that

2 (1 minus 120582120572) [(1 minus 119904) 119886119894 + V (120573 + 120579) minus 119908119894(119887119894+ 120579)]

minus 2119888 (119887119894+ 120579) + 120579 (1 minus 120582120572) ((119901

119894

1)119861lowast

+ (119901119894

1)119878lowast

)

gt 0

(B4)

Thus we have the following

(1) 120587119861lowast2

gt 120587119878lowast

2 if (1199011198711)119861lowast

gt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

gt (119901119867

1)119878lowast

(2) 120587119861lowast2

= 120587119878lowast

2 if (1199011198711)119861lowast

= (119901119871

1)119878lowast and (119901

119867

1)119861lowast

= (119901119867

1)119878lowast

(3) 120587119861lowast2

lt 120587119878lowast

2 if (1199011198711)119861lowast

lt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

lt (119901119867

1)119878lowast

Combined with Corollary 8 the proposition is proved

Discrete Dynamics in Nature and Society 13

C Proof of Corollary 10

The profit of hotel from the economy rooms is as follows

120587119871

= [(1 minus 120582120572) (119904119886119871 minus 120579V) minus 119888120579] 119901119871

1

+ [(1 minus 120582120572) (119886119871 minus 119904119886119871+ 120573V + 120579V) + 119888 (119887

119871+ 120579)] 119901

119871

2

+ 2120579 (1 minus 120582120572) 119901119871

1119901119871

2minus (1 minus 120582120572) (119887119871 + 120579) (119901

119871

1)2

minus (1 minus 120582120572) (119887119871 + 120579) (119901119871

2)2

minus (119886119871minus 119904119886119871+ 120573V + 120579V) 119888

(C1)

Define (119901119871

1)119861(119878)

= (119860119871

1)119861(119878)

+ (119861119871

1)119861(119878)

119908119871 (1199011198712)119861(119878)

=

(119860119871

2)119861(119878)

+ (119861119871

2)119861(119878)

119908119871 where

(119861119871

1)119861

=3120579 (119887119871+ 120579)

4 (119887119871+ 120579)2minus 1205792

(119861119871

1)119878

=120579 (119887119871+ 120579)

2 (119887119871+ 120579)2minus 1205792

(119861119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119861119871

1)119861(119878)

+1

2

(119860119871

1)119861

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

(119860119871

1)119878

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(119860119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119860119871

1)119861(119878)

+(1 minus 120582120572) [(1 minus 119904) 119886119871 + V (120579 + 120573)] + 119888 (119887

119871+ 120579)

2 (1 minus 120582120572) (119887119871 + 120579)

(C2)

Let 120597120587119871120597119908 = 0 then we get119908lowast

119871 Similarly we can get119908lowast

119867

D Proof of Proposition 12

Let 120587119889minus 120587119903gt 0 then we can get 119904

0 where the profits of hotel

from HA and OTA are as follows

120587119889= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1)

120587119903= (1 minus 120582120572) (119908119871119863

119871

2+ 119908119867119863119867

2)

(D1)

E Proof of Corollary 11

If Δ119862119871le 120582(1 minus 120582)119876

119871 then the profit of hotel is 120587119871

11 The

derivative of 12058711987111(Δ119862119871) is 120597120587119871

11120597Δ119862119871= (1 minus 120582120572)119901

119871

1gt 0 So

with the increase of Δ119862119871 12058711987111

will increase When Δ119862119871

=

120582(1 minus 120582)119876119871 12058711987111

is maximized If Δ119862119871

ge 120582(1 minus 120582)119876119871

then the profit of hotel is 12058711987112 The derivative of 120587119871

12(Δ119862119871) is

120597120587119871

12120597Δ119862119871= (1 minus 120582120572)119901

119871

1minus (1 minus 120582)(119901

119871

1+ 119888119871) lt 0 So with the

increase of Δ119862119871 12058711987111will decline When Δ119862

119871= 120582(1 minus 120582)119876

119871

120587119871

11is maximizedSimilarly we can get Δ119862lowast

119867

F Proof of Proposition 13

Assume that the overbooking proportion is 120574119871and 120574119867

(1) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) le 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

That is

120574119867lt

120582

1 minus 120582lt 120574119871

le120582119876119871+ 119876119867[1 minus (1 minus 120582) (1 + 120574

119867)]

(1 minus 120582)119876119871

(F1)

Thus the hotel would like to overbook to get more profitrather than room vacancy

(2) Consider (1198631198711+119863119871

2)(1minus120582) lt 119876

119871and (119863119867

1+119863119867

2)(1minus120582) gt

119876119867That is 120574

119871lt 120582(1 minus 120582) lt 120574

119867 Then the profit of hotel is

120587112

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F2)

Thenwhen 119888119867119906

lt (1minus120582120572)119901119867

1(1minus120582) that is120587

112minus120587111

gt 0the hotel would carry out overbooking

(3) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

14 Discrete Dynamics in Nature and Society

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867lt 120582(1 minus 120582) Then the profit of hotel is

120587113

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2+ 119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876]

(F3)

Then when 119888119871

119906lt (1 minus 120582120572)119901

119871

1(1 minus 120582) 120587

113minus120587111

gt 0 thusthe hotel would carry out overbooking

(4) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) gt 119876

119867

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867gt (120582119876

119867+ 119876119871[1 minus (1 minus 120582)(1 + 120574

119871)])(1 minus 120582)119876

119867

Then the profit of hotel is as follows

120587114

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2) (1 minus 120582) minus 119876

119871]

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F4)

Then when 119888119871119906lt (1minus120582120572)119901

119871

1(1minus120582) and 119888119867

119906lt (1minus120582120572)119901

119867

1

(1 minus 120582) 120587114

minus 120587111

gt 0 overbooking is preferred

G Threshold Values

Threshold values are as follows

1198711= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 3119908

1198941205792+ 3119908119894119887119894120579

minus 1205792V minus 2120579119887

119894V

1198712= 2119886119894(119887119894+ 120579) minus 119904119886

119894(2119887119894+ 120579) + 120579

2119908119894+ 2 (120579 + 120573) (119887

119894

+ 120579) V + 2119908119894(119887119894+ 120579)2minus 1205792V

1198713= 4120579V119887

119894120573 minus 120579119904119886

119894119887119894+ 2V1205731198872

119894+ 31198861198941205792+ 4119886119894119887119894120579

minus 21198861198941198872

119894119904 + 3120579

2V120573 + 1205792V119887119894+ 2120579V1198872

119894+ 21198861198941198872

119894

1198714= 3119886119894119887119894120579 + 3120579

2V120573 minus 2120579V1198872119894minus 1205792V119887119894+ 31198861198941205792

+ 21198861198941198872

119894119904 + 119886119887

119894119904120579 + 3119887

119894120573V120579

1198715= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 minus 120579

2V minus 2120579119887119894V

1198661= [(1 minus 120582120572) (119904119886119894 minus 120579V) minus 119888120579] (119861

119894

1)119861(119878)

+ [(1 minus 120582120572) (119886119894 minus 119904119886119894+ 120573V + 120579V) + 119888 (119887

119894+ 120579)]

sdot (119861119894

1)119861(119878)

+ 2120579 (1 minus 120582120572) [(119860119894

1)119861(119878)

(119861119894

2)119861(119878)

+ (119861119894

1)119861(119878)

(119860119894

2)119861(119878)

] minus 2 (1 minus 120582120572) (119887119894 + 120579)

sdot [(119860119894

1)119861(119878)

(119861119894

1)119861(119878)

+ (119860119894

2)119861(119878)

(119861119894

2)119861(119878)

]

1198662= 2 (1 minus 120582120572)

sdot (119887119894+ 120579) [((119861

119894

1)119861(119878)

)

2

+ ((119861119894

2)119861(119878)

)

2

]

minus 2120579 (119861119894

1)119861(119878)

(119861119894

2)119861(119878)

1199040= ((119887119871+ 120579) (119901

119871

1)2

+ (119887119867+ 120579) (119901

119867

1)2

+ 120579119908119871(119901119871

1minus 119901119871

2) + 120579119908

119867(119901119867

1minus 119901119867

2)

+ 120579V (1199011198711+ 119901119867

1) + (119908

119871+ 119908119867) (120573 + 120579) V

+ 119908119871(119886119871minus 119887119871119901119871

2) + 119908119867(119886119867minus 119887119867119901119867

2)

minus 120579 (119901119871

1119901119871

2+ 119901119867

1119901119867

2)) (119886119871(119901119871

1+ 119908119871)

+ 119886119867(119901119867

1+ 119908119867))minus1

(G1)

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The authors thank associate editor and anonymous refereesfor their numerous constructive comments and encourage-ment that have improved their paper greatly The work waspartly supported by (i) the National Natural Science Founda-tion ofChina (71201083 71572058 and 71571100) (ii) the Fun-damental Research Funds for the Central Universities SCUT(2015ZZ057) (iii) Jiangsu Province Science Foundation forYouths (BK2012379) and (iv) the Fundamental ResearchFunds for the Central Universities (NS2015076)

References

[1] J Li W N Zhang H Xu and J Jiang ldquoDynamic competitionand cooperation of road infrastructure investment of multipletourism destinations a case Study of Xidi and Hongcun WorldCulturalHeritagerdquoDiscreteDynamics inNature and Society vol2015 Article ID 962028 10 pages 2015

[2] T Paksoy EOzceylan andG-WWeber ldquoProfit oriented supplychain network optimizationrdquoCentral European Journal of Oper-ations Research vol 21 no 2 pp 455ndash478 2013

[3] X Zhang H Song and G Q Huang ldquoTourism supply chainmanagement a new research agendardquo Tourism Managementvol 30 no 3 pp 345ndash358 2009

[4] Z Yang and J Cai ldquoDo regional factors matter Determinantsof hotel industry performance in Chinardquo TourismManagementvol 52 pp 242ndash253 2016

[5] B Pan L Zhang and R Law ldquoThe complex matter of onlinehotel choicerdquoCornell Hospitality Quarterly vol 54 no 1 pp 74ndash83 2013

[6] L Ling X Guo and C Yang ldquoOpening the online marketplacean examination of hotel pricing and travel agency on-line

Discrete Dynamics in Nature and Society 15

distribution of roomsrdquo Tourism Management vol 45 pp 234ndash243 2014

[7] L Ling Y Dong X Guo and L Liang ldquoAvailability man-agement of hotel rooms under cooperation with online travelagenciesrdquo International Journal of Hospitality Management vol50 pp 145ndash152 2015

[8] J N K Liu andE Y Zhang ldquoAn investigation of factors affectingcustomer selection of online hotel booking channelsrdquo Interna-tional Journal of Hospitality Management vol 39 pp 71ndash832014

[9] L Fox ldquoFour Seasons Unveils $18 Million Website as LuxuryTravel Growsrdquo 2012 httpwwwtnoozcomarticlefour-sea-sons-unveils-18-million-dollar-website-as-luxury-travel-grows

[10] C-M Chen and Y-C Lin ldquoThe influence of uncertain demandon hotel capacityrdquo International Journal of Hospitality Manage-ment vol 34 no 1 pp 462ndash465 2013

[11] S Yang G Q Huang H Song and L Liang ldquoGame-theoreticapproach to competition dynamics in tourism supply chainsrdquoJournal of Travel Research vol 47 no 4 pp 425ndash439 2009

[12] G Q Huang H Song and X Zhang ldquoA comparative analysis ofquantity and price competitions in tourism supply chain net-works for package holidaysrdquo Service Industries Journal vol 30no 10 pp 1593ndash1606 2010

[13] Y Huang H Song G Q Huang and J Lou ldquoA comparativestudy of tourism supply chains with quantity competitionrdquoJournal of Travel Research vol 51 no 6 pp 717ndash729 2012

[14] H K Lee and Y Fernando ldquoThe antecedents and outcomes ofthe medical tourism supply chainrdquo Tourism Management vol46 pp 148ndash157 2015

[15] W-Y K Chiang D Chhajed and J D Hess ldquoDirect marketingindirect profits a strategic analysis of dual-channel supply-chain designrdquoManagement Science vol 49 no 1 pp 1ndash20 2003

[16] A A Tsay and N Agrawal ldquoChannel conflict and coordinationin the E-commerce agerdquo Production and Operations Manage-ment vol 13 no 1 pp 93ndash110 2004

[17] Q-H Li and B Li ldquoDual-channel supply chain equilibriumproblems regarding retail services and fairness concernsrdquoApplied Mathematical Modelling 2016

[18] S Panda N M Modak S S Sana and M Basu ldquoPricingand replenishment policies in dual-channel supply chain undercontinuous unit cost decreaserdquo Applied Mathematics and Com-putation vol 256 pp 913ndash929 2015

[19] Y Liu C Ding C Fan and X Chen ldquoPricing decision underdual-channel structure considering fairness and free-ridingbehaviorrdquo Discrete Dynamics in Nature and Society vol 2014Article ID 536576 10 pages 2014

[20] J Chen H Zhang and Y Sun ldquoImplementing coordinationcontracts in a manufacturer Stackelberg dual-channel supplychainrdquo Omega vol 40 no 5 pp 571ndash583 2012

[21] Q Ding C Dong and Z Pan ldquoA hierarchical pricing decisionprocess on a dual-channel problem with one manufacturer andone retailerrdquo International Journal of Production Economics vol175 pp 197ndash212 2016

[22] B Rodriguez and G Aydin ldquoPricing and assortment decisionsfor a manufacturer selling through dual channelsrdquo EuropeanJournal of Operational Research vol 242 no 3 pp 901ndash9092015

[23] T Lockyer ldquoThe perceived importance of price as one hotelselection dimensionrdquo Tourism Management vol 26 no 4 pp529ndash537 2005

[24] C-M Chen H-W Yang E Y Li and C-C Liu ldquoHow doeshotel pricing influence guest satisfaction by the moderatinginfluence of room occupancyrdquo International Journal of Hospi-tality Management vol 49 pp 136ndash138 2015

[25] J-M Espinet M Fluvia R Rigall-I-Torrent and A Salo ldquoHotelcharacteristics and seasonality in prices an analysis usingSpanish tour operatorsrsquo brochuresrdquo Tourism Economics vol 18no 4 pp 749ndash767 2012

[26] C Juaneda J M Raya and F Sastre ldquoPricing the time and loca-tion of a stay at a hotel or apartmentrdquo Tourism Economics vol17 no 2 pp 321ndash338 2011

[27] G Abrate G Fraquelli and G Viglia ldquoDynamic pricing strate-gies evidence from European hotelsrdquo International Journal ofHospitality Management vol 31 no 1 pp 160ndash168 2012

[28] D Q Yao and J J Liu ldquoCompetitive pricing of mixed retail ande-tail distribution channelsrdquo Omega vol 33 no 3 pp 235ndash2472005

[29] J Zhao and L Wang ldquoPricing and retail service decisionsin fuzzy uncertainty environmentsrdquo Applied Mathematics andComputation vol 250 pp 580ndash592 2015

[30] A A Tsay and N Agrawal ldquoChannel dynamics under priceand service competitionrdquo Manufacturing amp Service OperationsManagement vol 2 no 4 pp 372ndash391 2000

[31] S C Choi ldquoPrice competition in a duopoly common retailerchannelrdquo Journal of Retailing vol 72 no 2 pp 117ndash134 1996

[32] Y Bakos andE Brynjolfsson ldquoBundling and competition on theinternetrdquoMarketing Science vol 19 no 1 pp 63ndash82 2000

[33] H Song J H Kim and S Yang ldquoConfidence intervals fortourism demand elasticityrdquo Annals of Tourism Research vol 37no 2 pp 377ndash396 2010

[34] DMHanssens L J Parsons andR L SchultzMarket ResponseModels Econometric and Time Series Analysis Kluwer Aca-demic Publishers Boston Mass USA 2nd edition 2001

[35] H Kurata D-Q Yao and J J Liu ldquoPricing policies under directvs indirect channel competition and national vs store brandcompetitionrdquo European Journal of Operational Research vol180 no 1 pp 262ndash281 2007

[36] R Law and C Cheung ldquoA study of the perceived importance ofthe overall website quality of different classes of hotelsrdquo Inter-national Journal of Hospitality Management vol 25 no 3 pp525ndash531 2006

[37] K B Chen ldquoProcurement strategies and coordination mecha-nism of the supply chain with one manufacturer and multiplesuppliersrdquo International Journal of Production Economics vol138 no 1 pp 125ndash135 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Discrete Dynamics in Nature and Society 11

0 10 20 30 40 50 60 70 8018

2

22

24

26

28

3

32

34

36

38

4

Profi

t

HA channelOTA channel

times104

Value added by OTArsquos services ()

Figure 6 Channel profits in the integrated system

0 10 20 30 40 50 60 70 8005

1

15

2

25

3

35

4

45

Profi

t

HA channel in Bertrand gameOTA channel in Bertrand gameHA channel in Stackelberg gameOTA channel in Stackelberg game

times104

Value added by OTArsquos services ()

Figure 7 Channel profits in two games

service are enough to compensate for the cost In this casethe hotel and the OTA can get more profit from providing theservice However when V is high the additional profits fromOTArsquos service cannot make up for the high cost In such phe-nomenon the OTA should not increase investment in ser-vice

For both integrated model and Bertrand game modelwith the increase of V the profit of the HA channel willdecrease first and will then increase while in the Stackelberggamemodel the profit of theHA channel will always increase

with V With Figure 2 we can know that when OTA providesmore additional services it tends to increase its price Someof the customers will turn to reserve rooms from the HAbecause of the excessively high price in OTA As a result thehotel can gain more profits from the HA channel

8 Conclusion

With the development of e-commerce the providers oftourism products are more inclined to build dual-channelsIn this paper we consider the direct selling channel of HAand the traditional retail channel ofOTA from the perspectiveof tourism supply chain We develop a two-echelon tourismsupply chain model involving one hotel and one OTA wheretheOTAprovides related service Customers will be refundedpartially in case of cancelation or no-show We investigatethe optimal pricing strategies under several common casesThe integrated operation and the decentralized operationbased on Bertrand and Stackelberg games are studied andcorresponding equilibrium pricing policies are obtained

Our findings demonstrate that the hotel plays a crucialrole in optimizing the benefits of supply chain Consideringthe overall profit of the supply chain the hotel should act as aleader in dual-channel supply chain and formulate reasonablewholesale prices to improve the cooperative enthusiasm ofOTA so as to achieve optimization of the whole supplychain A lower wholesale price can help reduce OTArsquos loss ofprofit because of the opening of HA channel In addition weconsider the overbooking of the hotel and obtain the optimaloverbooking quantity We conclude that the hotel can alwaysobtain higher profits when the overbooking proportion iscontrolledwithin a certain range Otherwise if the overbook-ing proportion is too high the hotel can get extra profits onlywhen the overbooking cost is lower than a certain value

The contribution of this paper is that we extend tourismsupply chain to the dual-channel structure in which the hotelopens its direct channel to sell tourism products And theextant literature only refers to the single channel In additionwe realize that customer cancellations andno-showoccur fre-quently in hotel industry Thus we develop the game modelsbased on such phenomenon At last we derive the conditionsunder which the hotel dominant case is profitable for boththe supply chain members Our results can provide hotelsand OTAs with some new managerial insights under thedual-channel environment

This research can be extended in several directions infuture work For example in this paper we assume that allinformation is known to the hotel and OTA However someinformation could be asymmetric (eg see Chen [37]) Thuswe can explore the Bayesian equilibrium under asymmetricinformation settings Secondly the assumption of lineardemand is a limitation of this paperWe can further study thedynamic pricing in tourism dual-channel supply chain

Appendix

A Proof of Corollary 8

First we set (1199011198711)119861lowast

gt (119901119871

1)119878lowast which can be expressed as

12 Discrete Dynamics in Nature and Society

(1 minus 120582120572) (120579119886119871 + 120579119904119886119871+ 2119887119871119904119886119871+ 120579V120573 + 3119908

1198711205792+ 3119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

gt(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(A1)

The above equation can be simplified as

119908119871gt120579 [(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)]

4119887119871 (1 minus 120582120572) (119887119871 + 120579) (119887

119871+ 2120579)

(A2)

So we can get Corollary 8 B Proof of Corollary 9

If (1199011198941)119878lowast

gt (119901119894

1)119861lowast then

(1 minus 120582120572) (120579119886119894 + 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 2119908

1198941205792+ 2119908119894119887119894120579 minus 1205792V minus 2120579119887

119894V) + 119888120579 (119887

119894+ 120579)

minus (1 minus 120582120572) ((119901119894

1)119878lowast

+ (119901119894

1)119861lowast

) [2 (119887119894+ 120579)2minus 1205792] gt 0

120587119878lowast

1minus 120587119861lowast

1=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

2 (119887119871+ 120579)

((119901119871

1)119878lowast

minus (119901119871

1)119861lowast

)

+(1 minus 120582120572) (120579119886119867 + 120579119904119886

119867+ 2119887119867119904119886119867+ 120579V120573 + 2119908

1198671205792+ 2119908119867119887119867120579 minus 1205792V minus 2120579119887

119867V) + 119888120579 (119887

119867+ 120579)

2 (119887119867+ 120579)

((119901119867

1)119878lowast

minus (119901119867

1)119861lowast

)

minus (1 minus 120582120572)2 (119887119871+ 120579)2minus 1205792

2 (119887119871+ 120579)

[((119901119871

1)119878lowast

)2

minus ((119901119871

1)119861lowast

)2

] minus (1 minus 120582120572)2 (119887119867+ 120579)2minus 1205792

2 (119887119867+ 120579)

[((119901119867

1)119878lowast

)2

minus ((119901119867

1)119861lowast

)2

] gt 0

(B1)

If (1199011198711)119878lowast

lt (119901119871

1)119861lowast and (119901

119867

1)119878lowast

lt (119901119867

1)119861lowast we can prove

120587119878lowast

1gt 120587119861lowast

1similarly

From Propositions 3 and 7 with (3) we obtain that

120587119861lowast

2minus 120587119878lowast

2=

120579

4 (119887119871+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119871 + V (120573 + 120579) minus 119908119871(119887119871+ 120579)]

minus 2119888 (119887119871+ 120579) + 120579 (1 minus 120582120572) ((119901

119871

1)119861lowast

+ (119901119871

1)119878lowast

)

sdot ((119901119871

1)119861lowast

minus (119901119871

1)119878lowast

) +120579

4 (119887119867+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119867 + V (120573 + 120579) minus 119908 (119887119867+ 120579)]

minus 2119888 (119887119867+ 120579) + 120579 (1 minus 120582120572) ((119901

119867

1)119861lowast

+ (119901119867

1)119878lowast

)

sdot ((119901119867

1)119861lowast

minus (119901119867

1)119878lowast

)

(B2)

Note that

119863119894

2= [(1 minus 119904) 119886119894 minus 119887

119894119901119894

2] + 120573V + 120579 (119901

119894

1+ V minus 119901

119894

2) gt 0 (B3)

so we show that

2 (1 minus 120582120572) [(1 minus 119904) 119886119894 + V (120573 + 120579) minus 119908119894(119887119894+ 120579)]

minus 2119888 (119887119894+ 120579) + 120579 (1 minus 120582120572) ((119901

119894

1)119861lowast

+ (119901119894

1)119878lowast

)

gt 0

(B4)

Thus we have the following

(1) 120587119861lowast2

gt 120587119878lowast

2 if (1199011198711)119861lowast

gt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

gt (119901119867

1)119878lowast

(2) 120587119861lowast2

= 120587119878lowast

2 if (1199011198711)119861lowast

= (119901119871

1)119878lowast and (119901

119867

1)119861lowast

= (119901119867

1)119878lowast

(3) 120587119861lowast2

lt 120587119878lowast

2 if (1199011198711)119861lowast

lt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

lt (119901119867

1)119878lowast

Combined with Corollary 8 the proposition is proved

Discrete Dynamics in Nature and Society 13

C Proof of Corollary 10

The profit of hotel from the economy rooms is as follows

120587119871

= [(1 minus 120582120572) (119904119886119871 minus 120579V) minus 119888120579] 119901119871

1

+ [(1 minus 120582120572) (119886119871 minus 119904119886119871+ 120573V + 120579V) + 119888 (119887

119871+ 120579)] 119901

119871

2

+ 2120579 (1 minus 120582120572) 119901119871

1119901119871

2minus (1 minus 120582120572) (119887119871 + 120579) (119901

119871

1)2

minus (1 minus 120582120572) (119887119871 + 120579) (119901119871

2)2

minus (119886119871minus 119904119886119871+ 120573V + 120579V) 119888

(C1)

Define (119901119871

1)119861(119878)

= (119860119871

1)119861(119878)

+ (119861119871

1)119861(119878)

119908119871 (1199011198712)119861(119878)

=

(119860119871

2)119861(119878)

+ (119861119871

2)119861(119878)

119908119871 where

(119861119871

1)119861

=3120579 (119887119871+ 120579)

4 (119887119871+ 120579)2minus 1205792

(119861119871

1)119878

=120579 (119887119871+ 120579)

2 (119887119871+ 120579)2minus 1205792

(119861119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119861119871

1)119861(119878)

+1

2

(119860119871

1)119861

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

(119860119871

1)119878

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(119860119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119860119871

1)119861(119878)

+(1 minus 120582120572) [(1 minus 119904) 119886119871 + V (120579 + 120573)] + 119888 (119887

119871+ 120579)

2 (1 minus 120582120572) (119887119871 + 120579)

(C2)

Let 120597120587119871120597119908 = 0 then we get119908lowast

119871 Similarly we can get119908lowast

119867

D Proof of Proposition 12

Let 120587119889minus 120587119903gt 0 then we can get 119904

0 where the profits of hotel

from HA and OTA are as follows

120587119889= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1)

120587119903= (1 minus 120582120572) (119908119871119863

119871

2+ 119908119867119863119867

2)

(D1)

E Proof of Corollary 11

If Δ119862119871le 120582(1 minus 120582)119876

119871 then the profit of hotel is 120587119871

11 The

derivative of 12058711987111(Δ119862119871) is 120597120587119871

11120597Δ119862119871= (1 minus 120582120572)119901

119871

1gt 0 So

with the increase of Δ119862119871 12058711987111

will increase When Δ119862119871

=

120582(1 minus 120582)119876119871 12058711987111

is maximized If Δ119862119871

ge 120582(1 minus 120582)119876119871

then the profit of hotel is 12058711987112 The derivative of 120587119871

12(Δ119862119871) is

120597120587119871

12120597Δ119862119871= (1 minus 120582120572)119901

119871

1minus (1 minus 120582)(119901

119871

1+ 119888119871) lt 0 So with the

increase of Δ119862119871 12058711987111will decline When Δ119862

119871= 120582(1 minus 120582)119876

119871

120587119871

11is maximizedSimilarly we can get Δ119862lowast

119867

F Proof of Proposition 13

Assume that the overbooking proportion is 120574119871and 120574119867

(1) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) le 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

That is

120574119867lt

120582

1 minus 120582lt 120574119871

le120582119876119871+ 119876119867[1 minus (1 minus 120582) (1 + 120574

119867)]

(1 minus 120582)119876119871

(F1)

Thus the hotel would like to overbook to get more profitrather than room vacancy

(2) Consider (1198631198711+119863119871

2)(1minus120582) lt 119876

119871and (119863119867

1+119863119867

2)(1minus120582) gt

119876119867That is 120574

119871lt 120582(1 minus 120582) lt 120574

119867 Then the profit of hotel is

120587112

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F2)

Thenwhen 119888119867119906

lt (1minus120582120572)119901119867

1(1minus120582) that is120587

112minus120587111

gt 0the hotel would carry out overbooking

(3) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

14 Discrete Dynamics in Nature and Society

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867lt 120582(1 minus 120582) Then the profit of hotel is

120587113

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2+ 119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876]

(F3)

Then when 119888119871

119906lt (1 minus 120582120572)119901

119871

1(1 minus 120582) 120587

113minus120587111

gt 0 thusthe hotel would carry out overbooking

(4) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) gt 119876

119867

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867gt (120582119876

119867+ 119876119871[1 minus (1 minus 120582)(1 + 120574

119871)])(1 minus 120582)119876

119867

Then the profit of hotel is as follows

120587114

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2) (1 minus 120582) minus 119876

119871]

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F4)

Then when 119888119871119906lt (1minus120582120572)119901

119871

1(1minus120582) and 119888119867

119906lt (1minus120582120572)119901

119867

1

(1 minus 120582) 120587114

minus 120587111

gt 0 overbooking is preferred

G Threshold Values

Threshold values are as follows

1198711= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 3119908

1198941205792+ 3119908119894119887119894120579

minus 1205792V minus 2120579119887

119894V

1198712= 2119886119894(119887119894+ 120579) minus 119904119886

119894(2119887119894+ 120579) + 120579

2119908119894+ 2 (120579 + 120573) (119887

119894

+ 120579) V + 2119908119894(119887119894+ 120579)2minus 1205792V

1198713= 4120579V119887

119894120573 minus 120579119904119886

119894119887119894+ 2V1205731198872

119894+ 31198861198941205792+ 4119886119894119887119894120579

minus 21198861198941198872

119894119904 + 3120579

2V120573 + 1205792V119887119894+ 2120579V1198872

119894+ 21198861198941198872

119894

1198714= 3119886119894119887119894120579 + 3120579

2V120573 minus 2120579V1198872119894minus 1205792V119887119894+ 31198861198941205792

+ 21198861198941198872

119894119904 + 119886119887

119894119904120579 + 3119887

119894120573V120579

1198715= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 minus 120579

2V minus 2120579119887119894V

1198661= [(1 minus 120582120572) (119904119886119894 minus 120579V) minus 119888120579] (119861

119894

1)119861(119878)

+ [(1 minus 120582120572) (119886119894 minus 119904119886119894+ 120573V + 120579V) + 119888 (119887

119894+ 120579)]

sdot (119861119894

1)119861(119878)

+ 2120579 (1 minus 120582120572) [(119860119894

1)119861(119878)

(119861119894

2)119861(119878)

+ (119861119894

1)119861(119878)

(119860119894

2)119861(119878)

] minus 2 (1 minus 120582120572) (119887119894 + 120579)

sdot [(119860119894

1)119861(119878)

(119861119894

1)119861(119878)

+ (119860119894

2)119861(119878)

(119861119894

2)119861(119878)

]

1198662= 2 (1 minus 120582120572)

sdot (119887119894+ 120579) [((119861

119894

1)119861(119878)

)

2

+ ((119861119894

2)119861(119878)

)

2

]

minus 2120579 (119861119894

1)119861(119878)

(119861119894

2)119861(119878)

1199040= ((119887119871+ 120579) (119901

119871

1)2

+ (119887119867+ 120579) (119901

119867

1)2

+ 120579119908119871(119901119871

1minus 119901119871

2) + 120579119908

119867(119901119867

1minus 119901119867

2)

+ 120579V (1199011198711+ 119901119867

1) + (119908

119871+ 119908119867) (120573 + 120579) V

+ 119908119871(119886119871minus 119887119871119901119871

2) + 119908119867(119886119867minus 119887119867119901119867

2)

minus 120579 (119901119871

1119901119871

2+ 119901119867

1119901119867

2)) (119886119871(119901119871

1+ 119908119871)

+ 119886119867(119901119867

1+ 119908119867))minus1

(G1)

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The authors thank associate editor and anonymous refereesfor their numerous constructive comments and encourage-ment that have improved their paper greatly The work waspartly supported by (i) the National Natural Science Founda-tion ofChina (71201083 71572058 and 71571100) (ii) the Fun-damental Research Funds for the Central Universities SCUT(2015ZZ057) (iii) Jiangsu Province Science Foundation forYouths (BK2012379) and (iv) the Fundamental ResearchFunds for the Central Universities (NS2015076)

References

[1] J Li W N Zhang H Xu and J Jiang ldquoDynamic competitionand cooperation of road infrastructure investment of multipletourism destinations a case Study of Xidi and Hongcun WorldCulturalHeritagerdquoDiscreteDynamics inNature and Society vol2015 Article ID 962028 10 pages 2015

[2] T Paksoy EOzceylan andG-WWeber ldquoProfit oriented supplychain network optimizationrdquoCentral European Journal of Oper-ations Research vol 21 no 2 pp 455ndash478 2013

[3] X Zhang H Song and G Q Huang ldquoTourism supply chainmanagement a new research agendardquo Tourism Managementvol 30 no 3 pp 345ndash358 2009

[4] Z Yang and J Cai ldquoDo regional factors matter Determinantsof hotel industry performance in Chinardquo TourismManagementvol 52 pp 242ndash253 2016

[5] B Pan L Zhang and R Law ldquoThe complex matter of onlinehotel choicerdquoCornell Hospitality Quarterly vol 54 no 1 pp 74ndash83 2013

[6] L Ling X Guo and C Yang ldquoOpening the online marketplacean examination of hotel pricing and travel agency on-line

Discrete Dynamics in Nature and Society 15

distribution of roomsrdquo Tourism Management vol 45 pp 234ndash243 2014

[7] L Ling Y Dong X Guo and L Liang ldquoAvailability man-agement of hotel rooms under cooperation with online travelagenciesrdquo International Journal of Hospitality Management vol50 pp 145ndash152 2015

[8] J N K Liu andE Y Zhang ldquoAn investigation of factors affectingcustomer selection of online hotel booking channelsrdquo Interna-tional Journal of Hospitality Management vol 39 pp 71ndash832014

[9] L Fox ldquoFour Seasons Unveils $18 Million Website as LuxuryTravel Growsrdquo 2012 httpwwwtnoozcomarticlefour-sea-sons-unveils-18-million-dollar-website-as-luxury-travel-grows

[10] C-M Chen and Y-C Lin ldquoThe influence of uncertain demandon hotel capacityrdquo International Journal of Hospitality Manage-ment vol 34 no 1 pp 462ndash465 2013

[11] S Yang G Q Huang H Song and L Liang ldquoGame-theoreticapproach to competition dynamics in tourism supply chainsrdquoJournal of Travel Research vol 47 no 4 pp 425ndash439 2009

[12] G Q Huang H Song and X Zhang ldquoA comparative analysis ofquantity and price competitions in tourism supply chain net-works for package holidaysrdquo Service Industries Journal vol 30no 10 pp 1593ndash1606 2010

[13] Y Huang H Song G Q Huang and J Lou ldquoA comparativestudy of tourism supply chains with quantity competitionrdquoJournal of Travel Research vol 51 no 6 pp 717ndash729 2012

[14] H K Lee and Y Fernando ldquoThe antecedents and outcomes ofthe medical tourism supply chainrdquo Tourism Management vol46 pp 148ndash157 2015

[15] W-Y K Chiang D Chhajed and J D Hess ldquoDirect marketingindirect profits a strategic analysis of dual-channel supply-chain designrdquoManagement Science vol 49 no 1 pp 1ndash20 2003

[16] A A Tsay and N Agrawal ldquoChannel conflict and coordinationin the E-commerce agerdquo Production and Operations Manage-ment vol 13 no 1 pp 93ndash110 2004

[17] Q-H Li and B Li ldquoDual-channel supply chain equilibriumproblems regarding retail services and fairness concernsrdquoApplied Mathematical Modelling 2016

[18] S Panda N M Modak S S Sana and M Basu ldquoPricingand replenishment policies in dual-channel supply chain undercontinuous unit cost decreaserdquo Applied Mathematics and Com-putation vol 256 pp 913ndash929 2015

[19] Y Liu C Ding C Fan and X Chen ldquoPricing decision underdual-channel structure considering fairness and free-ridingbehaviorrdquo Discrete Dynamics in Nature and Society vol 2014Article ID 536576 10 pages 2014

[20] J Chen H Zhang and Y Sun ldquoImplementing coordinationcontracts in a manufacturer Stackelberg dual-channel supplychainrdquo Omega vol 40 no 5 pp 571ndash583 2012

[21] Q Ding C Dong and Z Pan ldquoA hierarchical pricing decisionprocess on a dual-channel problem with one manufacturer andone retailerrdquo International Journal of Production Economics vol175 pp 197ndash212 2016

[22] B Rodriguez and G Aydin ldquoPricing and assortment decisionsfor a manufacturer selling through dual channelsrdquo EuropeanJournal of Operational Research vol 242 no 3 pp 901ndash9092015

[23] T Lockyer ldquoThe perceived importance of price as one hotelselection dimensionrdquo Tourism Management vol 26 no 4 pp529ndash537 2005

[24] C-M Chen H-W Yang E Y Li and C-C Liu ldquoHow doeshotel pricing influence guest satisfaction by the moderatinginfluence of room occupancyrdquo International Journal of Hospi-tality Management vol 49 pp 136ndash138 2015

[25] J-M Espinet M Fluvia R Rigall-I-Torrent and A Salo ldquoHotelcharacteristics and seasonality in prices an analysis usingSpanish tour operatorsrsquo brochuresrdquo Tourism Economics vol 18no 4 pp 749ndash767 2012

[26] C Juaneda J M Raya and F Sastre ldquoPricing the time and loca-tion of a stay at a hotel or apartmentrdquo Tourism Economics vol17 no 2 pp 321ndash338 2011

[27] G Abrate G Fraquelli and G Viglia ldquoDynamic pricing strate-gies evidence from European hotelsrdquo International Journal ofHospitality Management vol 31 no 1 pp 160ndash168 2012

[28] D Q Yao and J J Liu ldquoCompetitive pricing of mixed retail ande-tail distribution channelsrdquo Omega vol 33 no 3 pp 235ndash2472005

[29] J Zhao and L Wang ldquoPricing and retail service decisionsin fuzzy uncertainty environmentsrdquo Applied Mathematics andComputation vol 250 pp 580ndash592 2015

[30] A A Tsay and N Agrawal ldquoChannel dynamics under priceand service competitionrdquo Manufacturing amp Service OperationsManagement vol 2 no 4 pp 372ndash391 2000

[31] S C Choi ldquoPrice competition in a duopoly common retailerchannelrdquo Journal of Retailing vol 72 no 2 pp 117ndash134 1996

[32] Y Bakos andE Brynjolfsson ldquoBundling and competition on theinternetrdquoMarketing Science vol 19 no 1 pp 63ndash82 2000

[33] H Song J H Kim and S Yang ldquoConfidence intervals fortourism demand elasticityrdquo Annals of Tourism Research vol 37no 2 pp 377ndash396 2010

[34] DMHanssens L J Parsons andR L SchultzMarket ResponseModels Econometric and Time Series Analysis Kluwer Aca-demic Publishers Boston Mass USA 2nd edition 2001

[35] H Kurata D-Q Yao and J J Liu ldquoPricing policies under directvs indirect channel competition and national vs store brandcompetitionrdquo European Journal of Operational Research vol180 no 1 pp 262ndash281 2007

[36] R Law and C Cheung ldquoA study of the perceived importance ofthe overall website quality of different classes of hotelsrdquo Inter-national Journal of Hospitality Management vol 25 no 3 pp525ndash531 2006

[37] K B Chen ldquoProcurement strategies and coordination mecha-nism of the supply chain with one manufacturer and multiplesuppliersrdquo International Journal of Production Economics vol138 no 1 pp 125ndash135 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

12 Discrete Dynamics in Nature and Society

(1 minus 120582120572) (120579119886119871 + 120579119904119886119871+ 2119887119871119904119886119871+ 120579V120573 + 3119908

1198711205792+ 3119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

gt(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(A1)

The above equation can be simplified as

119908119871gt120579 [(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)]

4119887119871 (1 minus 120582120572) (119887119871 + 120579) (119887

119871+ 2120579)

(A2)

So we can get Corollary 8 B Proof of Corollary 9

If (1199011198941)119878lowast

gt (119901119894

1)119861lowast then

(1 minus 120582120572) (120579119886119894 + 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 2119908

1198941205792+ 2119908119894119887119894120579 minus 1205792V minus 2120579119887

119894V) + 119888120579 (119887

119894+ 120579)

minus (1 minus 120582120572) ((119901119894

1)119878lowast

+ (119901119894

1)119861lowast

) [2 (119887119894+ 120579)2minus 1205792] gt 0

120587119878lowast

1minus 120587119861lowast

1=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 + 2119908

1198711205792+ 2119908119871119887119871120579 minus 1205792V minus 2120579119887

119871V) + 119888120579 (119887

119871+ 120579)

2 (119887119871+ 120579)

((119901119871

1)119878lowast

minus (119901119871

1)119861lowast

)

+(1 minus 120582120572) (120579119886119867 + 120579119904119886

119867+ 2119887119867119904119886119867+ 120579V120573 + 2119908

1198671205792+ 2119908119867119887119867120579 minus 1205792V minus 2120579119887

119867V) + 119888120579 (119887

119867+ 120579)

2 (119887119867+ 120579)

((119901119867

1)119878lowast

minus (119901119867

1)119861lowast

)

minus (1 minus 120582120572)2 (119887119871+ 120579)2minus 1205792

2 (119887119871+ 120579)

[((119901119871

1)119878lowast

)2

minus ((119901119871

1)119861lowast

)2

] minus (1 minus 120582120572)2 (119887119867+ 120579)2minus 1205792

2 (119887119867+ 120579)

[((119901119867

1)119878lowast

)2

minus ((119901119867

1)119861lowast

)2

] gt 0

(B1)

If (1199011198711)119878lowast

lt (119901119871

1)119861lowast and (119901

119867

1)119878lowast

lt (119901119867

1)119861lowast we can prove

120587119878lowast

1gt 120587119861lowast

1similarly

From Propositions 3 and 7 with (3) we obtain that

120587119861lowast

2minus 120587119878lowast

2=

120579

4 (119887119871+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119871 + V (120573 + 120579) minus 119908119871(119887119871+ 120579)]

minus 2119888 (119887119871+ 120579) + 120579 (1 minus 120582120572) ((119901

119871

1)119861lowast

+ (119901119871

1)119878lowast

)

sdot ((119901119871

1)119861lowast

minus (119901119871

1)119878lowast

) +120579

4 (119887119867+ 120579)

2 (1 minus 120582120572)

sdot [(1 minus 119904) 119886119867 + V (120573 + 120579) minus 119908 (119887119867+ 120579)]

minus 2119888 (119887119867+ 120579) + 120579 (1 minus 120582120572) ((119901

119867

1)119861lowast

+ (119901119867

1)119878lowast

)

sdot ((119901119867

1)119861lowast

minus (119901119867

1)119878lowast

)

(B2)

Note that

119863119894

2= [(1 minus 119904) 119886119894 minus 119887

119894119901119894

2] + 120573V + 120579 (119901

119894

1+ V minus 119901

119894

2) gt 0 (B3)

so we show that

2 (1 minus 120582120572) [(1 minus 119904) 119886119894 + V (120573 + 120579) minus 119908119894(119887119894+ 120579)]

minus 2119888 (119887119894+ 120579) + 120579 (1 minus 120582120572) ((119901

119894

1)119861lowast

+ (119901119894

1)119878lowast

)

gt 0

(B4)

Thus we have the following

(1) 120587119861lowast2

gt 120587119878lowast

2 if (1199011198711)119861lowast

gt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

gt (119901119867

1)119878lowast

(2) 120587119861lowast2

= 120587119878lowast

2 if (1199011198711)119861lowast

= (119901119871

1)119878lowast and (119901

119867

1)119861lowast

= (119901119867

1)119878lowast

(3) 120587119861lowast2

lt 120587119878lowast

2 if (1199011198711)119861lowast

lt (119901119871

1)119878lowast and (119901

119867

1)119861lowast

lt (119901119867

1)119878lowast

Combined with Corollary 8 the proposition is proved

Discrete Dynamics in Nature and Society 13

C Proof of Corollary 10

The profit of hotel from the economy rooms is as follows

120587119871

= [(1 minus 120582120572) (119904119886119871 minus 120579V) minus 119888120579] 119901119871

1

+ [(1 minus 120582120572) (119886119871 minus 119904119886119871+ 120573V + 120579V) + 119888 (119887

119871+ 120579)] 119901

119871

2

+ 2120579 (1 minus 120582120572) 119901119871

1119901119871

2minus (1 minus 120582120572) (119887119871 + 120579) (119901

119871

1)2

minus (1 minus 120582120572) (119887119871 + 120579) (119901119871

2)2

minus (119886119871minus 119904119886119871+ 120573V + 120579V) 119888

(C1)

Define (119901119871

1)119861(119878)

= (119860119871

1)119861(119878)

+ (119861119871

1)119861(119878)

119908119871 (1199011198712)119861(119878)

=

(119860119871

2)119861(119878)

+ (119861119871

2)119861(119878)

119908119871 where

(119861119871

1)119861

=3120579 (119887119871+ 120579)

4 (119887119871+ 120579)2minus 1205792

(119861119871

1)119878

=120579 (119887119871+ 120579)

2 (119887119871+ 120579)2minus 1205792

(119861119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119861119871

1)119861(119878)

+1

2

(119860119871

1)119861

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

(119860119871

1)119878

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(119860119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119860119871

1)119861(119878)

+(1 minus 120582120572) [(1 minus 119904) 119886119871 + V (120579 + 120573)] + 119888 (119887

119871+ 120579)

2 (1 minus 120582120572) (119887119871 + 120579)

(C2)

Let 120597120587119871120597119908 = 0 then we get119908lowast

119871 Similarly we can get119908lowast

119867

D Proof of Proposition 12

Let 120587119889minus 120587119903gt 0 then we can get 119904

0 where the profits of hotel

from HA and OTA are as follows

120587119889= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1)

120587119903= (1 minus 120582120572) (119908119871119863

119871

2+ 119908119867119863119867

2)

(D1)

E Proof of Corollary 11

If Δ119862119871le 120582(1 minus 120582)119876

119871 then the profit of hotel is 120587119871

11 The

derivative of 12058711987111(Δ119862119871) is 120597120587119871

11120597Δ119862119871= (1 minus 120582120572)119901

119871

1gt 0 So

with the increase of Δ119862119871 12058711987111

will increase When Δ119862119871

=

120582(1 minus 120582)119876119871 12058711987111

is maximized If Δ119862119871

ge 120582(1 minus 120582)119876119871

then the profit of hotel is 12058711987112 The derivative of 120587119871

12(Δ119862119871) is

120597120587119871

12120597Δ119862119871= (1 minus 120582120572)119901

119871

1minus (1 minus 120582)(119901

119871

1+ 119888119871) lt 0 So with the

increase of Δ119862119871 12058711987111will decline When Δ119862

119871= 120582(1 minus 120582)119876

119871

120587119871

11is maximizedSimilarly we can get Δ119862lowast

119867

F Proof of Proposition 13

Assume that the overbooking proportion is 120574119871and 120574119867

(1) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) le 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

That is

120574119867lt

120582

1 minus 120582lt 120574119871

le120582119876119871+ 119876119867[1 minus (1 minus 120582) (1 + 120574

119867)]

(1 minus 120582)119876119871

(F1)

Thus the hotel would like to overbook to get more profitrather than room vacancy

(2) Consider (1198631198711+119863119871

2)(1minus120582) lt 119876

119871and (119863119867

1+119863119867

2)(1minus120582) gt

119876119867That is 120574

119871lt 120582(1 minus 120582) lt 120574

119867 Then the profit of hotel is

120587112

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F2)

Thenwhen 119888119867119906

lt (1minus120582120572)119901119867

1(1minus120582) that is120587

112minus120587111

gt 0the hotel would carry out overbooking

(3) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

14 Discrete Dynamics in Nature and Society

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867lt 120582(1 minus 120582) Then the profit of hotel is

120587113

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2+ 119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876]

(F3)

Then when 119888119871

119906lt (1 minus 120582120572)119901

119871

1(1 minus 120582) 120587

113minus120587111

gt 0 thusthe hotel would carry out overbooking

(4) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) gt 119876

119867

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867gt (120582119876

119867+ 119876119871[1 minus (1 minus 120582)(1 + 120574

119871)])(1 minus 120582)119876

119867

Then the profit of hotel is as follows

120587114

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2) (1 minus 120582) minus 119876

119871]

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F4)

Then when 119888119871119906lt (1minus120582120572)119901

119871

1(1minus120582) and 119888119867

119906lt (1minus120582120572)119901

119867

1

(1 minus 120582) 120587114

minus 120587111

gt 0 overbooking is preferred

G Threshold Values

Threshold values are as follows

1198711= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 3119908

1198941205792+ 3119908119894119887119894120579

minus 1205792V minus 2120579119887

119894V

1198712= 2119886119894(119887119894+ 120579) minus 119904119886

119894(2119887119894+ 120579) + 120579

2119908119894+ 2 (120579 + 120573) (119887

119894

+ 120579) V + 2119908119894(119887119894+ 120579)2minus 1205792V

1198713= 4120579V119887

119894120573 minus 120579119904119886

119894119887119894+ 2V1205731198872

119894+ 31198861198941205792+ 4119886119894119887119894120579

minus 21198861198941198872

119894119904 + 3120579

2V120573 + 1205792V119887119894+ 2120579V1198872

119894+ 21198861198941198872

119894

1198714= 3119886119894119887119894120579 + 3120579

2V120573 minus 2120579V1198872119894minus 1205792V119887119894+ 31198861198941205792

+ 21198861198941198872

119894119904 + 119886119887

119894119904120579 + 3119887

119894120573V120579

1198715= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 minus 120579

2V minus 2120579119887119894V

1198661= [(1 minus 120582120572) (119904119886119894 minus 120579V) minus 119888120579] (119861

119894

1)119861(119878)

+ [(1 minus 120582120572) (119886119894 minus 119904119886119894+ 120573V + 120579V) + 119888 (119887

119894+ 120579)]

sdot (119861119894

1)119861(119878)

+ 2120579 (1 minus 120582120572) [(119860119894

1)119861(119878)

(119861119894

2)119861(119878)

+ (119861119894

1)119861(119878)

(119860119894

2)119861(119878)

] minus 2 (1 minus 120582120572) (119887119894 + 120579)

sdot [(119860119894

1)119861(119878)

(119861119894

1)119861(119878)

+ (119860119894

2)119861(119878)

(119861119894

2)119861(119878)

]

1198662= 2 (1 minus 120582120572)

sdot (119887119894+ 120579) [((119861

119894

1)119861(119878)

)

2

+ ((119861119894

2)119861(119878)

)

2

]

minus 2120579 (119861119894

1)119861(119878)

(119861119894

2)119861(119878)

1199040= ((119887119871+ 120579) (119901

119871

1)2

+ (119887119867+ 120579) (119901

119867

1)2

+ 120579119908119871(119901119871

1minus 119901119871

2) + 120579119908

119867(119901119867

1minus 119901119867

2)

+ 120579V (1199011198711+ 119901119867

1) + (119908

119871+ 119908119867) (120573 + 120579) V

+ 119908119871(119886119871minus 119887119871119901119871

2) + 119908119867(119886119867minus 119887119867119901119867

2)

minus 120579 (119901119871

1119901119871

2+ 119901119867

1119901119867

2)) (119886119871(119901119871

1+ 119908119871)

+ 119886119867(119901119867

1+ 119908119867))minus1

(G1)

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The authors thank associate editor and anonymous refereesfor their numerous constructive comments and encourage-ment that have improved their paper greatly The work waspartly supported by (i) the National Natural Science Founda-tion ofChina (71201083 71572058 and 71571100) (ii) the Fun-damental Research Funds for the Central Universities SCUT(2015ZZ057) (iii) Jiangsu Province Science Foundation forYouths (BK2012379) and (iv) the Fundamental ResearchFunds for the Central Universities (NS2015076)

References

[1] J Li W N Zhang H Xu and J Jiang ldquoDynamic competitionand cooperation of road infrastructure investment of multipletourism destinations a case Study of Xidi and Hongcun WorldCulturalHeritagerdquoDiscreteDynamics inNature and Society vol2015 Article ID 962028 10 pages 2015

[2] T Paksoy EOzceylan andG-WWeber ldquoProfit oriented supplychain network optimizationrdquoCentral European Journal of Oper-ations Research vol 21 no 2 pp 455ndash478 2013

[3] X Zhang H Song and G Q Huang ldquoTourism supply chainmanagement a new research agendardquo Tourism Managementvol 30 no 3 pp 345ndash358 2009

[4] Z Yang and J Cai ldquoDo regional factors matter Determinantsof hotel industry performance in Chinardquo TourismManagementvol 52 pp 242ndash253 2016

[5] B Pan L Zhang and R Law ldquoThe complex matter of onlinehotel choicerdquoCornell Hospitality Quarterly vol 54 no 1 pp 74ndash83 2013

[6] L Ling X Guo and C Yang ldquoOpening the online marketplacean examination of hotel pricing and travel agency on-line

Discrete Dynamics in Nature and Society 15

distribution of roomsrdquo Tourism Management vol 45 pp 234ndash243 2014

[7] L Ling Y Dong X Guo and L Liang ldquoAvailability man-agement of hotel rooms under cooperation with online travelagenciesrdquo International Journal of Hospitality Management vol50 pp 145ndash152 2015

[8] J N K Liu andE Y Zhang ldquoAn investigation of factors affectingcustomer selection of online hotel booking channelsrdquo Interna-tional Journal of Hospitality Management vol 39 pp 71ndash832014

[9] L Fox ldquoFour Seasons Unveils $18 Million Website as LuxuryTravel Growsrdquo 2012 httpwwwtnoozcomarticlefour-sea-sons-unveils-18-million-dollar-website-as-luxury-travel-grows

[10] C-M Chen and Y-C Lin ldquoThe influence of uncertain demandon hotel capacityrdquo International Journal of Hospitality Manage-ment vol 34 no 1 pp 462ndash465 2013

[11] S Yang G Q Huang H Song and L Liang ldquoGame-theoreticapproach to competition dynamics in tourism supply chainsrdquoJournal of Travel Research vol 47 no 4 pp 425ndash439 2009

[12] G Q Huang H Song and X Zhang ldquoA comparative analysis ofquantity and price competitions in tourism supply chain net-works for package holidaysrdquo Service Industries Journal vol 30no 10 pp 1593ndash1606 2010

[13] Y Huang H Song G Q Huang and J Lou ldquoA comparativestudy of tourism supply chains with quantity competitionrdquoJournal of Travel Research vol 51 no 6 pp 717ndash729 2012

[14] H K Lee and Y Fernando ldquoThe antecedents and outcomes ofthe medical tourism supply chainrdquo Tourism Management vol46 pp 148ndash157 2015

[15] W-Y K Chiang D Chhajed and J D Hess ldquoDirect marketingindirect profits a strategic analysis of dual-channel supply-chain designrdquoManagement Science vol 49 no 1 pp 1ndash20 2003

[16] A A Tsay and N Agrawal ldquoChannel conflict and coordinationin the E-commerce agerdquo Production and Operations Manage-ment vol 13 no 1 pp 93ndash110 2004

[17] Q-H Li and B Li ldquoDual-channel supply chain equilibriumproblems regarding retail services and fairness concernsrdquoApplied Mathematical Modelling 2016

[18] S Panda N M Modak S S Sana and M Basu ldquoPricingand replenishment policies in dual-channel supply chain undercontinuous unit cost decreaserdquo Applied Mathematics and Com-putation vol 256 pp 913ndash929 2015

[19] Y Liu C Ding C Fan and X Chen ldquoPricing decision underdual-channel structure considering fairness and free-ridingbehaviorrdquo Discrete Dynamics in Nature and Society vol 2014Article ID 536576 10 pages 2014

[20] J Chen H Zhang and Y Sun ldquoImplementing coordinationcontracts in a manufacturer Stackelberg dual-channel supplychainrdquo Omega vol 40 no 5 pp 571ndash583 2012

[21] Q Ding C Dong and Z Pan ldquoA hierarchical pricing decisionprocess on a dual-channel problem with one manufacturer andone retailerrdquo International Journal of Production Economics vol175 pp 197ndash212 2016

[22] B Rodriguez and G Aydin ldquoPricing and assortment decisionsfor a manufacturer selling through dual channelsrdquo EuropeanJournal of Operational Research vol 242 no 3 pp 901ndash9092015

[23] T Lockyer ldquoThe perceived importance of price as one hotelselection dimensionrdquo Tourism Management vol 26 no 4 pp529ndash537 2005

[24] C-M Chen H-W Yang E Y Li and C-C Liu ldquoHow doeshotel pricing influence guest satisfaction by the moderatinginfluence of room occupancyrdquo International Journal of Hospi-tality Management vol 49 pp 136ndash138 2015

[25] J-M Espinet M Fluvia R Rigall-I-Torrent and A Salo ldquoHotelcharacteristics and seasonality in prices an analysis usingSpanish tour operatorsrsquo brochuresrdquo Tourism Economics vol 18no 4 pp 749ndash767 2012

[26] C Juaneda J M Raya and F Sastre ldquoPricing the time and loca-tion of a stay at a hotel or apartmentrdquo Tourism Economics vol17 no 2 pp 321ndash338 2011

[27] G Abrate G Fraquelli and G Viglia ldquoDynamic pricing strate-gies evidence from European hotelsrdquo International Journal ofHospitality Management vol 31 no 1 pp 160ndash168 2012

[28] D Q Yao and J J Liu ldquoCompetitive pricing of mixed retail ande-tail distribution channelsrdquo Omega vol 33 no 3 pp 235ndash2472005

[29] J Zhao and L Wang ldquoPricing and retail service decisionsin fuzzy uncertainty environmentsrdquo Applied Mathematics andComputation vol 250 pp 580ndash592 2015

[30] A A Tsay and N Agrawal ldquoChannel dynamics under priceand service competitionrdquo Manufacturing amp Service OperationsManagement vol 2 no 4 pp 372ndash391 2000

[31] S C Choi ldquoPrice competition in a duopoly common retailerchannelrdquo Journal of Retailing vol 72 no 2 pp 117ndash134 1996

[32] Y Bakos andE Brynjolfsson ldquoBundling and competition on theinternetrdquoMarketing Science vol 19 no 1 pp 63ndash82 2000

[33] H Song J H Kim and S Yang ldquoConfidence intervals fortourism demand elasticityrdquo Annals of Tourism Research vol 37no 2 pp 377ndash396 2010

[34] DMHanssens L J Parsons andR L SchultzMarket ResponseModels Econometric and Time Series Analysis Kluwer Aca-demic Publishers Boston Mass USA 2nd edition 2001

[35] H Kurata D-Q Yao and J J Liu ldquoPricing policies under directvs indirect channel competition and national vs store brandcompetitionrdquo European Journal of Operational Research vol180 no 1 pp 262ndash281 2007

[36] R Law and C Cheung ldquoA study of the perceived importance ofthe overall website quality of different classes of hotelsrdquo Inter-national Journal of Hospitality Management vol 25 no 3 pp525ndash531 2006

[37] K B Chen ldquoProcurement strategies and coordination mecha-nism of the supply chain with one manufacturer and multiplesuppliersrdquo International Journal of Production Economics vol138 no 1 pp 125ndash135 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Discrete Dynamics in Nature and Society 13

C Proof of Corollary 10

The profit of hotel from the economy rooms is as follows

120587119871

= [(1 minus 120582120572) (119904119886119871 minus 120579V) minus 119888120579] 119901119871

1

+ [(1 minus 120582120572) (119886119871 minus 119904119886119871+ 120573V + 120579V) + 119888 (119887

119871+ 120579)] 119901

119871

2

+ 2120579 (1 minus 120582120572) 119901119871

1119901119871

2minus (1 minus 120582120572) (119887119871 + 120579) (119901

119871

1)2

minus (1 minus 120582120572) (119887119871 + 120579) (119901119871

2)2

minus (119886119871minus 119904119886119871+ 120573V + 120579V) 119888

(C1)

Define (119901119871

1)119861(119878)

= (119860119871

1)119861(119878)

+ (119861119871

1)119861(119878)

119908119871 (1199011198712)119861(119878)

=

(119860119871

2)119861(119878)

+ (119861119871

2)119861(119878)

119908119871 where

(119861119871

1)119861

=3120579 (119887119871+ 120579)

4 (119887119871+ 120579)2minus 1205792

(119861119871

1)119878

=120579 (119887119871+ 120579)

2 (119887119871+ 120579)2minus 1205792

(119861119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119861119871

1)119861(119878)

+1

2

(119860119871

1)119861

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 1205792]

(119860119871

1)119878

=(1 minus 120582120572) (120579119886119871 + 120579119904119886

119871+ 2119887119871119904119886119871+ 120579V120573 minus 120579

2V minus 2120579119887119871V) + 119888120579 (119887

119871+ 120579)

(1 minus 120582120572) [4 (119887119871 + 120579)2minus 21205792]

(119860119871

2)119861(119878)

=120579

2 (119887119871+ 120579)

(119860119871

1)119861(119878)

+(1 minus 120582120572) [(1 minus 119904) 119886119871 + V (120579 + 120573)] + 119888 (119887

119871+ 120579)

2 (1 minus 120582120572) (119887119871 + 120579)

(C2)

Let 120597120587119871120597119908 = 0 then we get119908lowast

119871 Similarly we can get119908lowast

119867

D Proof of Proposition 12

Let 120587119889minus 120587119903gt 0 then we can get 119904

0 where the profits of hotel

from HA and OTA are as follows

120587119889= (1 minus 120582120572) (119901

119871

1119863119871

1+ 119901119867

1119863119867

1)

120587119903= (1 minus 120582120572) (119908119871119863

119871

2+ 119908119867119863119867

2)

(D1)

E Proof of Corollary 11

If Δ119862119871le 120582(1 minus 120582)119876

119871 then the profit of hotel is 120587119871

11 The

derivative of 12058711987111(Δ119862119871) is 120597120587119871

11120597Δ119862119871= (1 minus 120582120572)119901

119871

1gt 0 So

with the increase of Δ119862119871 12058711987111

will increase When Δ119862119871

=

120582(1 minus 120582)119876119871 12058711987111

is maximized If Δ119862119871

ge 120582(1 minus 120582)119876119871

then the profit of hotel is 12058711987112 The derivative of 120587119871

12(Δ119862119871) is

120597120587119871

12120597Δ119862119871= (1 minus 120582120572)119901

119871

1minus (1 minus 120582)(119901

119871

1+ 119888119871) lt 0 So with the

increase of Δ119862119871 12058711987111will decline When Δ119862

119871= 120582(1 minus 120582)119876

119871

120587119871

11is maximizedSimilarly we can get Δ119862lowast

119867

F Proof of Proposition 13

Assume that the overbooking proportion is 120574119871and 120574119867

(1) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) le 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

That is

120574119867lt

120582

1 minus 120582lt 120574119871

le120582119876119871+ 119876119867[1 minus (1 minus 120582) (1 + 120574

119867)]

(1 minus 120582)119876119871

(F1)

Thus the hotel would like to overbook to get more profitrather than room vacancy

(2) Consider (1198631198711+119863119871

2)(1minus120582) lt 119876

119871and (119863119867

1+119863119867

2)(1minus120582) gt

119876119867That is 120574

119871lt 120582(1 minus 120582) lt 120574

119867 Then the profit of hotel is

120587112

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F2)

Thenwhen 119888119867119906

lt (1minus120582120572)119901119867

1(1minus120582) that is120587

112minus120587111

gt 0the hotel would carry out overbooking

(3) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) lt 119876

119867

14 Discrete Dynamics in Nature and Society

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867lt 120582(1 minus 120582) Then the profit of hotel is

120587113

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2+ 119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876]

(F3)

Then when 119888119871

119906lt (1 minus 120582120572)119901

119871

1(1 minus 120582) 120587

113minus120587111

gt 0 thusthe hotel would carry out overbooking

(4) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) gt 119876

119867

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867gt (120582119876

119867+ 119876119871[1 minus (1 minus 120582)(1 + 120574

119871)])(1 minus 120582)119876

119867

Then the profit of hotel is as follows

120587114

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2) (1 minus 120582) minus 119876

119871]

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F4)

Then when 119888119871119906lt (1minus120582120572)119901

119871

1(1minus120582) and 119888119867

119906lt (1minus120582120572)119901

119867

1

(1 minus 120582) 120587114

minus 120587111

gt 0 overbooking is preferred

G Threshold Values

Threshold values are as follows

1198711= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 3119908

1198941205792+ 3119908119894119887119894120579

minus 1205792V minus 2120579119887

119894V

1198712= 2119886119894(119887119894+ 120579) minus 119904119886

119894(2119887119894+ 120579) + 120579

2119908119894+ 2 (120579 + 120573) (119887

119894

+ 120579) V + 2119908119894(119887119894+ 120579)2minus 1205792V

1198713= 4120579V119887

119894120573 minus 120579119904119886

119894119887119894+ 2V1205731198872

119894+ 31198861198941205792+ 4119886119894119887119894120579

minus 21198861198941198872

119894119904 + 3120579

2V120573 + 1205792V119887119894+ 2120579V1198872

119894+ 21198861198941198872

119894

1198714= 3119886119894119887119894120579 + 3120579

2V120573 minus 2120579V1198872119894minus 1205792V119887119894+ 31198861198941205792

+ 21198861198941198872

119894119904 + 119886119887

119894119904120579 + 3119887

119894120573V120579

1198715= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 minus 120579

2V minus 2120579119887119894V

1198661= [(1 minus 120582120572) (119904119886119894 minus 120579V) minus 119888120579] (119861

119894

1)119861(119878)

+ [(1 minus 120582120572) (119886119894 minus 119904119886119894+ 120573V + 120579V) + 119888 (119887

119894+ 120579)]

sdot (119861119894

1)119861(119878)

+ 2120579 (1 minus 120582120572) [(119860119894

1)119861(119878)

(119861119894

2)119861(119878)

+ (119861119894

1)119861(119878)

(119860119894

2)119861(119878)

] minus 2 (1 minus 120582120572) (119887119894 + 120579)

sdot [(119860119894

1)119861(119878)

(119861119894

1)119861(119878)

+ (119860119894

2)119861(119878)

(119861119894

2)119861(119878)

]

1198662= 2 (1 minus 120582120572)

sdot (119887119894+ 120579) [((119861

119894

1)119861(119878)

)

2

+ ((119861119894

2)119861(119878)

)

2

]

minus 2120579 (119861119894

1)119861(119878)

(119861119894

2)119861(119878)

1199040= ((119887119871+ 120579) (119901

119871

1)2

+ (119887119867+ 120579) (119901

119867

1)2

+ 120579119908119871(119901119871

1minus 119901119871

2) + 120579119908

119867(119901119867

1minus 119901119867

2)

+ 120579V (1199011198711+ 119901119867

1) + (119908

119871+ 119908119867) (120573 + 120579) V

+ 119908119871(119886119871minus 119887119871119901119871

2) + 119908119867(119886119867minus 119887119867119901119867

2)

minus 120579 (119901119871

1119901119871

2+ 119901119867

1119901119867

2)) (119886119871(119901119871

1+ 119908119871)

+ 119886119867(119901119867

1+ 119908119867))minus1

(G1)

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The authors thank associate editor and anonymous refereesfor their numerous constructive comments and encourage-ment that have improved their paper greatly The work waspartly supported by (i) the National Natural Science Founda-tion ofChina (71201083 71572058 and 71571100) (ii) the Fun-damental Research Funds for the Central Universities SCUT(2015ZZ057) (iii) Jiangsu Province Science Foundation forYouths (BK2012379) and (iv) the Fundamental ResearchFunds for the Central Universities (NS2015076)

References

[1] J Li W N Zhang H Xu and J Jiang ldquoDynamic competitionand cooperation of road infrastructure investment of multipletourism destinations a case Study of Xidi and Hongcun WorldCulturalHeritagerdquoDiscreteDynamics inNature and Society vol2015 Article ID 962028 10 pages 2015

[2] T Paksoy EOzceylan andG-WWeber ldquoProfit oriented supplychain network optimizationrdquoCentral European Journal of Oper-ations Research vol 21 no 2 pp 455ndash478 2013

[3] X Zhang H Song and G Q Huang ldquoTourism supply chainmanagement a new research agendardquo Tourism Managementvol 30 no 3 pp 345ndash358 2009

[4] Z Yang and J Cai ldquoDo regional factors matter Determinantsof hotel industry performance in Chinardquo TourismManagementvol 52 pp 242ndash253 2016

[5] B Pan L Zhang and R Law ldquoThe complex matter of onlinehotel choicerdquoCornell Hospitality Quarterly vol 54 no 1 pp 74ndash83 2013

[6] L Ling X Guo and C Yang ldquoOpening the online marketplacean examination of hotel pricing and travel agency on-line

Discrete Dynamics in Nature and Society 15

distribution of roomsrdquo Tourism Management vol 45 pp 234ndash243 2014

[7] L Ling Y Dong X Guo and L Liang ldquoAvailability man-agement of hotel rooms under cooperation with online travelagenciesrdquo International Journal of Hospitality Management vol50 pp 145ndash152 2015

[8] J N K Liu andE Y Zhang ldquoAn investigation of factors affectingcustomer selection of online hotel booking channelsrdquo Interna-tional Journal of Hospitality Management vol 39 pp 71ndash832014

[9] L Fox ldquoFour Seasons Unveils $18 Million Website as LuxuryTravel Growsrdquo 2012 httpwwwtnoozcomarticlefour-sea-sons-unveils-18-million-dollar-website-as-luxury-travel-grows

[10] C-M Chen and Y-C Lin ldquoThe influence of uncertain demandon hotel capacityrdquo International Journal of Hospitality Manage-ment vol 34 no 1 pp 462ndash465 2013

[11] S Yang G Q Huang H Song and L Liang ldquoGame-theoreticapproach to competition dynamics in tourism supply chainsrdquoJournal of Travel Research vol 47 no 4 pp 425ndash439 2009

[12] G Q Huang H Song and X Zhang ldquoA comparative analysis ofquantity and price competitions in tourism supply chain net-works for package holidaysrdquo Service Industries Journal vol 30no 10 pp 1593ndash1606 2010

[13] Y Huang H Song G Q Huang and J Lou ldquoA comparativestudy of tourism supply chains with quantity competitionrdquoJournal of Travel Research vol 51 no 6 pp 717ndash729 2012

[14] H K Lee and Y Fernando ldquoThe antecedents and outcomes ofthe medical tourism supply chainrdquo Tourism Management vol46 pp 148ndash157 2015

[15] W-Y K Chiang D Chhajed and J D Hess ldquoDirect marketingindirect profits a strategic analysis of dual-channel supply-chain designrdquoManagement Science vol 49 no 1 pp 1ndash20 2003

[16] A A Tsay and N Agrawal ldquoChannel conflict and coordinationin the E-commerce agerdquo Production and Operations Manage-ment vol 13 no 1 pp 93ndash110 2004

[17] Q-H Li and B Li ldquoDual-channel supply chain equilibriumproblems regarding retail services and fairness concernsrdquoApplied Mathematical Modelling 2016

[18] S Panda N M Modak S S Sana and M Basu ldquoPricingand replenishment policies in dual-channel supply chain undercontinuous unit cost decreaserdquo Applied Mathematics and Com-putation vol 256 pp 913ndash929 2015

[19] Y Liu C Ding C Fan and X Chen ldquoPricing decision underdual-channel structure considering fairness and free-ridingbehaviorrdquo Discrete Dynamics in Nature and Society vol 2014Article ID 536576 10 pages 2014

[20] J Chen H Zhang and Y Sun ldquoImplementing coordinationcontracts in a manufacturer Stackelberg dual-channel supplychainrdquo Omega vol 40 no 5 pp 571ndash583 2012

[21] Q Ding C Dong and Z Pan ldquoA hierarchical pricing decisionprocess on a dual-channel problem with one manufacturer andone retailerrdquo International Journal of Production Economics vol175 pp 197ndash212 2016

[22] B Rodriguez and G Aydin ldquoPricing and assortment decisionsfor a manufacturer selling through dual channelsrdquo EuropeanJournal of Operational Research vol 242 no 3 pp 901ndash9092015

[23] T Lockyer ldquoThe perceived importance of price as one hotelselection dimensionrdquo Tourism Management vol 26 no 4 pp529ndash537 2005

[24] C-M Chen H-W Yang E Y Li and C-C Liu ldquoHow doeshotel pricing influence guest satisfaction by the moderatinginfluence of room occupancyrdquo International Journal of Hospi-tality Management vol 49 pp 136ndash138 2015

[25] J-M Espinet M Fluvia R Rigall-I-Torrent and A Salo ldquoHotelcharacteristics and seasonality in prices an analysis usingSpanish tour operatorsrsquo brochuresrdquo Tourism Economics vol 18no 4 pp 749ndash767 2012

[26] C Juaneda J M Raya and F Sastre ldquoPricing the time and loca-tion of a stay at a hotel or apartmentrdquo Tourism Economics vol17 no 2 pp 321ndash338 2011

[27] G Abrate G Fraquelli and G Viglia ldquoDynamic pricing strate-gies evidence from European hotelsrdquo International Journal ofHospitality Management vol 31 no 1 pp 160ndash168 2012

[28] D Q Yao and J J Liu ldquoCompetitive pricing of mixed retail ande-tail distribution channelsrdquo Omega vol 33 no 3 pp 235ndash2472005

[29] J Zhao and L Wang ldquoPricing and retail service decisionsin fuzzy uncertainty environmentsrdquo Applied Mathematics andComputation vol 250 pp 580ndash592 2015

[30] A A Tsay and N Agrawal ldquoChannel dynamics under priceand service competitionrdquo Manufacturing amp Service OperationsManagement vol 2 no 4 pp 372ndash391 2000

[31] S C Choi ldquoPrice competition in a duopoly common retailerchannelrdquo Journal of Retailing vol 72 no 2 pp 117ndash134 1996

[32] Y Bakos andE Brynjolfsson ldquoBundling and competition on theinternetrdquoMarketing Science vol 19 no 1 pp 63ndash82 2000

[33] H Song J H Kim and S Yang ldquoConfidence intervals fortourism demand elasticityrdquo Annals of Tourism Research vol 37no 2 pp 377ndash396 2010

[34] DMHanssens L J Parsons andR L SchultzMarket ResponseModels Econometric and Time Series Analysis Kluwer Aca-demic Publishers Boston Mass USA 2nd edition 2001

[35] H Kurata D-Q Yao and J J Liu ldquoPricing policies under directvs indirect channel competition and national vs store brandcompetitionrdquo European Journal of Operational Research vol180 no 1 pp 262ndash281 2007

[36] R Law and C Cheung ldquoA study of the perceived importance ofthe overall website quality of different classes of hotelsrdquo Inter-national Journal of Hospitality Management vol 25 no 3 pp525ndash531 2006

[37] K B Chen ldquoProcurement strategies and coordination mecha-nism of the supply chain with one manufacturer and multiplesuppliersrdquo International Journal of Production Economics vol138 no 1 pp 125ndash135 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

14 Discrete Dynamics in Nature and Society

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867lt 120582(1 minus 120582) Then the profit of hotel is

120587113

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2+ 119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876]

(F3)

Then when 119888119871

119906lt (1 minus 120582120572)119901

119871

1(1 minus 120582) 120587

113minus120587111

gt 0 thusthe hotel would carry out overbooking

(4) Consider (1198631198711+119863119871

2+119863119867

1+119863119867

2)(1 minus 120582) gt 119876 and (119863119871

1+

119863119871

2)(1 minus 120582) gt 119876

119871 (1198631198671+ 119863119867

2)(1 minus 120582) gt 119876

119867

That is 120574119871gt (120582119876

119871+ 119876119867[1 minus (1 minus 120582)(1 + 120574

119867)])(1 minus 120582)119876

119871

and 120574119867gt (120582119876

119867+ 119876119871[1 minus (1 minus 120582)(1 + 120574

119871)])(1 minus 120582)119876

119867

Then the profit of hotel is as follows

120587114

= (1 minus 120582120572) (119901119871

1119863119871

1+ 119901119867

1119863119867

1+ 119908119871119863119871

2+ 119908119867119863119867

2)

minus 119888119871

119906[(119863119871

1+ 119863119871

2) (1 minus 120582) minus 119876

119871]

minus 119888119867

119906[(119863119867

1+ 119863119867

2) (1 minus 120582) minus 119876

119867]

(F4)

Then when 119888119871119906lt (1minus120582120572)119901

119871

1(1minus120582) and 119888119867

119906lt (1minus120582120572)119901

119867

1

(1 minus 120582) 120587114

minus 120587111

gt 0 overbooking is preferred

G Threshold Values

Threshold values are as follows

1198711= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 + 3119908

1198941205792+ 3119908119894119887119894120579

minus 1205792V minus 2120579119887

119894V

1198712= 2119886119894(119887119894+ 120579) minus 119904119886

119894(2119887119894+ 120579) + 120579

2119908119894+ 2 (120579 + 120573) (119887

119894

+ 120579) V + 2119908119894(119887119894+ 120579)2minus 1205792V

1198713= 4120579V119887

119894120573 minus 120579119904119886

119894119887119894+ 2V1205731198872

119894+ 31198861198941205792+ 4119886119894119887119894120579

minus 21198861198941198872

119894119904 + 3120579

2V120573 + 1205792V119887119894+ 2120579V1198872

119894+ 21198861198941198872

119894

1198714= 3119886119894119887119894120579 + 3120579

2V120573 minus 2120579V1198872119894minus 1205792V119887119894+ 31198861198941205792

+ 21198861198941198872

119894119904 + 119886119887

119894119904120579 + 3119887

119894120573V120579

1198715= 120579119886119894+ 120579119904119886119894+ 2119887119894119904119886119894+ 120579V120573 minus 120579

2V minus 2120579119887119894V

1198661= [(1 minus 120582120572) (119904119886119894 minus 120579V) minus 119888120579] (119861

119894

1)119861(119878)

+ [(1 minus 120582120572) (119886119894 minus 119904119886119894+ 120573V + 120579V) + 119888 (119887

119894+ 120579)]

sdot (119861119894

1)119861(119878)

+ 2120579 (1 minus 120582120572) [(119860119894

1)119861(119878)

(119861119894

2)119861(119878)

+ (119861119894

1)119861(119878)

(119860119894

2)119861(119878)

] minus 2 (1 minus 120582120572) (119887119894 + 120579)

sdot [(119860119894

1)119861(119878)

(119861119894

1)119861(119878)

+ (119860119894

2)119861(119878)

(119861119894

2)119861(119878)

]

1198662= 2 (1 minus 120582120572)

sdot (119887119894+ 120579) [((119861

119894

1)119861(119878)

)

2

+ ((119861119894

2)119861(119878)

)

2

]

minus 2120579 (119861119894

1)119861(119878)

(119861119894

2)119861(119878)

1199040= ((119887119871+ 120579) (119901

119871

1)2

+ (119887119867+ 120579) (119901

119867

1)2

+ 120579119908119871(119901119871

1minus 119901119871

2) + 120579119908

119867(119901119867

1minus 119901119867

2)

+ 120579V (1199011198711+ 119901119867

1) + (119908

119871+ 119908119867) (120573 + 120579) V

+ 119908119871(119886119871minus 119887119871119901119871

2) + 119908119867(119886119867minus 119887119867119901119867

2)

minus 120579 (119901119871

1119901119871

2+ 119901119867

1119901119867

2)) (119886119871(119901119871

1+ 119908119871)

+ 119886119867(119901119867

1+ 119908119867))minus1

(G1)

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The authors thank associate editor and anonymous refereesfor their numerous constructive comments and encourage-ment that have improved their paper greatly The work waspartly supported by (i) the National Natural Science Founda-tion ofChina (71201083 71572058 and 71571100) (ii) the Fun-damental Research Funds for the Central Universities SCUT(2015ZZ057) (iii) Jiangsu Province Science Foundation forYouths (BK2012379) and (iv) the Fundamental ResearchFunds for the Central Universities (NS2015076)

References

[1] J Li W N Zhang H Xu and J Jiang ldquoDynamic competitionand cooperation of road infrastructure investment of multipletourism destinations a case Study of Xidi and Hongcun WorldCulturalHeritagerdquoDiscreteDynamics inNature and Society vol2015 Article ID 962028 10 pages 2015

[2] T Paksoy EOzceylan andG-WWeber ldquoProfit oriented supplychain network optimizationrdquoCentral European Journal of Oper-ations Research vol 21 no 2 pp 455ndash478 2013

[3] X Zhang H Song and G Q Huang ldquoTourism supply chainmanagement a new research agendardquo Tourism Managementvol 30 no 3 pp 345ndash358 2009

[4] Z Yang and J Cai ldquoDo regional factors matter Determinantsof hotel industry performance in Chinardquo TourismManagementvol 52 pp 242ndash253 2016

[5] B Pan L Zhang and R Law ldquoThe complex matter of onlinehotel choicerdquoCornell Hospitality Quarterly vol 54 no 1 pp 74ndash83 2013

[6] L Ling X Guo and C Yang ldquoOpening the online marketplacean examination of hotel pricing and travel agency on-line

Discrete Dynamics in Nature and Society 15

distribution of roomsrdquo Tourism Management vol 45 pp 234ndash243 2014

[7] L Ling Y Dong X Guo and L Liang ldquoAvailability man-agement of hotel rooms under cooperation with online travelagenciesrdquo International Journal of Hospitality Management vol50 pp 145ndash152 2015

[8] J N K Liu andE Y Zhang ldquoAn investigation of factors affectingcustomer selection of online hotel booking channelsrdquo Interna-tional Journal of Hospitality Management vol 39 pp 71ndash832014

[9] L Fox ldquoFour Seasons Unveils $18 Million Website as LuxuryTravel Growsrdquo 2012 httpwwwtnoozcomarticlefour-sea-sons-unveils-18-million-dollar-website-as-luxury-travel-grows

[10] C-M Chen and Y-C Lin ldquoThe influence of uncertain demandon hotel capacityrdquo International Journal of Hospitality Manage-ment vol 34 no 1 pp 462ndash465 2013

[11] S Yang G Q Huang H Song and L Liang ldquoGame-theoreticapproach to competition dynamics in tourism supply chainsrdquoJournal of Travel Research vol 47 no 4 pp 425ndash439 2009

[12] G Q Huang H Song and X Zhang ldquoA comparative analysis ofquantity and price competitions in tourism supply chain net-works for package holidaysrdquo Service Industries Journal vol 30no 10 pp 1593ndash1606 2010

[13] Y Huang H Song G Q Huang and J Lou ldquoA comparativestudy of tourism supply chains with quantity competitionrdquoJournal of Travel Research vol 51 no 6 pp 717ndash729 2012

[14] H K Lee and Y Fernando ldquoThe antecedents and outcomes ofthe medical tourism supply chainrdquo Tourism Management vol46 pp 148ndash157 2015

[15] W-Y K Chiang D Chhajed and J D Hess ldquoDirect marketingindirect profits a strategic analysis of dual-channel supply-chain designrdquoManagement Science vol 49 no 1 pp 1ndash20 2003

[16] A A Tsay and N Agrawal ldquoChannel conflict and coordinationin the E-commerce agerdquo Production and Operations Manage-ment vol 13 no 1 pp 93ndash110 2004

[17] Q-H Li and B Li ldquoDual-channel supply chain equilibriumproblems regarding retail services and fairness concernsrdquoApplied Mathematical Modelling 2016

[18] S Panda N M Modak S S Sana and M Basu ldquoPricingand replenishment policies in dual-channel supply chain undercontinuous unit cost decreaserdquo Applied Mathematics and Com-putation vol 256 pp 913ndash929 2015

[19] Y Liu C Ding C Fan and X Chen ldquoPricing decision underdual-channel structure considering fairness and free-ridingbehaviorrdquo Discrete Dynamics in Nature and Society vol 2014Article ID 536576 10 pages 2014

[20] J Chen H Zhang and Y Sun ldquoImplementing coordinationcontracts in a manufacturer Stackelberg dual-channel supplychainrdquo Omega vol 40 no 5 pp 571ndash583 2012

[21] Q Ding C Dong and Z Pan ldquoA hierarchical pricing decisionprocess on a dual-channel problem with one manufacturer andone retailerrdquo International Journal of Production Economics vol175 pp 197ndash212 2016

[22] B Rodriguez and G Aydin ldquoPricing and assortment decisionsfor a manufacturer selling through dual channelsrdquo EuropeanJournal of Operational Research vol 242 no 3 pp 901ndash9092015

[23] T Lockyer ldquoThe perceived importance of price as one hotelselection dimensionrdquo Tourism Management vol 26 no 4 pp529ndash537 2005

[24] C-M Chen H-W Yang E Y Li and C-C Liu ldquoHow doeshotel pricing influence guest satisfaction by the moderatinginfluence of room occupancyrdquo International Journal of Hospi-tality Management vol 49 pp 136ndash138 2015

[25] J-M Espinet M Fluvia R Rigall-I-Torrent and A Salo ldquoHotelcharacteristics and seasonality in prices an analysis usingSpanish tour operatorsrsquo brochuresrdquo Tourism Economics vol 18no 4 pp 749ndash767 2012

[26] C Juaneda J M Raya and F Sastre ldquoPricing the time and loca-tion of a stay at a hotel or apartmentrdquo Tourism Economics vol17 no 2 pp 321ndash338 2011

[27] G Abrate G Fraquelli and G Viglia ldquoDynamic pricing strate-gies evidence from European hotelsrdquo International Journal ofHospitality Management vol 31 no 1 pp 160ndash168 2012

[28] D Q Yao and J J Liu ldquoCompetitive pricing of mixed retail ande-tail distribution channelsrdquo Omega vol 33 no 3 pp 235ndash2472005

[29] J Zhao and L Wang ldquoPricing and retail service decisionsin fuzzy uncertainty environmentsrdquo Applied Mathematics andComputation vol 250 pp 580ndash592 2015

[30] A A Tsay and N Agrawal ldquoChannel dynamics under priceand service competitionrdquo Manufacturing amp Service OperationsManagement vol 2 no 4 pp 372ndash391 2000

[31] S C Choi ldquoPrice competition in a duopoly common retailerchannelrdquo Journal of Retailing vol 72 no 2 pp 117ndash134 1996

[32] Y Bakos andE Brynjolfsson ldquoBundling and competition on theinternetrdquoMarketing Science vol 19 no 1 pp 63ndash82 2000

[33] H Song J H Kim and S Yang ldquoConfidence intervals fortourism demand elasticityrdquo Annals of Tourism Research vol 37no 2 pp 377ndash396 2010

[34] DMHanssens L J Parsons andR L SchultzMarket ResponseModels Econometric and Time Series Analysis Kluwer Aca-demic Publishers Boston Mass USA 2nd edition 2001

[35] H Kurata D-Q Yao and J J Liu ldquoPricing policies under directvs indirect channel competition and national vs store brandcompetitionrdquo European Journal of Operational Research vol180 no 1 pp 262ndash281 2007

[36] R Law and C Cheung ldquoA study of the perceived importance ofthe overall website quality of different classes of hotelsrdquo Inter-national Journal of Hospitality Management vol 25 no 3 pp525ndash531 2006

[37] K B Chen ldquoProcurement strategies and coordination mecha-nism of the supply chain with one manufacturer and multiplesuppliersrdquo International Journal of Production Economics vol138 no 1 pp 125ndash135 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Discrete Dynamics in Nature and Society 15

distribution of roomsrdquo Tourism Management vol 45 pp 234ndash243 2014

[7] L Ling Y Dong X Guo and L Liang ldquoAvailability man-agement of hotel rooms under cooperation with online travelagenciesrdquo International Journal of Hospitality Management vol50 pp 145ndash152 2015

[8] J N K Liu andE Y Zhang ldquoAn investigation of factors affectingcustomer selection of online hotel booking channelsrdquo Interna-tional Journal of Hospitality Management vol 39 pp 71ndash832014

[9] L Fox ldquoFour Seasons Unveils $18 Million Website as LuxuryTravel Growsrdquo 2012 httpwwwtnoozcomarticlefour-sea-sons-unveils-18-million-dollar-website-as-luxury-travel-grows

[10] C-M Chen and Y-C Lin ldquoThe influence of uncertain demandon hotel capacityrdquo International Journal of Hospitality Manage-ment vol 34 no 1 pp 462ndash465 2013

[11] S Yang G Q Huang H Song and L Liang ldquoGame-theoreticapproach to competition dynamics in tourism supply chainsrdquoJournal of Travel Research vol 47 no 4 pp 425ndash439 2009

[12] G Q Huang H Song and X Zhang ldquoA comparative analysis ofquantity and price competitions in tourism supply chain net-works for package holidaysrdquo Service Industries Journal vol 30no 10 pp 1593ndash1606 2010

[13] Y Huang H Song G Q Huang and J Lou ldquoA comparativestudy of tourism supply chains with quantity competitionrdquoJournal of Travel Research vol 51 no 6 pp 717ndash729 2012

[14] H K Lee and Y Fernando ldquoThe antecedents and outcomes ofthe medical tourism supply chainrdquo Tourism Management vol46 pp 148ndash157 2015

[15] W-Y K Chiang D Chhajed and J D Hess ldquoDirect marketingindirect profits a strategic analysis of dual-channel supply-chain designrdquoManagement Science vol 49 no 1 pp 1ndash20 2003

[16] A A Tsay and N Agrawal ldquoChannel conflict and coordinationin the E-commerce agerdquo Production and Operations Manage-ment vol 13 no 1 pp 93ndash110 2004

[17] Q-H Li and B Li ldquoDual-channel supply chain equilibriumproblems regarding retail services and fairness concernsrdquoApplied Mathematical Modelling 2016

[18] S Panda N M Modak S S Sana and M Basu ldquoPricingand replenishment policies in dual-channel supply chain undercontinuous unit cost decreaserdquo Applied Mathematics and Com-putation vol 256 pp 913ndash929 2015

[19] Y Liu C Ding C Fan and X Chen ldquoPricing decision underdual-channel structure considering fairness and free-ridingbehaviorrdquo Discrete Dynamics in Nature and Society vol 2014Article ID 536576 10 pages 2014

[20] J Chen H Zhang and Y Sun ldquoImplementing coordinationcontracts in a manufacturer Stackelberg dual-channel supplychainrdquo Omega vol 40 no 5 pp 571ndash583 2012

[21] Q Ding C Dong and Z Pan ldquoA hierarchical pricing decisionprocess on a dual-channel problem with one manufacturer andone retailerrdquo International Journal of Production Economics vol175 pp 197ndash212 2016

[22] B Rodriguez and G Aydin ldquoPricing and assortment decisionsfor a manufacturer selling through dual channelsrdquo EuropeanJournal of Operational Research vol 242 no 3 pp 901ndash9092015

[23] T Lockyer ldquoThe perceived importance of price as one hotelselection dimensionrdquo Tourism Management vol 26 no 4 pp529ndash537 2005

[24] C-M Chen H-W Yang E Y Li and C-C Liu ldquoHow doeshotel pricing influence guest satisfaction by the moderatinginfluence of room occupancyrdquo International Journal of Hospi-tality Management vol 49 pp 136ndash138 2015

[25] J-M Espinet M Fluvia R Rigall-I-Torrent and A Salo ldquoHotelcharacteristics and seasonality in prices an analysis usingSpanish tour operatorsrsquo brochuresrdquo Tourism Economics vol 18no 4 pp 749ndash767 2012

[26] C Juaneda J M Raya and F Sastre ldquoPricing the time and loca-tion of a stay at a hotel or apartmentrdquo Tourism Economics vol17 no 2 pp 321ndash338 2011

[27] G Abrate G Fraquelli and G Viglia ldquoDynamic pricing strate-gies evidence from European hotelsrdquo International Journal ofHospitality Management vol 31 no 1 pp 160ndash168 2012

[28] D Q Yao and J J Liu ldquoCompetitive pricing of mixed retail ande-tail distribution channelsrdquo Omega vol 33 no 3 pp 235ndash2472005

[29] J Zhao and L Wang ldquoPricing and retail service decisionsin fuzzy uncertainty environmentsrdquo Applied Mathematics andComputation vol 250 pp 580ndash592 2015

[30] A A Tsay and N Agrawal ldquoChannel dynamics under priceand service competitionrdquo Manufacturing amp Service OperationsManagement vol 2 no 4 pp 372ndash391 2000

[31] S C Choi ldquoPrice competition in a duopoly common retailerchannelrdquo Journal of Retailing vol 72 no 2 pp 117ndash134 1996

[32] Y Bakos andE Brynjolfsson ldquoBundling and competition on theinternetrdquoMarketing Science vol 19 no 1 pp 63ndash82 2000

[33] H Song J H Kim and S Yang ldquoConfidence intervals fortourism demand elasticityrdquo Annals of Tourism Research vol 37no 2 pp 377ndash396 2010

[34] DMHanssens L J Parsons andR L SchultzMarket ResponseModels Econometric and Time Series Analysis Kluwer Aca-demic Publishers Boston Mass USA 2nd edition 2001

[35] H Kurata D-Q Yao and J J Liu ldquoPricing policies under directvs indirect channel competition and national vs store brandcompetitionrdquo European Journal of Operational Research vol180 no 1 pp 262ndash281 2007

[36] R Law and C Cheung ldquoA study of the perceived importance ofthe overall website quality of different classes of hotelsrdquo Inter-national Journal of Hospitality Management vol 25 no 3 pp525ndash531 2006

[37] K B Chen ldquoProcurement strategies and coordination mecha-nism of the supply chain with one manufacturer and multiplesuppliersrdquo International Journal of Production Economics vol138 no 1 pp 125ndash135 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of