Research ArticleStrategic Conditions for Opening an Internet Store and PricingPolicies in a Retailer-Dominant Supply Chain

Yonghong Cheng12 and Zhongkai Xiong12

1 School of Economics and Business Administration Chongqing University Chongqing 400030 China2 Chongqing Key Laboratory of Logistics Chongqing University Chongqing 400030 China

Correspondence should be addressed to Zhongkai Xiong xiongzhongkaicqueducn

Received 30 May 2014 Revised 12 October 2014 Accepted 12 October 2014

Academic Editor Hari M Srivastava

Copyright copy 2015 Y Cheng and Z Xiong This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

To examine when the manufacturer and dominant retailer open their own Internet stores and how setting prices to ensure openingInternet stores are profitable We consider a two-echelon supply chain with one manufacturer and one dominant retailer Theretailer has a physical store in a monopolist market Depending on whether the Internet stores are opened successfully by themwe firstly obtain equilibrium prices and profits under four possible supply chain structures Secondly we identify several strategicconditions when it is optimal to open an Internet store for the manufacturer and dominant retailer and discuss its implicationsIt is interesting to note that multichannel retailing is not necessarily the best strategy for the dominant retailer In addition weinvestigate the impacts of problem parameters (the dominant retailerrsquos bargaining power and consumersrsquo disutility of purchasing aproduct from Internet store) on the manufacturer and dominant retailerrsquos pricing policies We find that the manufacturerrsquos optimalprice at her Internet store is not always being lower than the dominant retailerrsquos Finally we conduct numerical examples to illustratethe theoretical results

1 Introduction

The Internet environment enables some companies to try toopen their own Internet stores In practice themanufacturers(such as Apple IBM Hewlett-Packard Dell Nike andSamsung) sell their products through both retailerrsquos physicalstore and its Internet store And some retailers also openInternet stores and keep their physical stores in place such asWal-Mart Best Buy Barnes amp Noble Office Depot StaplesGOME and Suning Appliance among others However it isacknowledged that some well-known manufacturers such asAcer Colgate Gillette and Tylenol only sell their productsexclusively through retailerrsquos physical store and they do notopen their Internet store On the retailersrsquo side such as 7-Eleven andCarrefour they do not provide the Internet storesso consumers can only purchase products from their physicalstores [1] Consequently a question arises The question isthat why the Internet store sometimes was opened by themanufacturers whereas in other cases the Internet stores areopened by the retailers

In the manufacturerrsquos point of view opening an Internetstore not only motivates the downstream retailer to performmore effectively but also mitigates supply chainrsquos doublemarginalization problem [2ndash7] However some smart con-sumers often get more product information and experiencefrom the retailersrsquo physical stores but shift to purchasingtheir ideal product from the manufacturerrsquo Internet storewith a lower price Thus these consumersrsquo buying behaviormay reduce the retailerrsquos profit To cope with the abovefree-riding problem some retailers have no choice but toopen their own Internet stores and keep physical stores inplace [8ndash10] Moreover the retailers (such as Wal-Mart BestBuy Barnes amp Noble and Office Depot) sell an identicalproduct with the same price across their Internet stores andphysical stores In their views these pricing policies canretain the advantage of their retail services and increase theirsales base due to customers purchasing from their Internetstores Those successful retailers are well known as ldquocategorykillersrdquo or ldquodominant retailersrdquo However the first paragraphillustrates that neither each manufacturer nor each retailer

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 640719 15 pageshttpdxdoiorg1011552015640719

2 Mathematical Problems in Engineering

opens their own Internet stores In addition as Iyer andVillas-Boas [11] Dukes and Liu [12] point out that the keymeasurements of supply chain members features such as thedominant retailerrsquos bargaining power in the supply chainand the consumersrsquo disutility buying from Internet store mayinfluence the conditions for opening an Internet store

Although these emerging trends are particularly notice-able in the E-commerce market there is scant literatureaddressing the interactions between manufacturer and dom-inant retailer whether to open their own Internet stores withdifferent setup costs in a supply chain To fill this gap in theliterature we answer the following critical problems faced bythe manufacturer and dominant retailer

(1) When should themanufacturer and dominant retaileropen their own Internet stores in a supply chain

(2) How would the manufacturer and dominant retailerdifferentially set retail price between their Internetstores to ensure that opening an Internet store isprofitable in a competition environment

(3) How do the manufacturer and dominant retaileradjust their pricing policies according to the domi-nant retailerrsquos bargaining power in the supply chainand the consumersrsquo disutility buying from Internetstore

Our work is intended to develop game-theoretic modelsto gain insights into these problems To this end we firstformulate four possible supply chain structures (T-channelRD-channel MD-channel and M-channel) which dependon whether the Internet stores are opened by the manu-facturer and dominant retailer Meanwhile we analyse andcompare the manufacturer and dominant retailerrsquos optimalpricing policies and equilibrium profits among four supplychain structures Our analysis suggests that no matter whoopens an Internet store the player opening Internet storewill affect the supply chain structure and optimal pricingpolicies in different ways It should be noted that boththe manufacturer and dominant retailerrsquos optimal choicesfor opening an Internet store are largely determined bytheir respective setup costs which are closely related tothe dominant retailerrsquos bargaining power and consumersrsquodisutility buying from Internet store

The remainder of this paper is organized as followsSection 2 reviews the related literature and shows our contri-butions in more detail In Section 3 we describe the modelsand propose some assumptions related to our study InSection 4 we first present the equilibrium outcomes amongthe different supply chain structures and then discuss thestrategic conditions for the manufacturer and dominantretailer to open an Internet store In Section 5 we investigatethe impacts of the dominant retailerrsquos bargaining power andconsumersrsquo disutility of purchasing a product from Internetstore on both the manufacturer and dominant retailerrsquospricing strategies In Section 6 we illustrate the theoreticalresults by numerical examples We conclude the resultsand managerial implications and suggest topics for futureresearch in Section 7 All relevant proofs are relegated to theappendix

2 Literature Review

There is a growing amount of literature on the Internetchannel management strategies in electronic commerce eraHowever most of them focus on the competitive pricingdecisions and channel coordination problem in which themanufacturer sells products through both retailerrsquos physicalstore and its Internet store which is called dual-channelsupply chain In particular a large amount of literatureexplore the price-setting game in a dual-channel environ-ment [13ndash20] In addition it should be noted that when themanufacturer opens an Internet store as its direct channelconsumers have alternatives to choose store that is bettersuited to their needs then the retailerrsquos profit may reduce andresult in ldquochannel conflictrdquo Therefore a considerable bodyof research also exists on channel conflict and coordinationin the dual-channel supply chain [21ndash27] In those studiesthey show that a manufacturer would choose one contract(ie quantity discounts or two-part tariffs profit sharingcontract) to coordinate the distribution channel However allthe above papers are devoted to discussing the manufacturerand retailerrsquos pricing strategies and channel coordination butneglect the dominance of retailer and by default the retailer isunable to open an Internet store

Although our research is also related to the literature onthe dominant retailer opening an Internet store the literatureis limited Yao and Liu [28] propose the mixed retail and e-tail distribution channels and discuss the dominant retailerrsquospricing strategywhen opening an Internet store Liu et al [29]develop a game-theoretical model to show that a brick-and-mortar retailer can open an Internet store to preempt the e-tailorrsquos entry Cheng andNault [30] study how existingmarketcoverage affects the outcome of opening an Internet storegame between an existing retailer and a new entrant Zhang[31] studies the retailerrsquosmultichannel (between Internet storeand physical store) and price advertising decisions Huangand Swaminathan [32] study the optimal pricing strategieswhen a product is sold in two stores such as Internet store andphysical store It should be noted that the authors focus on thedominant retailer having the ability to open an Internet storebut does not consider the interactions with manufacturer ina supply chain and neglect the dominant retailerrsquos bargainingpower in the distribution channel

In contrast to the papers that are investigated above ourwork differs in two important aspects First in the lightof the manufacturer and dominant retailer having tried toopen their Internet store we assume that both of themare able to commit whether to open an Internet store ina supply chain and attempt to provide theoretical insightsinto the strategic conditions and pricing policies for themto open an Internet store Interestingly we find that thedominant retailer opening an Internet store can induce themanufacturer to open an Internet store to compete withhim and the manufacturerrsquos optimal price at her Internetstore is not always being lower than the dominant retailerrsquosSecond in order to characterize the dominant retailerrsquosbargaining power in the distribution channel we assumethat thewholesale price betweenmanufacturer and dominantretailer is derived by means of the bargaining process In

Mathematical Problems in Engineering 3

R

PS

M

(a) T-channel

M

R

PS RIS

(b) RD-channel

M

R

PS MIS

(c) MD-channel

M

R

PS RIS MIS

(d) M-channel

Figure 1 The supply chain configuration of scenarios T- RD- MD- and M-channels

our study we note that the dominant retailerrsquos bargainingpower plays a critical role in influencing equilibrium pricesand profits in the distribution system as well as the strategicconditions for the manufacturer and dominant retailer toopen an Internet store

3 Model Fundamentals

Consider a two-echelon supply chain consisting of onemanufacturer denoted by M (referred to as ldquosherdquo) and onedominant retailer with a physical store in a monopolist mar-ket denoted by R (referred to as ldquoherdquo) who sells the productsof the manufacturer to the consumers With the prevailingpopularity of consumers purchasing products online theyhave to redesign their distribution channel structures Basedon marketing cases about the manufacturerrsquos direct channelstrategy and the dominant retailerrsquos multichannel retailingactivities we assume that each of them is able to commitwhether to open an Internet store is faced with differentsetup costs Since the manufacturer and dominant retailermay open the Internet stores successfully or not there are 4possible channel structures

Case (A) Both of them do not open their Internet storesdenoted by T-channel

Case (B) The manufacturer does not open an Internet storebut dominant retailer opens an Internet store denoted by RD-channel

Case (C) The manufacturer opens an Internet store butdominant retailer does not and is denoted by MD-channel

Case (D) Both of them open their Internet stores simultane-ously denoted by M-channel

Figure 1 depicts 4 possible cases For convenience letPS denotes the dominant retailerrsquos physical store MISthe manufacturer-owned Internet store RIS the dominantretailer-owned Internet store

Parameters and decision variablesrsquo notations used in thepaper are listed in Abbreviations section

Before establishing themodels we give some assumptionsrelated to this study as follows

Assumption 1 The manufacturer produces the product at aconstant unit (marginal) cost which is normalized to zero andsells product to the dominant retailer with a wholesale price119908

j= (1 minus 120573)119901

j119903in the j-channel which is derived by means of

the bargaining process where 119901j119903is the retail price charged by

the dominant retailer in the j-channel and the value of 120573 isin

(0 1) denotes his bargaining power The wholesale price thatis determined in the supply chain by a negotiation process issimilar to the previous researches such as [11 12]

Assumption 2 The dominant retailer acts as a Stackelbergprice leader in the distribution channel and his physicalstore has located at the left end point of a Hotelling linearcity bounded between zero and one as seen in the previousliterature [29 33ndash37] Without loss of generality we assumethat the size of the market is one and consumers areuniformly distributed over the line of the city with a unittravel cost (119905 gt 0) for traveling to the dominant retailerrsquosphysical store to shop and each consumer buys at most oneunit of the product

Assumption 3 The dominant retailer sets the same priceacross his physical store and Internet store In marketingpractice some dominant retailers such as Circuit CityTiffany Gap and Staples fully integrate their offline andonline operations which can make consumer not figure outwhether it is cheaper to purchase from its physical storesand Internet stores In fact this assumption is similar to[29 31 38]

Assumption 4 The value of consumers willing to pay for theproduct is sufficiently large (119881 gt 119905) so as to ensure thefull market coverage Otherwise the dominant retailer neveropens a physical store to serve consumers

Assumption 5 If a consumer chooses to purchase the productfrom the Internet stores (MIS or RIS) the purchasing incursa unit disutility (120575 gt 0) To ensure that at least one of themanufacturers and the dominant retailer has an incentive to

4 Mathematical Problems in Engineering

Table 1

Mrsquos wholesale price MISrsquos price PSRISrsquos price Mrsquos profit Rrsquos profitT-channel (1 minus 120573)(119881 minus 119905) NA 119881 minus 119905 (1 minus 120573)(119881 minus 119905) 120573(119881 minus 119905)

RD-channel (1 minus 120573)(119881 minus 120575) NA 119881 minus 120575 (1 minus 120573)(119881 minus 120575) 120573(119881 minus 120575) minus 119865119903

MD-channel(1 minus 120573)(119905 + 120575)

2120573

(2 + 120573)119905 + (2 minus 3120573)120575

4120573

119905 + 120575

2120573

119905 + 120575

2120573

+

(119905 minus 120575)2

minus 12119905120575

16119905

minus 119865119898

(119905 + 120575)2

8119905

Table 2

Mrsquos wholesale price MISrsquos price PSRISrsquos price Mrsquos profit Rrsquos profit

120575 lt

119905

3

(1 minus 120573)(119905 minus 120575)

120573

119905 minus 120575

120573

119905 minus 120575

120573

119905 minus 120575

120573

minus

(119905 minus 120575)120575

119905

minus 119865119898

(119905 minus 120575)120575

119905

minus 119865119903

120575 gt

119905

3

(1 minus 120573)(119905 + 120575)

2120573

(2 + 120573)119905 + (2 minus 3120573)120575

4120573

119905 + 120575

2120573

119905 + 120575

2120573

+

(119905 minus 120575)2

minus 12119905120575

16119905

minus 119865119898

(119905 + 120575)2

8119905

minus 119865119903

open an Internet store let 120575 lt 119905 in our study which is similarto previous studies [3 14 17]

Consumersrsquo disutility 120575 capturing various factors makesonline shopping inconvenient such as quality uncertainty(eg the inability to touch and feel) discomfort with onlinesecurity waiting time until delivery and shipping charge

Based on the above assumptions it is clear that for aconsumer located at 119909 isin [0 1] he will get utilities 119880PS =

119881minus119901119903minus 119905119909 when purchasing the product from the dominant

retailerrsquos physical store and 119880MIS = 119881 minus 119901119898minus 120575 when

purchasing the product from the manufacturerrsquos Internetstore and 119880RIS = 119881 minus 119901

119903minus 120575 when purchasing the product

from the dominant retailerrsquos Internet store

4 Equilibrium Outcomes and StrategicConditions for Opening an Internet Store

In this section we first present the equilibrium outcomesamong the different channel structures and then discussthe strategic conditions for the manufacturer and dominantretailer to open their Internet stores The equilibrium out-comes are given by the following Lemmas 6 and 7 and theproofs are provided in Appendix A

41 Equilibrium Outcomes

Lemma 6 In the T-channel MD-channel and RD-channelthe equilibrium prices and profits for the manufacturer anddominant retailer can be summarized as shown in Table 1

Lemma7 In theM-channel the equilibriumprices and profitsfor manufacturer and dominant retailer can be summarized asshown in Table 2

From Lemmas 6 and 7 we observe that no matter themanufacturer and dominant retailer open an Internet storewill affect the supply chain structure and equilibrium pricesand profits in different ways Let T-channel be a benchmarkwe note that the dominant retailer should lower retail priceonly when his Internet store in the market and when thesetup cost of opening an Internet store 119865

119903lt 120573(119905 minus 120575) then

he can get more profit than that of not opening an Internetstore In addition we find that when the manufacturer anddominant retailer open their Internet stores simultaneouslyif consumersrsquo disutility of purchasing a product from Internetstore is low enough (ie 120575 lt 1199053) the manufacturer can setthe retail price at her Internet store same to the dominantretailerrsquos retail price However if consumersrsquo disutility ofpurchasing a product from Internet store is relatively larger(ie 120575 gt 1199053) the equilibrium prices are same to the caseof the manufacturer only open an Internet store that isMD-channel Furthermore the manufacturerrsquos profit doesnot change but the dominant retailerrsquos profit decreasesTherefore we will discuss the strategic conditions for themanufacturer and dominant retailer to open an Internetstore according to the equilibrium profits among the differentchannel structures

42 Strategic Conditions for Opening an Internet Store Nowas one of the critical problems to obtain the strategic con-ditions for the manufacturer and dominant retailer to openan Internet store we compare the equilibrium profits in RD-channel MD-channel and M-channel to the equilibriumprofits in T-channel and compare the equilibrium profitsin M-channel to the equilibrium profits in RD-channeland MD-channel respectively The following propositionsand corollaries summarize the strategic conditions and itsimplications The proofs are given in Appendix B

Proposition 8 Suppose that themanufacturer has not openedan Internet store when the setup cost of opening an Internetstore by the dominant retailer 119865

119903lt 120573(119905 minus 120575) he can begin to

open an Internet store

Proposition 8 implies that under the condition of themanufacturer has not opened an Internet store onlywhen thesetup cost of opening an Internet store is relatively small thedominant retailer will getmore profit than that of not openingan Internet store Otherwise his profit will decrease due tocostly setup cost

Obviously an immediate consequence of above proposi-tions is the following corollary

Mathematical Problems in Engineering 5

Corollary 9 If the manufacturer has not opened an Internetstore the dominant retailerrsquos strategic motive for opening anInternet store would be weakened by increasing consumersrsquodisutility of purchasing a product from Internet store

Proposition 10 Suppose that the dominant retailer has notopened an Internet store when the setup cost of opening anInternet store by the manufacturer 119865

119898lt (119905 + 120575)2120573 + [(119905 minus

120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905) she can begin to open anInternet store

Proposition 10 implies that under the condition of thedominant retailer has not opened an Internet store onlywhenthe setup cost of opening an Internet store is relatively smallthemanufacturer will getmore profit than that of not openingan Internet store Otherwise her profit will decrease due tocostly setup cost

Based on Proposition 10 we have the following corollary

Corollary 11 If the dominant retailer has not opened anInternet store and his bargaining power is relatively small (ie120573 lt 4119905(7119905 minus 120575)) the manufacturerrsquos strategic motive foropening an Internet store would be strengthened by increasingconsumersrsquo disutility of purchasing a product from Internetstore Otherwise her strategic motive would be weakened

Proposition 12 There are two choices for the manufacturerand dominant retailer to open their Internet stores simultane-ously which are summarized as follows

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) and the setupcosts of opening an Internet store by the manufacturerand dominant retailer meet 119865

119898lt (119905 minus 120575)120573 minus (119905 minus

120575)120575119905 minus (1 minus 120573)(119881 minus 119905) and 119865119903lt (119905 minus 120575)120575119905 minus 120573(119881 minus 119905)

respectively both of them can open their own Internetstores simultaneously

(2) If consumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) andthe setup costs of opening an Internet store by themanufacturer and dominant retailer meet 119865

119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905) and119865119903lt (119905 + 120575)

2

8119905 minus 120573(119881 minus 119905) respectively both of themcan open their own Internet stores simultaneously

Proposition 12 implies that consumersrsquo disutility of pur-chasing a product from Internet store plays an importantrole for opening Internet stores simultaneously by the man-ufacturer and dominant retailer And only when the setupcosts of opening Internet stores by them are relatively smallrespectively then both will get more profit than that of notopening Internet stores Otherwise their profits will decreasedue to costly setup costs

It should be noted that the upper bounds of 119865119898and 119865119903are

related to 120575 for a given 120573 in Proposition 12 so we have thefollowing corollary

Corollary 13 If both the manufacturer and dominant retailerhave not operated their Internet stores then

(1) when consumersrsquo disutility of purchasing a productfrom Internet store is low enough (ie 120575 lt 1199053) themanufacturerrsquos strategic motive for opening an Internetstore would be weakened by increasing consumersrsquodisutility of purchasing a product from Internet storebut the dominant retailerrsquos strategic motive for openingan Internet store would be strengthened

(2) when consumersrsquo disutility of purchasing a productfrom Internet store is relatively larger (ie 120575 gt 1199053)the dominant retailerrsquos strategic motive for opening anInternet store would be strengthened by increasing con-sumersrsquo disutility of purchasing a product from Internetstore For the manufacturer only if the dominantretailerrsquos bargaining power is relatively small (ie 120573 lt

4119905(7119905minus120575)) her strategicmotive for opening an Internetstore would be strengthened by increasing consumersrsquodisutility of purchasing a product from Internet storeOtherwise her strategic motive would be weakened

Proposition 14 Suppose that the dominant retailer has oper-ated an Internet store themanufacturer has two choices to openan Internet store which are summarized as follows

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) and the setupcost of opening an Internet store by the manufacturer119865119898lt (119905 minus 120575)120573 minus (119905 minus 120575)120575119905 minus (1 minus 120573)(119881 minus 120575) she can

also open an Internet store(2) If consumersrsquo disutility of purchasing a product from

Internet store is relatively larger (ie 120575 gt 1199053) andthe setup cost of opening an Internet store by themanufacturer 119865

119898lt (119905+120575)2120573+[(119905minus120575)

2

minus12119905120575]16119905minus

(1 minus 120573)(119881 minus 120575) she can also open an Internet store

Proposition 14 implies that under the condition of thedominant retailer has operated an Internet store consumersrsquodisutility of purchasing a product from Internet store alsoplays an important role in opening an Internet store by themanufacturer And only when the setup cost of opening anInternet store is relatively small then the manufacturer willget more profit than that of not opening an Internet storeOtherwise her profit will decrease due to costly set-up cost

Based on Proposition 14 we have the following corollary

Corollary 15 If the dominant retailer has operated an Internetstore then

(1) when consumersrsquo disutility of purchasing a productfrom Internet store is low enough (ie 120575 lt 1199053) themanufacturerrsquos strategic motive for opening an Internetstore would be weakened by increasing consumersrsquodisutility of purchasing a product from Internet store

(2) when consumersrsquo disutility of purchasing a productfrom Internet store is relatively larger (ie 120575 gt 1199053) andonly if the dominant retailerrsquos bargaining power is rela-tively small (ie 120573 lt [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905)the manufacturerrsquos strategic motive for opening anInternet store would be strengthened by increasing

6 Mathematical Problems in Engineering

consumersrsquo disutility of purchasing a product fromInternet store Otherwise her strategic motive would beweakened

Proposition 16 Suppose that the manufacturer has operatedan Internet store the best choice for dominant retailer is not toopen an Internet store

Proposition 16 implies that under the condition of themanufacturer has operated an Internet store regardless ofconsumersrsquo disutility of purchasing a product from Internetstore is small or larger it is best for the dominant retailer notto open an Internet store Otherwise his profit will decreasedue to costly setup cost or the manufacturerrsquos low pricestrategy that attract more consumers to buy the product fromher Internet store

Proposition 17 Suppose that the manufacturer has notopened an Internet store if consumersrsquo disutility of purchasinga product from Internet store is low enough (ie 120575 lt 1199053) andthe setup cost of opening an Internet store for the manufactureris intermediate 119865

119898isin [(119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 (119905 minus

120575)120573 minus (119905 minus 120575)120575119905] the dominant retailer opening an Internetstore can lead to the well-known contagion-like effect

Proposition 17 implies that under the condition of themanufacturer has not opened an Internet store when con-sumersrsquo disutility of purchasing a product from Internet storeis relatively small and the set-up cost of opening an Internetstore for the manufacturer is intermediate the dominantretailerrsquos Internet store entry may induce the manufacturerto open her own Internet store competing with him

FromProposition 17 we observe that the upper and lowerbounds of 119865

119898are related to 120575 for a given 120573 so we have the

following corollary

Corollary 18 When consumersrsquo disutility of purchasing aproduct from Internet store is low enough (ie 120575 lt 1199053) ifthe dominant retailerrsquos bargaining power is relatively small (ie120573 lt 4119905(7119905minus120575)) the contagion-like effect would be expanded byincreasing consumersrsquo disutility of purchasing a product fromInternet store However if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 gt 4119905(7119905 minus 120575)) the contagion-like effect would be diminished

Based on aforementioned propositions we now showwhen do the manufacturer and dominant retailer open theirown Internet stores to a traditional supply chain and how dothey set prices after opening Internet stores in Table 3

5 Analytical Results onBoth Playersrsquo Pricing Policies

From Lemmas 6 and 7 we know that the T-channel andRD-channel are monopoly settings So the dominant retailercharges the optimal monopoly price and sells the productto all consumers However under the MD-channel and M-channel the manufacturer and dominant retailer engage in

price competition To investigate the impacts of the dom-inant retailerrsquos bargaining power and consumersrsquo disutilityof purchasing a product from Internet store on the manu-facturer and dominant retailerrsquos pricing strategies we obtainthe following propositions and the proofs are provided inAppendix C

Proposition 19 Suppose that only the manufacturer can openan Internet store then

(1) 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0(2) 120597119901MD

119903120597120575 = 12120573 gt 0 and 120597119901MD

119898120597120575 = (2 minus 3120573)4120573

and if 120573 isin (0 23) then 120597119901MD119898

120597120575 gt 0 if 120573 isin (23 1)then 120597119901MD

119898120597120575 lt 0

(3) if 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

if 120575 = 1199053 then 119901MD119898

=

119901MD119903

and if 120575 gt 1199053 then 119901MD119898

lt 119901MD119903

Proposition 19 indicates that when the manufacturer canopen an Internet store

(1) she should also lower the price to induce consumersto purchase the product from her Internet store asthe increasing dominant retailerrsquos bargaining powerotherwise the dominant retailer will also provideprice incentives for consumers to buy the productfrom his physical store

(2) if the dominant retailerrsquos bargaining power is rela-tively small (ie 120573 lt 23) she should raise the pricein her Internet store with increasing consumersrsquo disu-tility However if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 gt 23) she should cutdown the price in her Internet store with increasingconsumersrsquo disutility

(3) if consumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) shemust provide strong price incentives for consumersto purchase the product from her Internet storeotherwise her profits will cut down owing to someconsumers buying the product from the dominantretailerrsquos physical store on the contrary the domi-nant retailer will provide strong price incentives forconsumers to purchase the product from his physicalstore when consumersrsquo disutility of purchasing aproduct from Internet store is low enough (ie 120575 lt

1199053) then the manufacturerrsquos retail price is higherthan the dominant retailerrsquos If and only if consumersrsquodisutility of purchasing a product from Internet storesatisfies 120575 = 1199053 the manufacturer can set her retailprice to be equal to the dominant retailerrsquos

Proposition 20 Suppose that both the manufacturer anddominant retailer can open their Internet stores simultaneouslythen

(1) If 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0120597119901

M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0

(2) If 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 120597119901M119898120597120575 = (2 minus 3120573)4120573 120597119901M

119903120597120575 = 12120573 gt 0 and

Mathematical Problems in Engineering 7

Table 3 Strategic conditions for opening Internet stores to T-channel and pricing policies

Strategic conditions M and Rrsquos activities Pricing policiesM has not opened an Internet store and119865119903lt 120573(119905 minus 120575)

R can open an Internet store Monopoly pricing

R has not opened an Internet store and119865119898lt (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905)

M can open an Internet store

When 120575 lt 1199053then 119901MD

119898gt 119901

MD119903

When 120575 = 1199053then 119901MD

119898= 119901

MD119903

When 120575 gt 1199053then 119901MD

119898lt 119901

MD119903

When 120575 lt 1199053 119865119903lt (119905 minus 120575)120575119905 minus 120573(119881 minus 119905) and

119865119898lt (119905 minus 120575)120573 minus (119905 minus 120575)120575119905 minus (1 minus 120573)(119881 minus 119905)

Both M and R can open their Internet stores simultaneously119901M119898= 119901

M119903

When 120575 gt 1199053 119865119903lt (119905 + 120575)

2

8119905 minus 120573(119881 minus 119905) and119865119898lt (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905)

119901M119898lt 119901

M119903

when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0 but when 120573 isin

(23 1) then 120597119901M119898120597120575 lt 0

(3) If 120575 le 3119905 then 119901M119898= 119901

M119903 if 120575 gt 1199053 then 119901M

119898lt 119901

M119903

Proposition 20 indicates when both the manufacturerand dominant retailer can open their Internet stores simul-taneously

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) bothof them can set same price and lower prices as theincreasing consumersrsquo disutility On the contrary ifconsumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) themanufacturer must provide lower price incentivesthan the dominant retailer which may induce con-sumers to purchase the product from her Internetstore It should be pointed out that when the dom-inant retailerrsquos bargaining power is relatively small(ie 120573 lt 23) the manufacturerrsquos price increaseswith increasing consumersrsquo disutility but when thedominant retailerrsquos bargaining power is relativelylarger (ie 120573 gt 23) the manufacturerrsquos retail pricedecreases with increasing consumersrsquo disutility

(2) When consumersrsquo disutility of purchasing a prod-uct from Internet store is low enough (ie 120575 lt

1199053) the dominant retailerrsquos price decreases reducewith increasing consumersrsquo disutility but when con-sumersrsquo disutility of purchasing a product from Inter-net store is relatively larger (ie 120575 gt 1199053) thedominant retailerrsquos price decreases with increasingconsumersrsquo disutility Speaking frankly that is thedominant retailerrsquos smart pricing strategiesThe dom-inant retailer will raise the retail price when mostof consumers with a large disutility of purchasing aproduct from Internet store buy the product from hisphysical store and lower the retail price when mostof consumers with a small disutility of purchasing aproduct from Internet store buy the product from themanufacturerrsquos Internet store

Proposition 21 Given that the dominant retailerrsquos bargainingpower we obtain the following results about the manufacturerrsquoswholesale price under RD-channel MD-channel and M-channel

(1) 120597119908RD120597120575 = minus(1 minus 120573) lt 0

(2) 120597119908MD120597120575 = (1 minus 120573)2120573 gt 0

(3) if 120575 lt 1199053 then 120597119908M120597120575 = minus(1 minus 120573)120573 lt 0 if 120575 gt 1199053

then 120597119908M120597120575 = (1 minus 120573)2120573 gt 0

Proposition 21 indicates that the manufacturer should setthe wholesale prices differentially across the RD-channelMD-channel andM-channel and raise or lower thewholesaleprices in the light of consumersrsquo disutility of buying theproduct from Internet store More specifically the man-ufacturer can lower the wholesale price with increasingconsumersrsquo disutility of buying the product from Internetstore in the RD-channel but in theMD-channel she can raisethe wholesale price with increasing consumersrsquo disutility ofbuying from Internet store However in theM-channel whenthe consumersrsquo disutility of buying from Internet store is lowenough (ie 120575 lt 1199053) she can lower the wholesale pricewith increasing consumersrsquo disutility but when consumersrsquodisutility of buying from Internet store is relatively larger (ie120575 gt 1199053) she should raise the wholesale price with increasingconsumersrsquo disutility

Proposition 22 Given that the dominant retailerrsquos bargainingpower we obtain the following results about the manufacturerrsquosretail price at her Internet store under MD-channel and M-channel

(1) If 120575 lt 1199053 when 120573 isin (0 23) then 120597119901MD119898

120597120575 =

(2 minus 3120573)4120573 gt 0 120597119901M119898120597120575 = minus1120573 lt 0 but when 120573 isin

(23 1) then 120597119901MD119898

120597120575 = (2 minus 3120573)4120573 lt 0 120597119901M119898120597120575 =

minus1120573 lt 0(2) If 120575 gt 1199053 when 120573 isin (0 23) then 120597119901

MD119898

120597120575 =

120597119901M119898120597120575 gt 0 but when 120573 isin (23 1) then 120597119901MD

119898120597120575 =

120597119901M119898120597120575 lt 0

Proposition 22 indicates that themanufacturer should setthe retail prices at her Internet store differentially across the

8 Mathematical Problems in Engineering

MD-channel and M-channel and raise or lower the prices inthe light of consumersrsquo disutility of buying the product fromInternet store More specifically if the consumersrsquo disutilityof buying from Internet store is low enough (ie 120575 lt 1199053)the manufacturer can raise the retail price at her Internetstore with increasing consumersrsquo disutility of buying fromInternet store when the dominant retailerrsquos bargaining poweris relatively small (ie 120573 lt 23) and the dominant retailerdoes not open Internet store However if the dominantretailer also opens an Internet store the manufacturer shouldlower the retail price at her Internet store so as to attractconsumers to buy the product from her Internet store On thecontrary if the consumersrsquo disutility of buying from Internetstore is relatively larger (ie 120575 gt 1199053) and the dominantretailer also opens an Internet store then the manufacturershould set the same price with the dominant retailerrsquos andadjust the price following the dominant retailer

Proposition 23 Given that the dominant retailerrsquos bargainingpower we obtain the following results about dominant retailerrsquosretail price under RD-channel MD-channel and M-channel

(1) If 120575 lt 1199053 then 120597119901RD119903120597120575 = minus1 lt 0 120597119901MD

119903120597120575 = 12120573 gt

0 and 120597119901M119903120597120575 = minus1120573 lt 0

(2) If 120575 gt 1199053 then 120597119901RD119903120597120575 = minus1 lt 0 120597119901

MD119903

120597120575 =

12120573 gt 0 and 120597119901M119903120597120575 = 12120573 gt 0

Proposition 23 indicates that no matter when the con-sumersrsquo disutility of buying from Internet store is small orlarger the dominant retailer should lower the retail price withincreasing consumersrsquo disutility buying from Internet store inthe RD-channel but in the MD-channel he always raises theretail price with increasing consumersrsquo disutility Howeverin the M-channel when consumersrsquo disutility buying fromInternet store is low enough (ie 120575 lt 1199053) he should lowerthe price with increasing consumersrsquo disutility but whenconsumersrsquo disutility is relatively larger (ie 120575 gt 1199053) he canset the price same as the price in the MD-channel and raisethe price with increasing consumersrsquo disutility

6 Numerical Examples

In this section we present numerical examples to illustratethe theoretical results about impacts of consumersrsquo disutilityof buying from Internet store on the manufacturer anddominant retailerrsquos pricing policies with different bargainingpower for the dominant retailerrsquos among RD-channel MD-channel and M-channel which are summarized in Figures2ndash11 where 119881 = 14 119905 = 6 120575 isin (0 6) and 120573 = 02 120573 = 08The parametersrsquo values satisfy the assumptions in Section 3 inorder to make the models feasible and meaningful

Comparing Figure 2 with Figure 3 we can observe thatwhen the dominant retailerrsquos bargaining power is relativelysmall (ie 120573 = 02) both of them can increase prices asincreasing consumersrsquo disutility of purchasing from Internetstore in MD-channel However when the dominant retailerrsquosbargaining power is relatively larger (ie 120573 = 08) themanufacturer has no choice but to lower the retail price soas to attract consumers to buy the product from her Internet

0 1 2 3 4 5 612

14

16

18

20

22

24

26

28

30

wMD

pMDm

pMDr

120575

Figure 2 Impacts of 120575 on prices in the MD-channel when 120573 = 02

0 1 2 3 4 5 60

1

2

3

4

5

6

7

8

wMD

pMDm

pMDr

120575

Figure 3 Impacts of 120575 on prices in the MD-channel when 120573 = 08

store In addition Figures 2 and 3 show that when consumersrsquodisutility buying from Internet store is low enough (ie 120575 lt

2) the manufacturer can set her retail price to be larger thanthe dominant retailerrsquos However when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2)the manufacturer can set her retail price to be lower than thedominant retailerrsquos

Figures 4 and 5 show that when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)both the manufacturer and dominant retailer should lowerprices to increase consumersrsquo disutility buying from Internet

Mathematical Problems in Engineering 9

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

wM

pMm

pMr

Figure 4 Impacts of 120575 on prices in the M-channel when 120573 = 02

0 1 2 3 4 5 61

2

3

4

5

6

7

8

120575

wM

pMm

pMr

Figure 5 Impacts of 120575 on prices in the M-channel when 120573 = 08

store It is noted that the rate of change of manufacturerrsquosretail price with respect to consumersrsquo disutility buying fromInternet store is equal to that of dominant retailerrsquos retailprice However when consumersrsquo disutility buying fromInternet store is relatively larger (ie 120575 gt 2) if the dominantretailerrsquos bargaining power is relatively small (ie 120573 =

02) the manufacturer can raise retail price following thedominant retailer as increasing consumersrsquo disutility buyingfrom Internet store if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 = 08) the manufacturershould cut down the retail price in her Internet store withincreasing consumersrsquo disutility

0 1 2 3 4 5 66

8

10

12

14

16

18

20

22

24

wMD

wRD

wM

120575

Figure 6 The wholesale prices in different channels when 120573 = 02

0 1 2 3 4 5 605

1

15

2

25

3

120575

wMD

wRD

wM

Figure 7 The wholesale prices in different channels when 120573 = 08

Figures 6 and 7 show that no matter whether thedominant retailerrsquos bargaining power is small or large themanufacturer can raise the wholesale price with increasingconsumersrsquo disutility buying from Internet store in the MD-channel but in the RD-channel the manufacturer shouldlower the wholesale price with increasing consumersrsquo disutil-ity However in the M-channel when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower the wholesale price withincreasing consumersrsquo disutility when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2) themanufacturer can raise the wholesale price with increasing

10 Mathematical Problems in Engineering

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

pMDm

pMm

Figure 8 Manufacturerrsquos retail prices in different channels when120573 = 02

0 1 2 3 4 5 645

5

55

6

65

7

75

120575

pMDm

pMm

Figure 9 Manufacturerrsquos retail prices in different channels when120573 = 08

consumersrsquo disutility and set the wholesale price the same asin the MD-channel

Figures 8 and 9 show that when the dominant retailerrsquosbargaining power is relatively small (ie 120573 = 02) inthe MD-channel the manufacturer can raise retail pricewith increasing consumersrsquo disutility buying from Internetstore but when the dominant retailerrsquos bargaining power isrelatively larger (ie 120573 = 08) the manufacturer should lowerretail price with increasing consumersrsquo disutility Howeverin the M-channel no matter whether the dominant retailerrsquosbargaining power is small or large when consumersrsquo disutility

0 1 2 3 4 5 65

10

15

20

25

30

120575

pRDr

pMDr

pMr

Figure 10 Dominant retailerrsquos prices in different channels when120573 =02

buying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower retail price with increasingconsumersrsquo disutility but when consumersrsquo disutility buyingfrom Internet store is relatively larger (ie 120575 gt 2) if thedominant retailerrsquos bargaining power is relatively small (ie120573 = 02) the manufacturer can raise retail price withincreasing consumersrsquo disutility buying from Internet storeif the dominant retailerrsquos bargaining power is relatively larger(ie 120573 = 08) themanufacturer should lower retail price withincreasing consumersrsquo disutility

Figures 10 and 11 show that no matter whether thedominant retailerrsquos bargaining power is small or larger healways lowers the retail price with increasing consumersrsquodisutility buying from Internet store in the RD-channel butin the MD-channel he always raises the retail price withincreasing consumersrsquo disutility However in the M-channelwhen consumersrsquo disutility buying from Internet store islow enough (ie 120575 lt 2) the dominant retailer shouldlower retail price with increasing consumersrsquo disutility butwhen consumersrsquo disutility is relatively larger (ie 120575 gt 2)the dominant retailer can raise retail price with increasingconsumersrsquo disutility buying from Internet store

7 Conclusions and Future Research

To investigate when the manufacturer and dominant retaileropen their own Internet stores with different setup costsand how set prices to ensure opening Internet stores areprofitable in a supply chain we first present the equilibriumoutcomes under four possible supply chain structures andthen discuss the strategic conditions for the manufacturerand dominant retailer when it is optimal to open an Internetstore In addition we analyze both playersrsquo pricing policies

Mathematical Problems in Engineering 11

0 1 2 3 4 5 62

4

6

8

10

12

14

120575

pMDr

pRDr

pMr

Figure 11 Dominant retailerrsquos prices in different channels when 120573 =08

after they open their Internet stores and discuss the impactsof the dominant retailerrsquos bargaining power and consumersrsquodisutility of purchasing a product from Internet store onthe manufacturer and dominant retailerrsquos pricing strategiesFinally we conduct numerical examples to illustrate thetheoretical results

We obtain some new results differing from those inthe literature We find that the optimal choices for themanufacturer and dominant retailer to open an Internetstore are largely determined by their respective setup costswhich are closely related to the dominant retailerrsquos bargainingpower and consumersrsquo disutility of buying from Internetstore It is worth mentioning that multichannel retailing forthe dominant retailer is not necessarily the best strategyIn other words if the dominant retailer opens an Internetstore the marketing plan for him to attract more consumersby charging a lower price is impossible to achieve and hecan induce the manufacturer to open an Internet store tocompetewith himOnlywhen the setup cost for the dominantretailer to open an Internet store is sufficiently low then he isprofitable

What is more we also find that the manufacturerrsquosoptimal price at her Internet store is not always being lowerthan the dominant retailerrsquos For example if the consumersrsquodisutility of buying from Internet store is sufficiently highthe manufacturer must provide strong price incentives forconsumers to purchase the product from the Internet store

Although this research provides new insights for themanufacturer and dominant retailer to open an Internetstore and set prices in a supply chain there are severaldirections that could be extended First this study assumedthat all information is known to the manufacturer anddominant retailer in our model However information couldbe asymmetric in the supply chain since both players haveprivate information about their own internal variable costs

for example the setup cost of opening an Internet storecustomersrsquo purchase patterns and search costsTherefore wecan explore the competitive equilibrium under asymmetricinformation settings Second we assume that consumersrsquodisutility of buy from Internet store is independent of theunit transportation cost which can be relaxed in the futureresearch Third trade credit is widely used in practice andhas important impact on supply chain management [39ndash41] In recent years trade credit has become one of themajor transactions between suppliers and retailers in a valuechain For example Wal-Mart Carrefour and GOME (alarge Chinese home appliance chain retailer) even delayedpayments to their suppliers for as long as one year [42]Hence it is worthy to understand how the trade creditaffects supply channel configuration together with pricingstrategies in the E-commerce market A final issue worthyof investigation is how different types of customers affectthe manufacturer and dominant retailerrsquos channel selectionstrategies We leave these questions for future research

Appendices

A Equilibrium Outcome ofthe Four Channel Structures

Proof of Lemma 6 (1) In the T-channel both the manufac-turer and dominant retailer do not open their Internet storesThere is only the dominant retailerrsquos physical store in themarket So the dominant retailer acts as a monopolist andoptimally charges a price 119881 minus 119905 such that the market isjust covered For the manufacturer given that the dominantretailerrsquos optimal retail price the optimal wholesale price is119908

T= (1 minus 120573)(119881 minus 119905) Since the manufacturer produces

the product at a constant unit (marginal) cost which isnormalized to zero and the market is just covered that is thesize of the market is one the profit for the manufacturer isprod

T119898= (1minus120573)(119881minus119905) Accordingly the profit for the dominant

retailer isprodT119903= 120573(119881 minus 119905)

(2) In RD-channel only the dominant retailer opens anInternet store (RIS) If a consumer locates at a distance fromphysical store (PS) he will get a net utility of by purchasingthe product from PS and a net utility of by purchasing theproduct from RIS To ensure the full market coverage thedominant retailer charges the monopoly price 119881 minus 120575 acrosshis two stores and sells the product to all consumers Forthe manufacturer given the dominant retailerrsquos optimal retailprice the optimal wholesale price is 119908RD

= (1 minus 120573)(119881 minus 120575)Since the manufacturer produces the product at a constantunit (marginal) cost which is normalized to zero and 119905 thesize of the market is one the profits for the manufacturer anddominant retailer are prodRD

119898= (1 minus 120573)(119881 minus 120575) and prod

RD119903

=

120573(119881 minus 120575) respectively(3) In MD-channel the manufacturer opens an Internet

store but dominant retailer does not So consumers canhave convenient access to the product through the dominantretailerrsquos physical store (PS) at price 119901

119903or the manufacturerrsquos

Internet store (MIS) at price 119901119898 their decision about which

store to buy revolves around the comparison of their net

12 Mathematical Problems in Engineering

utility derived fromPS119880PS = 119881minus119901119903minus119905119909 and119880MIS = 119881minus119901119898minus120575by buying the product from MIS Therefore the marginalconsumers are located at 119909 = (119901

119898minus 119901119903+ 120575)119905 So the profit

functions for the manufacturer and dominant retailer can bewritten as

prod

119898

= 119908[

(119901119898minus 119901119903+ 120575)

119905

] + 119901119898[

(119901119903minus 119901119898+ 119905 minus 120575)

119905

] minus 119865119898

(A1)

prod

119903

= (119901119903minus 119908) [

(119901119898minus 119901119903+ 120575)

119905

] (A2)

Under the assumption proposed in Section 3 the dom-inant retailer is the price leader and the manufacturer isthe follower As before the game is solved backwards Inthis market we firstly need to calculate the manufacturerrsquosoptimal price given any dominant retailerrsquos price

Themanufacturerrsquos reaction function can be derived fromthe first-order condition

120597prod119898

120597119901119898

=

[(2 minus 120573) 119901119903minus 2119901119898+ 119905 minus 120575]

119905

= 0

that is 119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A3)

Substituting (A3) into (A2) we get

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

(A4)

Taking the first-order derivative of (A4) with respect to119901119903and letting the derivative be zero we have

119901MD119903

=

(119905 + 120575)

2120573

(A5)

Given the wholesale price bargaining process we canobtain the manufacturerrsquos optimal wholesale price 119908MD

=

(1 minus 120573)(119905 + 120575)2120573 and substituting (A5) into (A3) we getthe manufacturerrsquos optimal retail price

119901MD119898

=

(2 + 120573) 119905 + (2 minus 3120573) 120575

4120573

(A6)

Substituting (A5) and (A6) into (A1) and (A2) wecan obtain the equilibrium profits for the manufacturers anddominant retailer respectively

MDprod

119898

=

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus 119865119898

MDprod

119903

=

(119905 + 120575)2

8119905

(A7)

Proof of Lemma 7 In the M-channel both the manufacturerand dominant retailer simultaneously open their own Inter-net stores then customers are able to purchase a product

either from the dominant retailerrsquos physical store (PS) or fromthe alternative Internet stores (MISRIS) They can get a netutility of 119880PS = 119881 minus 119901

119903minus 119905119909 by buying the product from PS

and a net utility of 119880MIS = 119881 minus 119901119898minus 120575 by buying the product

fromMIS and a net utility of119880RIS = 119881minus 119901119903minus 120575 by buying the

product from RISAccording to the basicmodel we know that the dominant

retailer firstmakes pricing decision as the price leader and themanufacturer is the follower If the dominant retailer chargesa price higher than the manufacturerrsquos price (119901

119903gt 119901119898) then

no consumer will buy the product from his Internet storeUnder this condition the dominant retailer makes no sale inhis Internet store and makes a profit of minus119865

119903 Therefore the

demand functions for the manufacturerrsquos Internet store anddominant retailerrsquos physical store are given respectively asfollows

119863MIS =(119901119903minus 119901119898+ 119905 minus 120575)

119905

(A8)

119863PS =(119901119898minus 119901119903+ 120575)

119905

(A9)

Hence the manufacturerrsquos profit function can be written as

prod

119898

=

[119908 (119901119898minus 119901119903+ 120575) + 119901

119898(119901119903minus 119901119898+ 119905 minus 120575)]

119905

minus 119865119898

(A10)

From the first-order condition we have

119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A11)

Given the condition of 119901119903gt 119901119898 this implies that 119901

119903gt (119905 minus

120575)120573 However when 119901119903le (119905 minus 120575)120573 and 119901

119903gt 119901119898 we always

have 120597prodM119898120597119901119898= [(2 minus 120573)119901

119903minus 2119901119898+ 119905 minus 120575]119905 gt 0

Therefore the manufacturer optimally sets its price at119901119898= 119901119903 and her optimal pricing schedule is as follows

119901119898=

119901119903 119901

119903le

119905 minus 120575

120572

(2 minus 120573) 119901119903+ 119905 minus 120575

2

119901119903gt

119905 minus 120575

120572

(A12)

Given the manufacturerrsquos pricing schedule the dominantretailerrsquos profit is given as follows

prod

119903

=

(119901119903minus 119908)

120575

119905

minus 119865119903 119901

119903le

119905 minus 120575

120573

(119901119903minus 119908)

119905 + 120575 minus 120573119901119903

2119905

minus 119865119903 119901119903gt

119905 minus 120575

120573

(A13)

Under the condition of 119901119903gt (119905 minus 120575)120573 the dominant

retailerrsquos profit is

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

minus 119865119903 (A14)

Taking the first-order derivative of (A14) with respect to 119901119903

and letting the derivative be zero we have 119901M119903= (119905 + 120575)2120573

Mathematical Problems in Engineering 13

Submitting it into (A11) we get the manufacturerrsquos optimalprice in her Internet store 119901M

119898= [(2 + 120573)119905 + (2 minus 3120573)120575]4120573

Hence the manufacturer and dominant retailerrsquos optimalprofits are prodM

119898= (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus 119865119898

andprodM119903= (119905 + 120575)

2

8119905 minus 119865119903 respectively

According to the previous assumption 119901119903gt (119905 minus 120575)120573

which implies that (119905 + 120575)2120573 gt (119905 minus 120575)120573 120575must satisfy 120575 gt1199053 However when 120575 lt 1199053 we always have

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](minus)

gt 0

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](+)

lt 0 (A15)

So the dominant retailerrsquos optimal retail price in the M-channel is 119901M

119903= (119905 minus 120575)120573 Therefore the manufacturer and

dominant retailerrsquos optimal profits areprodM119898= (119905 minus 120575)120573 minus [(119905 minus

120575)120575]119905 minus 119865119898andprodM

119903= [(119905 minus 120575)120575]119905 minus 119865

119903 respectively

B Strategic Conditions forOpening an Internet Store

Proofs of Proposition 8 and Corollary 9 From Lemma 6 weanalyse the equilibrium profits for the dominant retailerbetween the T-channel and RD-channel and note that onlywhen 119865

119903lt 120573(119905 minus 120575) then prodRD

119903gt prod

T119903 This implies that as

long as the setup cost of opening an Internet store satisfies119865119903

lt 120573(119905 minus 120575) ≜ 1198611 it is always optimal to open an

Internet store for the dominant retailer In addition we notethat 120597119861

1120597120575 = minus120573 lt 0 So the dominant retailerrsquos strategic

motive for opening an Internet store would be weakened byincreasing consumersrsquo disutility of purchasing a product fromInternet store

Proofs of Proposition 10 and Corollary 11 From Lemma 6 weanalyse the equilibrium profits for the manufacturer betweenthe T-channel and MD-channel and note that only when thesetup cost of opening an Internet store satisfies 119865

119898lt (119905 +

120575)2120573+[(119905minus120575)2

minus12119905120575]16119905minus(1minus120573)(119881minus119905) ≜ 1198612 thenprodMD

119898gt

prodT119898 In addition we note that 120597119861

2120597120575 = [4119905 minus 120573(7119905 minus 120575)]8120573119905

and find when 0 lt 120573 lt 4119905(7119905 minus 120575) then 1205971198612120597120575 gt 0 and

when 4119905(7119905 minus 120575) lt 120573 lt 1 then 1205971198612120597120575 lt 0

Proofs of Proposition 12 and Corollary 13 FromLemmas 6 and7 we analyse the equilibriumprofits for themanufacturer anddominant retailer between the T-channel andM-channel wenote that under the condition of 120575 lt 1199053 only when the setupcosts of opening an Internet store for the manufacturer anddominant retailer simultaneously satisfy

119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198613

119865119903lt

[(119905 minus 120575) 120575]

119905

minus 120573 (119881 minus 119905) ≜ 1198614

(B1)

thenMprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B2)

Similarly under the condition of 120575 gt 1199053 only when thesetup costs of opening an Internet store for the manufacturerand dominant retailer simultaneously satisfy

119865119898lt

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198615

119865119903lt

(119905 + 120575)2

8119905

minus 120573 (119881 minus 119905) ≜ 1198616

(B3)

then

Mprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B4)

In addition we note that both 1205971198613120597120575 = minus[119905 + 120573(119905 minus

2120575)]120573119905 lt 0 and 1205971198614120597120575 = (119905 minus 2120575)119905 gt 0 are held under

the condition of 120575 lt 1199053 Furthermore under the conditionof 120575 gt 1199053 we also find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198615120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

5120597120575 lt 0

1205971198616120597120575 = 2(119905 + 120575)8119905 gt 0

Proofs of Proposition 14 and Corollary 15 From Lemmas 6and 7 we analyse the manufacturerrsquos equilibrium profits inthe RD-channel and M-channel we note that under thecondition of 120575 lt 1199053 only when the setup cost of opening anInternet store for her satisfies 119865

119898lt (119905 minus 120575)120573 minus [(119905 minus 120575)120575]119905 minus

(1 minus 120573)(119881 minus 120575) ≜ 1198617 thenprodM

119898gt prod

RD119898 In addition we find

1205971198617120597120575 = minus[(1 + 120573

2

)119905 minus 2120573120575]120573119905 lt 0But under the condition of 120575 gt 1199053 only when the setup

cost of opening an Internet store for her satisfies 119865119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 120575) ≜ 1198618 then

prodM119898gt prod

RD119898 In addition 120597119861

8120597120575 = [120573(119905+120575)+4119905(1minus2120573

2

)]8120573119905

we find that when 0 lt 120573 lt [(119905 + 120575) + radic(119905 + 120575)2

+ 1281199052]16119905

then 1205971198618120597120575 gt 0 andwhen [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905 lt

120573 lt 1 then 1205971198618120597120575 lt 0

Proofs of Proposition 16 From Lemmas 6 and 7 we analysethe dominant retailerrsquos equilibriumprofits in theMD-channeland M-channel and note that when 120575 lt 1199053 then prod

M119903minus

prodMD119903

= minus(119905 minus 3120575)2

8119905 minus 119865119903lt 0 and when 120575 gt 1199053

then prodM119903minus prod

MD119903

= minus119865119903lt 0 These imply that when the

manufacturer has operated an Internet store the best choicefor dominant retailer is not to open an Internet store

Proofs of Proposition 17 and Corollary 18 From Lemmas 6and 7 we analyse the dominant retailerrsquos equilibrium profitsin the MD-channel and M-channel and note that under thecondition of 120575 lt 1199053 thenprodM

119898minus prod

MD119898

= [8119905(119905 minus 3120575) minus 120573[(119905 +

120575)2

minus 161205752

]8119905]16120573119905 This implies that the manufacturer willopen her Internet store when the dominant retailer opens an

14 Mathematical Problems in Engineering

Internet store and the setup costs of opening an Internet storefor her satisfies

1198619≜

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

lt 119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

≜ 11986110

(B5)

In addition we find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198619120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

9120597120575 lt 0

and 12059711986110120597120575 = minus[119905 + 120573(119905 minus 2120575)]120573119905 lt 0

C The ManufacturerDominantRetailers Pricing Policies

Proof of Proposition 19 In the MD-channel we respectivelydifferentiate between119901MD

119898and119901MD

119903with respect to 120573 and find

that 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0 For any given120573 differentiating between 119901MD

119898and 119901MD

119903with respect to 120575 we

have 120597119901MD119903

120597120575 = 12120573 gt 0 and 120597119901MD119898

120597120575 = (2 minus 3120573)4120573and if 120573 isin (0 23) then 120597119901MD

119898120597120575 gt 0 if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 In addition we find that 119901MD119898

minus 119901MD119903

= (119905 minus

3120575)4 it is obvious that when 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

when 120575 = 1199053 then 119901MD

119898= 119901

MD119903

and when 120575 gt 1199053 then119901MD119898

lt 119901MD119903

Proof of Proposition 20 In the M-channel we respectivelydifferentiate between 119901M

119898and 119901M

119903with respect to 120573 and find

that when 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0

and when 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 For any given 120573 we respectively differentiate between 119901M119898

and 119901M119903with respect to 120575 and find that when 120575 lt 1199053 then

120597119901M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0 when 120575 gt 1199053 then

120597119901M119898120597120575 = (2 minus 3120573)4120573 and 120597119901M

119903120597120575 = 12120573 gt 0

It is easy to note that when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0

but when 120573 isin (23 1) then 120597119901M119898120597120575 lt 0

Proof of Proposition 21 From Lemmas 6 and 7 we note that120597119908

RD120597120575 = minus(1 minus 120573) lt 0 and 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0In addition if 120575 lt 1199053 then 120597119908M

120597120575 = minus(1 minus 120573)120573 lt 0 if120575 gt 1199053 then 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0

Proof of Proposition 22 From the proofs of Propositions 19and 20 we note that when 120575 lt 1199053 if 120573 isin (0 23) then120597119901

MD119898

120597120575 gt 0 120597119901M119898120597120575 lt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 120597119901M119898120597120575 lt 0 when 120575 gt 1199053 if 120573 isin (0 23)

then 120597119901MD119898

120597120575 = 120597119901M119898120597120575 gt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 = 120597119901M119898120597120575 lt 0

Proof of Proposition 23 From Lemmas 6 and 7 we note that120597119901

RD119903120597120575 = minus1 lt 0 and 120597119901MD

119903120597120575 = 12120572 gt 0 In addition if

120575 lt 1199053 then 120597119901M119903120597120575 = minus1120572 lt 0 if 120575 gt 1199053 then 120597119901M

119903120597120575 =

12120572 gt 0

Abbreviations

UK The consumerrsquos utility of purchasing theproduct from K storeK isin PSRISMIS

119881 The value of consumers willing to payfor the product

120575 The consumersrsquo disutility of purchasingthe product from Internet store(MISRIS)

119905 The per unit transportation cost ofpurchasing the product from physicalstore (PS)

120573 The dominant retailerrsquos bargainingpower in the distribution channel

119908j The manufacturerrsquos wholesale price in

the j-channel j isin TRDMDM

119901j119903 The dominant retailerrsquos price in the

j-channel j isin TRDMDM

119901j119898 The manufacturerrsquos price in the

j-channel j isin MDM

119865119898119865119903 The setup cost of opening an Internetstore by the manufacturerdominantretailer

Πj119898Πj119903 The manufacturerdominant retailerrsquosprofit in the j-channelj isin TRDMDM

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been supported by theNational Natural Sci-ence Foundation of China (71271225) Chongqingrsquos NaturalScience Foundation (cstc2012jjA1404) and the Open Fund ofChongqing Key Laboratory of Logistics (CQKLL12001)

References

[1] L Hsiao and Y-J Chen ldquoStrategic motive for introducinginternet channels in a supply chainrdquo Production and OperationsManagement vol 23 no 1 pp 36ndash47 2014

[2] I Geyskens K Gielens and M G Dekimpe ldquoThe marketvaluation of Internet channel additionsrdquo Journal of Marketingvol 66 no 2 pp 102ndash119 2002

[3] 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

[4] S-H Chun and J-C Kim ldquoPricing strategies in B2C electroniccommerce analytical and empirical approachesrdquo Decision Sup-port Systems vol 40 no 2 pp 375ndash388 2005

[5] S K Mukhopadhyay X Zhu and X Yue ldquoOptimal contractdesign for mixed channels under information asymmetryrdquoProduction and Operations Management vol 17 no 6 pp 641ndash650 2008

Mathematical Problems in Engineering 15

[6] G S Cai ldquoChannel selection and coordination in dual-channelsupply chainsrdquo Journal of Retailing vol 86 no 1 pp 22ndash36 2010

[7] K Takahashi T Aoi D Hirotani and K Morikawa ldquoInventorycontrol in a two-echelon dual-channel supply chain with setupof production and deliveryrdquo International Journal of ProductionEconomics vol 133 no 1 pp 403ndash415 2011

[8] D W Carlton and J A Chevalier ldquoFree riding and salesstrategies for the Internetrdquo Journal of Industrial Economics vol49 no 4 pp 441ndash461 2001

[9] K D Antia M Bergen and S Dutta ldquoCompeting with graymarketsrdquoMIT SloanManagement Review vol 46 no 1 pp 63ndash69 2004

[10] J Shin ldquoHow does free riding on customer service affectcompetitionrdquo Marketing Science vol 26 no 4 pp 488ndash5032007

[11] G Iyer and J M Villas-Boas ldquoA bargaining theory of distribu-tion channelsrdquo Journal of Marketing Research vol 40 no 1 pp80ndash100 2003

[12] A Dukes and Y Liu ldquoIn-store media and distribution channelcoordinationrdquoMarketing Science vol 29 no 1 pp 94ndash107 2010

[13] H Ahn I Duenyas and R Zhang ldquoPrice competition betweenretailers and manufacturer-owned storesrdquoWorking Paper Uni-versity of California at Berkeley 2002

[14] K Cattani W Gilland H S Heese and J SwaminathanldquoBoiling frogs pricing strategies for a manufacturer addinga direct channel that competes with the traditional channelrdquoProduction and Operations Management vol 15 no 1 pp 40ndash56 2006

[15] K-Y Chen M Kaya and O Ozer ldquoDual sales channel man-agement with service competitionrdquo Manufacturing and ServiceOperations Management vol 10 no 4 pp 654ndash675 2008

[16] G Hua S Wang and T C E Cheng ldquoPrice and lead timedecisions in dual-channel supply chainsrdquo European Journal ofOperational Research vol 205 no 1 pp 113ndash126 2010

[17] W S Yoo andE Lee ldquoInternet channel entry a strategic analysisof mixed channel structuresrdquo Marketing Science vol 30 no 1pp 29ndash41 2011

[18] Y Xiong W Yan K Fernandes Z-K Xiong and N GuoldquoldquoBricks vs clicksrdquo the impact of manufacturer encroachmentwith a dealer leasing and selling of durable goodsrdquo EuropeanJournal of Operational Research vol 217 no 1 pp 75ndash83 2012

[19] Q Lu and N Liu ldquoPricing games of mixed conventional ande-commerce distribution channelsrdquo Computers and IndustrialEngineering vol 64 no 1 pp 122ndash132 2013

[20] Q Xu Z Liu and B Shen ldquoThe impact of price comparisonservice on pricing strategy in a dual-channel supply chainrdquoMathematical Problems in Engineering vol 2013 Article ID613528 13 pages 2013

[21] C A Ingene and M E Parry ldquoChannel coordination whenretailers competerdquoMarketing Science vol 14 no 4 pp 360ndash3771995

[22] 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

[23] J Raju and Z J Zhang ldquoChannel coordination in the presenceof a dominant retailerrdquoMarketing Science vol 24 no 2 pp 254ndash262 2005

[24] K L Webb and C J Lambe ldquoInternal multi-channel conflictan exploratory investigation and conceptual frameworkrdquo Indus-trial Marketing Management vol 36 no 1 pp 29ndash43 2007

[25] S K Mukhopadhyay D-Q Yao and X Yue ldquoInformationsharing of value-adding retailer in a mixed channel hi-techsupply chainrdquo Journal of Business Research vol 61 no 9 pp950ndash958 2008

[26] R Yan ldquoManaging channel coordination in a multi-channelmanufacturer-retailer supply chainrdquo Industrial Marketing Man-agement vol 40 no 4 pp 636ndash642 2011

[27] E Cao YMa CWan andM Lai ldquoContracting with asymmet-ric cost information in a dual-channel supply chainrdquoOperationsResearch Letters vol 41 no 4 pp 410ndash414 2013

[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] Y Liu S Gupta and Z J Zhang ldquoNote on self-restraint as anonline entry-deterrence strategyrdquoManagement Science vol 52no 11 pp 1799ndash1809 2006

[30] Z Cheng and B R Nault ldquoInternet channel entry retailcoverage and entry cost advantagerdquo Information Technology andManagement vol 8 no 2 pp 111ndash132 2007

[31] X Zhang ldquoRetailersrsquo multichannel and price advertising strate-giesrdquoMarketing Science vol 28 no 6 pp 1080ndash1094 2009

[32] W Huang and J M Swaminathan ldquoIntroduction of a secondchannel implications for pricing and profitsrdquo European Journalof Operational Research vol 194 no 1 pp 258ndash279 2009

[33] H Hotelling ldquoStability in competitionrdquo The Economic Journalvol 39 no 153 pp 41ndash57 1929

[34] J Zhang ldquoThe perils of behavior-based personalizationrdquo Mar-keting Science vol 30 no 1 pp 170ndash186 2011

[35] T Kabiraj and C Lee ldquoLicensing contracts in hotelling struc-turerdquoTheoretical Economics Letters vol 1 no 3 pp 57ndash62 2011

[36] HWang andTNariu ldquoDistribution channelmanagement in aninternet age equilibrium and social welfarerdquo Journal of IndustryCompetition and Trade vol 12 no 3 pp 285ndash298 2012

[37] M Lijesen ldquoHotellingrsquos webshoprdquo Journal of Economics vol 109no 2 pp 193ndash200 2013

[38] R Gulati and J Garino ldquoGet the right mix of bricks amp clicksrdquoHarvard Business Review vol 78 no 3 pp 107ndash214 2000

[39] K-J Chung S-D Lin and H M Srivastava ldquoThe completesolution procedures for the mathematical analysis of somefamilies of optimal inventorymodels with order-size dependenttrade credit and deterministic and constant demandrdquo AppliedMathematics and Computation vol 219 no 1 pp 142ndash157 2012

[40] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels under conditional trade credit in a supply chain systemrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 24 pp10036ndash10052 2013

[41] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels for deteriorating items in the discounted cash-flowsapproach under conditional trade credit and cash discount ina supply chain systemrdquo Applied Mathematics and InformationSciences vol 8 no 5 pp 2103ndash2111 2014

[42] J Luo and Q Zhang ldquoTrade credit a new mechanism tocoordinate supply chainrdquo Operations Research Letters vol 40no 5 pp 378ndash384 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

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Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

opens their own Internet stores In addition as Iyer andVillas-Boas [11] Dukes and Liu [12] point out that the keymeasurements of supply chain members features such as thedominant retailerrsquos bargaining power in the supply chainand the consumersrsquo disutility buying from Internet store mayinfluence the conditions for opening an Internet store

Although these emerging trends are particularly notice-able in the E-commerce market there is scant literatureaddressing the interactions between manufacturer and dom-inant retailer whether to open their own Internet stores withdifferent setup costs in a supply chain To fill this gap in theliterature we answer the following critical problems faced bythe manufacturer and dominant retailer

(1) When should themanufacturer and dominant retaileropen their own Internet stores in a supply chain

(2) How would the manufacturer and dominant retailerdifferentially set retail price between their Internetstores to ensure that opening an Internet store isprofitable in a competition environment

(3) How do the manufacturer and dominant retaileradjust their pricing policies according to the domi-nant retailerrsquos bargaining power in the supply chainand the consumersrsquo disutility buying from Internetstore

Our work is intended to develop game-theoretic modelsto gain insights into these problems To this end we firstformulate four possible supply chain structures (T-channelRD-channel MD-channel and M-channel) which dependon whether the Internet stores are opened by the manu-facturer and dominant retailer Meanwhile we analyse andcompare the manufacturer and dominant retailerrsquos optimalpricing policies and equilibrium profits among four supplychain structures Our analysis suggests that no matter whoopens an Internet store the player opening Internet storewill affect the supply chain structure and optimal pricingpolicies in different ways It should be noted that boththe manufacturer and dominant retailerrsquos optimal choicesfor opening an Internet store are largely determined bytheir respective setup costs which are closely related tothe dominant retailerrsquos bargaining power and consumersrsquodisutility buying from Internet store

The remainder of this paper is organized as followsSection 2 reviews the related literature and shows our contri-butions in more detail In Section 3 we describe the modelsand propose some assumptions related to our study InSection 4 we first present the equilibrium outcomes amongthe different supply chain structures and then discuss thestrategic conditions for the manufacturer and dominantretailer to open an Internet store In Section 5 we investigatethe impacts of the dominant retailerrsquos bargaining power andconsumersrsquo disutility of purchasing a product from Internetstore on both the manufacturer and dominant retailerrsquospricing strategies In Section 6 we illustrate the theoreticalresults by numerical examples We conclude the resultsand managerial implications and suggest topics for futureresearch in Section 7 All relevant proofs are relegated to theappendix

2 Literature Review

There is a growing amount of literature on the Internetchannel management strategies in electronic commerce eraHowever most of them focus on the competitive pricingdecisions and channel coordination problem in which themanufacturer sells products through both retailerrsquos physicalstore and its Internet store which is called dual-channelsupply chain In particular a large amount of literatureexplore the price-setting game in a dual-channel environ-ment [13ndash20] In addition it should be noted that when themanufacturer opens an Internet store as its direct channelconsumers have alternatives to choose store that is bettersuited to their needs then the retailerrsquos profit may reduce andresult in ldquochannel conflictrdquo Therefore a considerable bodyof research also exists on channel conflict and coordinationin the dual-channel supply chain [21ndash27] In those studiesthey show that a manufacturer would choose one contract(ie quantity discounts or two-part tariffs profit sharingcontract) to coordinate the distribution channel However allthe above papers are devoted to discussing the manufacturerand retailerrsquos pricing strategies and channel coordination butneglect the dominance of retailer and by default the retailer isunable to open an Internet store

Although our research is also related to the literature onthe dominant retailer opening an Internet store the literatureis limited Yao and Liu [28] propose the mixed retail and e-tail distribution channels and discuss the dominant retailerrsquospricing strategywhen opening an Internet store Liu et al [29]develop a game-theoretical model to show that a brick-and-mortar retailer can open an Internet store to preempt the e-tailorrsquos entry Cheng andNault [30] study how existingmarketcoverage affects the outcome of opening an Internet storegame between an existing retailer and a new entrant Zhang[31] studies the retailerrsquosmultichannel (between Internet storeand physical store) and price advertising decisions Huangand Swaminathan [32] study the optimal pricing strategieswhen a product is sold in two stores such as Internet store andphysical store It should be noted that the authors focus on thedominant retailer having the ability to open an Internet storebut does not consider the interactions with manufacturer ina supply chain and neglect the dominant retailerrsquos bargainingpower in the distribution channel

In contrast to the papers that are investigated above ourwork differs in two important aspects First in the lightof the manufacturer and dominant retailer having tried toopen their Internet store we assume that both of themare able to commit whether to open an Internet store ina supply chain and attempt to provide theoretical insightsinto the strategic conditions and pricing policies for themto open an Internet store Interestingly we find that thedominant retailer opening an Internet store can induce themanufacturer to open an Internet store to compete withhim and the manufacturerrsquos optimal price at her Internetstore is not always being lower than the dominant retailerrsquosSecond in order to characterize the dominant retailerrsquosbargaining power in the distribution channel we assumethat thewholesale price betweenmanufacturer and dominantretailer is derived by means of the bargaining process In

Mathematical Problems in Engineering 3

R

PS

M

(a) T-channel

M

R

PS RIS

(b) RD-channel

M

R

PS MIS

(c) MD-channel

M

R

PS RIS MIS

(d) M-channel

Figure 1 The supply chain configuration of scenarios T- RD- MD- and M-channels

our study we note that the dominant retailerrsquos bargainingpower plays a critical role in influencing equilibrium pricesand profits in the distribution system as well as the strategicconditions for the manufacturer and dominant retailer toopen an Internet store

3 Model Fundamentals

Consider a two-echelon supply chain consisting of onemanufacturer denoted by M (referred to as ldquosherdquo) and onedominant retailer with a physical store in a monopolist mar-ket denoted by R (referred to as ldquoherdquo) who sells the productsof the manufacturer to the consumers With the prevailingpopularity of consumers purchasing products online theyhave to redesign their distribution channel structures Basedon marketing cases about the manufacturerrsquos direct channelstrategy and the dominant retailerrsquos multichannel retailingactivities we assume that each of them is able to commitwhether to open an Internet store is faced with differentsetup costs Since the manufacturer and dominant retailermay open the Internet stores successfully or not there are 4possible channel structures

Case (A) Both of them do not open their Internet storesdenoted by T-channel

Case (B) The manufacturer does not open an Internet storebut dominant retailer opens an Internet store denoted by RD-channel

Case (C) The manufacturer opens an Internet store butdominant retailer does not and is denoted by MD-channel

Case (D) Both of them open their Internet stores simultane-ously denoted by M-channel

Figure 1 depicts 4 possible cases For convenience letPS denotes the dominant retailerrsquos physical store MISthe manufacturer-owned Internet store RIS the dominantretailer-owned Internet store

Parameters and decision variablesrsquo notations used in thepaper are listed in Abbreviations section

Before establishing themodels we give some assumptionsrelated to this study as follows

Assumption 1 The manufacturer produces the product at aconstant unit (marginal) cost which is normalized to zero andsells product to the dominant retailer with a wholesale price119908

j= (1 minus 120573)119901

j119903in the j-channel which is derived by means of

the bargaining process where 119901j119903is the retail price charged by

the dominant retailer in the j-channel and the value of 120573 isin

(0 1) denotes his bargaining power The wholesale price thatis determined in the supply chain by a negotiation process issimilar to the previous researches such as [11 12]

Assumption 2 The dominant retailer acts as a Stackelbergprice leader in the distribution channel and his physicalstore has located at the left end point of a Hotelling linearcity bounded between zero and one as seen in the previousliterature [29 33ndash37] Without loss of generality we assumethat the size of the market is one and consumers areuniformly distributed over the line of the city with a unittravel cost (119905 gt 0) for traveling to the dominant retailerrsquosphysical store to shop and each consumer buys at most oneunit of the product

Assumption 3 The dominant retailer sets the same priceacross his physical store and Internet store In marketingpractice some dominant retailers such as Circuit CityTiffany Gap and Staples fully integrate their offline andonline operations which can make consumer not figure outwhether it is cheaper to purchase from its physical storesand Internet stores In fact this assumption is similar to[29 31 38]

Assumption 4 The value of consumers willing to pay for theproduct is sufficiently large (119881 gt 119905) so as to ensure thefull market coverage Otherwise the dominant retailer neveropens a physical store to serve consumers

Assumption 5 If a consumer chooses to purchase the productfrom the Internet stores (MIS or RIS) the purchasing incursa unit disutility (120575 gt 0) To ensure that at least one of themanufacturers and the dominant retailer has an incentive to

4 Mathematical Problems in Engineering

Table 1

Mrsquos wholesale price MISrsquos price PSRISrsquos price Mrsquos profit Rrsquos profitT-channel (1 minus 120573)(119881 minus 119905) NA 119881 minus 119905 (1 minus 120573)(119881 minus 119905) 120573(119881 minus 119905)

RD-channel (1 minus 120573)(119881 minus 120575) NA 119881 minus 120575 (1 minus 120573)(119881 minus 120575) 120573(119881 minus 120575) minus 119865119903

MD-channel(1 minus 120573)(119905 + 120575)

2120573

(2 + 120573)119905 + (2 minus 3120573)120575

4120573

119905 + 120575

2120573

119905 + 120575

2120573

+

(119905 minus 120575)2

minus 12119905120575

16119905

minus 119865119898

(119905 + 120575)2

8119905

Table 2

Mrsquos wholesale price MISrsquos price PSRISrsquos price Mrsquos profit Rrsquos profit

120575 lt

119905

3

(1 minus 120573)(119905 minus 120575)

120573

119905 minus 120575

120573

119905 minus 120575

120573

119905 minus 120575

120573

minus

(119905 minus 120575)120575

119905

minus 119865119898

(119905 minus 120575)120575

119905

minus 119865119903

120575 gt

119905

3

(1 minus 120573)(119905 + 120575)

2120573

(2 + 120573)119905 + (2 minus 3120573)120575

4120573

119905 + 120575

2120573

119905 + 120575

2120573

+

(119905 minus 120575)2

minus 12119905120575

16119905

minus 119865119898

(119905 + 120575)2

8119905

minus 119865119903

open an Internet store let 120575 lt 119905 in our study which is similarto previous studies [3 14 17]

Consumersrsquo disutility 120575 capturing various factors makesonline shopping inconvenient such as quality uncertainty(eg the inability to touch and feel) discomfort with onlinesecurity waiting time until delivery and shipping charge

Based on the above assumptions it is clear that for aconsumer located at 119909 isin [0 1] he will get utilities 119880PS =

119881minus119901119903minus 119905119909 when purchasing the product from the dominant

retailerrsquos physical store and 119880MIS = 119881 minus 119901119898minus 120575 when

purchasing the product from the manufacturerrsquos Internetstore and 119880RIS = 119881 minus 119901

119903minus 120575 when purchasing the product

from the dominant retailerrsquos Internet store

4 Equilibrium Outcomes and StrategicConditions for Opening an Internet Store

In this section we first present the equilibrium outcomesamong the different channel structures and then discussthe strategic conditions for the manufacturer and dominantretailer to open their Internet stores The equilibrium out-comes are given by the following Lemmas 6 and 7 and theproofs are provided in Appendix A

41 Equilibrium Outcomes

Lemma 6 In the T-channel MD-channel and RD-channelthe equilibrium prices and profits for the manufacturer anddominant retailer can be summarized as shown in Table 1

Lemma7 In theM-channel the equilibriumprices and profitsfor manufacturer and dominant retailer can be summarized asshown in Table 2

From Lemmas 6 and 7 we observe that no matter themanufacturer and dominant retailer open an Internet storewill affect the supply chain structure and equilibrium pricesand profits in different ways Let T-channel be a benchmarkwe note that the dominant retailer should lower retail priceonly when his Internet store in the market and when thesetup cost of opening an Internet store 119865

119903lt 120573(119905 minus 120575) then

he can get more profit than that of not opening an Internetstore In addition we find that when the manufacturer anddominant retailer open their Internet stores simultaneouslyif consumersrsquo disutility of purchasing a product from Internetstore is low enough (ie 120575 lt 1199053) the manufacturer can setthe retail price at her Internet store same to the dominantretailerrsquos retail price However if consumersrsquo disutility ofpurchasing a product from Internet store is relatively larger(ie 120575 gt 1199053) the equilibrium prices are same to the caseof the manufacturer only open an Internet store that isMD-channel Furthermore the manufacturerrsquos profit doesnot change but the dominant retailerrsquos profit decreasesTherefore we will discuss the strategic conditions for themanufacturer and dominant retailer to open an Internetstore according to the equilibrium profits among the differentchannel structures

42 Strategic Conditions for Opening an Internet Store Nowas one of the critical problems to obtain the strategic con-ditions for the manufacturer and dominant retailer to openan Internet store we compare the equilibrium profits in RD-channel MD-channel and M-channel to the equilibriumprofits in T-channel and compare the equilibrium profitsin M-channel to the equilibrium profits in RD-channeland MD-channel respectively The following propositionsand corollaries summarize the strategic conditions and itsimplications The proofs are given in Appendix B

Proposition 8 Suppose that themanufacturer has not openedan Internet store when the setup cost of opening an Internetstore by the dominant retailer 119865

119903lt 120573(119905 minus 120575) he can begin to

open an Internet store

Proposition 8 implies that under the condition of themanufacturer has not opened an Internet store onlywhen thesetup cost of opening an Internet store is relatively small thedominant retailer will getmore profit than that of not openingan Internet store Otherwise his profit will decrease due tocostly setup cost

Obviously an immediate consequence of above proposi-tions is the following corollary

Mathematical Problems in Engineering 5

Corollary 9 If the manufacturer has not opened an Internetstore the dominant retailerrsquos strategic motive for opening anInternet store would be weakened by increasing consumersrsquodisutility of purchasing a product from Internet store

Proposition 10 Suppose that the dominant retailer has notopened an Internet store when the setup cost of opening anInternet store by the manufacturer 119865

119898lt (119905 + 120575)2120573 + [(119905 minus

120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905) she can begin to open anInternet store

Proposition 10 implies that under the condition of thedominant retailer has not opened an Internet store onlywhenthe setup cost of opening an Internet store is relatively smallthemanufacturer will getmore profit than that of not openingan Internet store Otherwise her profit will decrease due tocostly setup cost

Based on Proposition 10 we have the following corollary

Corollary 11 If the dominant retailer has not opened anInternet store and his bargaining power is relatively small (ie120573 lt 4119905(7119905 minus 120575)) the manufacturerrsquos strategic motive foropening an Internet store would be strengthened by increasingconsumersrsquo disutility of purchasing a product from Internetstore Otherwise her strategic motive would be weakened

Proposition 12 There are two choices for the manufacturerand dominant retailer to open their Internet stores simultane-ously which are summarized as follows

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) and the setupcosts of opening an Internet store by the manufacturerand dominant retailer meet 119865

119898lt (119905 minus 120575)120573 minus (119905 minus

120575)120575119905 minus (1 minus 120573)(119881 minus 119905) and 119865119903lt (119905 minus 120575)120575119905 minus 120573(119881 minus 119905)

respectively both of them can open their own Internetstores simultaneously

(2) If consumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) andthe setup costs of opening an Internet store by themanufacturer and dominant retailer meet 119865

119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905) and119865119903lt (119905 + 120575)

2

8119905 minus 120573(119881 minus 119905) respectively both of themcan open their own Internet stores simultaneously

Proposition 12 implies that consumersrsquo disutility of pur-chasing a product from Internet store plays an importantrole for opening Internet stores simultaneously by the man-ufacturer and dominant retailer And only when the setupcosts of opening Internet stores by them are relatively smallrespectively then both will get more profit than that of notopening Internet stores Otherwise their profits will decreasedue to costly setup costs

It should be noted that the upper bounds of 119865119898and 119865119903are

related to 120575 for a given 120573 in Proposition 12 so we have thefollowing corollary

Corollary 13 If both the manufacturer and dominant retailerhave not operated their Internet stores then

(1) when consumersrsquo disutility of purchasing a productfrom Internet store is low enough (ie 120575 lt 1199053) themanufacturerrsquos strategic motive for opening an Internetstore would be weakened by increasing consumersrsquodisutility of purchasing a product from Internet storebut the dominant retailerrsquos strategic motive for openingan Internet store would be strengthened

(2) when consumersrsquo disutility of purchasing a productfrom Internet store is relatively larger (ie 120575 gt 1199053)the dominant retailerrsquos strategic motive for opening anInternet store would be strengthened by increasing con-sumersrsquo disutility of purchasing a product from Internetstore For the manufacturer only if the dominantretailerrsquos bargaining power is relatively small (ie 120573 lt

4119905(7119905minus120575)) her strategicmotive for opening an Internetstore would be strengthened by increasing consumersrsquodisutility of purchasing a product from Internet storeOtherwise her strategic motive would be weakened

Proposition 14 Suppose that the dominant retailer has oper-ated an Internet store themanufacturer has two choices to openan Internet store which are summarized as follows

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) and the setupcost of opening an Internet store by the manufacturer119865119898lt (119905 minus 120575)120573 minus (119905 minus 120575)120575119905 minus (1 minus 120573)(119881 minus 120575) she can

also open an Internet store(2) If consumersrsquo disutility of purchasing a product from

Internet store is relatively larger (ie 120575 gt 1199053) andthe setup cost of opening an Internet store by themanufacturer 119865

119898lt (119905+120575)2120573+[(119905minus120575)

2

minus12119905120575]16119905minus

(1 minus 120573)(119881 minus 120575) she can also open an Internet store

Proposition 14 implies that under the condition of thedominant retailer has operated an Internet store consumersrsquodisutility of purchasing a product from Internet store alsoplays an important role in opening an Internet store by themanufacturer And only when the setup cost of opening anInternet store is relatively small then the manufacturer willget more profit than that of not opening an Internet storeOtherwise her profit will decrease due to costly set-up cost

Based on Proposition 14 we have the following corollary

Corollary 15 If the dominant retailer has operated an Internetstore then

(1) when consumersrsquo disutility of purchasing a productfrom Internet store is low enough (ie 120575 lt 1199053) themanufacturerrsquos strategic motive for opening an Internetstore would be weakened by increasing consumersrsquodisutility of purchasing a product from Internet store

(2) when consumersrsquo disutility of purchasing a productfrom Internet store is relatively larger (ie 120575 gt 1199053) andonly if the dominant retailerrsquos bargaining power is rela-tively small (ie 120573 lt [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905)the manufacturerrsquos strategic motive for opening anInternet store would be strengthened by increasing

6 Mathematical Problems in Engineering

consumersrsquo disutility of purchasing a product fromInternet store Otherwise her strategic motive would beweakened

Proposition 16 Suppose that the manufacturer has operatedan Internet store the best choice for dominant retailer is not toopen an Internet store

Proposition 16 implies that under the condition of themanufacturer has operated an Internet store regardless ofconsumersrsquo disutility of purchasing a product from Internetstore is small or larger it is best for the dominant retailer notto open an Internet store Otherwise his profit will decreasedue to costly setup cost or the manufacturerrsquos low pricestrategy that attract more consumers to buy the product fromher Internet store

Proposition 17 Suppose that the manufacturer has notopened an Internet store if consumersrsquo disutility of purchasinga product from Internet store is low enough (ie 120575 lt 1199053) andthe setup cost of opening an Internet store for the manufactureris intermediate 119865

119898isin [(119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 (119905 minus

120575)120573 minus (119905 minus 120575)120575119905] the dominant retailer opening an Internetstore can lead to the well-known contagion-like effect

Proposition 17 implies that under the condition of themanufacturer has not opened an Internet store when con-sumersrsquo disutility of purchasing a product from Internet storeis relatively small and the set-up cost of opening an Internetstore for the manufacturer is intermediate the dominantretailerrsquos Internet store entry may induce the manufacturerto open her own Internet store competing with him

FromProposition 17 we observe that the upper and lowerbounds of 119865

119898are related to 120575 for a given 120573 so we have the

following corollary

Corollary 18 When consumersrsquo disutility of purchasing aproduct from Internet store is low enough (ie 120575 lt 1199053) ifthe dominant retailerrsquos bargaining power is relatively small (ie120573 lt 4119905(7119905minus120575)) the contagion-like effect would be expanded byincreasing consumersrsquo disutility of purchasing a product fromInternet store However if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 gt 4119905(7119905 minus 120575)) the contagion-like effect would be diminished

Based on aforementioned propositions we now showwhen do the manufacturer and dominant retailer open theirown Internet stores to a traditional supply chain and how dothey set prices after opening Internet stores in Table 3

5 Analytical Results onBoth Playersrsquo Pricing Policies

From Lemmas 6 and 7 we know that the T-channel andRD-channel are monopoly settings So the dominant retailercharges the optimal monopoly price and sells the productto all consumers However under the MD-channel and M-channel the manufacturer and dominant retailer engage in

price competition To investigate the impacts of the dom-inant retailerrsquos bargaining power and consumersrsquo disutilityof purchasing a product from Internet store on the manu-facturer and dominant retailerrsquos pricing strategies we obtainthe following propositions and the proofs are provided inAppendix C

Proposition 19 Suppose that only the manufacturer can openan Internet store then

(1) 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0(2) 120597119901MD

119903120597120575 = 12120573 gt 0 and 120597119901MD

119898120597120575 = (2 minus 3120573)4120573

and if 120573 isin (0 23) then 120597119901MD119898

120597120575 gt 0 if 120573 isin (23 1)then 120597119901MD

119898120597120575 lt 0

(3) if 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

if 120575 = 1199053 then 119901MD119898

=

119901MD119903

and if 120575 gt 1199053 then 119901MD119898

lt 119901MD119903

Proposition 19 indicates that when the manufacturer canopen an Internet store

(1) she should also lower the price to induce consumersto purchase the product from her Internet store asthe increasing dominant retailerrsquos bargaining powerotherwise the dominant retailer will also provideprice incentives for consumers to buy the productfrom his physical store

(2) if the dominant retailerrsquos bargaining power is rela-tively small (ie 120573 lt 23) she should raise the pricein her Internet store with increasing consumersrsquo disu-tility However if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 gt 23) she should cutdown the price in her Internet store with increasingconsumersrsquo disutility

(3) if consumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) shemust provide strong price incentives for consumersto purchase the product from her Internet storeotherwise her profits will cut down owing to someconsumers buying the product from the dominantretailerrsquos physical store on the contrary the domi-nant retailer will provide strong price incentives forconsumers to purchase the product from his physicalstore when consumersrsquo disutility of purchasing aproduct from Internet store is low enough (ie 120575 lt

1199053) then the manufacturerrsquos retail price is higherthan the dominant retailerrsquos If and only if consumersrsquodisutility of purchasing a product from Internet storesatisfies 120575 = 1199053 the manufacturer can set her retailprice to be equal to the dominant retailerrsquos

Proposition 20 Suppose that both the manufacturer anddominant retailer can open their Internet stores simultaneouslythen

(1) If 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0120597119901

M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0

(2) If 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 120597119901M119898120597120575 = (2 minus 3120573)4120573 120597119901M

119903120597120575 = 12120573 gt 0 and

Mathematical Problems in Engineering 7

Table 3 Strategic conditions for opening Internet stores to T-channel and pricing policies

Strategic conditions M and Rrsquos activities Pricing policiesM has not opened an Internet store and119865119903lt 120573(119905 minus 120575)

R can open an Internet store Monopoly pricing

R has not opened an Internet store and119865119898lt (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905)

M can open an Internet store

When 120575 lt 1199053then 119901MD

119898gt 119901

MD119903

When 120575 = 1199053then 119901MD

119898= 119901

MD119903

When 120575 gt 1199053then 119901MD

119898lt 119901

MD119903

When 120575 lt 1199053 119865119903lt (119905 minus 120575)120575119905 minus 120573(119881 minus 119905) and

119865119898lt (119905 minus 120575)120573 minus (119905 minus 120575)120575119905 minus (1 minus 120573)(119881 minus 119905)

Both M and R can open their Internet stores simultaneously119901M119898= 119901

M119903

When 120575 gt 1199053 119865119903lt (119905 + 120575)

2

8119905 minus 120573(119881 minus 119905) and119865119898lt (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905)

119901M119898lt 119901

M119903

when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0 but when 120573 isin

(23 1) then 120597119901M119898120597120575 lt 0

(3) If 120575 le 3119905 then 119901M119898= 119901

M119903 if 120575 gt 1199053 then 119901M

119898lt 119901

M119903

Proposition 20 indicates when both the manufacturerand dominant retailer can open their Internet stores simul-taneously

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) bothof them can set same price and lower prices as theincreasing consumersrsquo disutility On the contrary ifconsumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) themanufacturer must provide lower price incentivesthan the dominant retailer which may induce con-sumers to purchase the product from her Internetstore It should be pointed out that when the dom-inant retailerrsquos bargaining power is relatively small(ie 120573 lt 23) the manufacturerrsquos price increaseswith increasing consumersrsquo disutility but when thedominant retailerrsquos bargaining power is relativelylarger (ie 120573 gt 23) the manufacturerrsquos retail pricedecreases with increasing consumersrsquo disutility

(2) When consumersrsquo disutility of purchasing a prod-uct from Internet store is low enough (ie 120575 lt

1199053) the dominant retailerrsquos price decreases reducewith increasing consumersrsquo disutility but when con-sumersrsquo disutility of purchasing a product from Inter-net store is relatively larger (ie 120575 gt 1199053) thedominant retailerrsquos price decreases with increasingconsumersrsquo disutility Speaking frankly that is thedominant retailerrsquos smart pricing strategiesThe dom-inant retailer will raise the retail price when mostof consumers with a large disutility of purchasing aproduct from Internet store buy the product from hisphysical store and lower the retail price when mostof consumers with a small disutility of purchasing aproduct from Internet store buy the product from themanufacturerrsquos Internet store

Proposition 21 Given that the dominant retailerrsquos bargainingpower we obtain the following results about the manufacturerrsquoswholesale price under RD-channel MD-channel and M-channel

(1) 120597119908RD120597120575 = minus(1 minus 120573) lt 0

(2) 120597119908MD120597120575 = (1 minus 120573)2120573 gt 0

(3) if 120575 lt 1199053 then 120597119908M120597120575 = minus(1 minus 120573)120573 lt 0 if 120575 gt 1199053

then 120597119908M120597120575 = (1 minus 120573)2120573 gt 0

Proposition 21 indicates that the manufacturer should setthe wholesale prices differentially across the RD-channelMD-channel andM-channel and raise or lower thewholesaleprices in the light of consumersrsquo disutility of buying theproduct from Internet store More specifically the man-ufacturer can lower the wholesale price with increasingconsumersrsquo disutility of buying the product from Internetstore in the RD-channel but in theMD-channel she can raisethe wholesale price with increasing consumersrsquo disutility ofbuying from Internet store However in theM-channel whenthe consumersrsquo disutility of buying from Internet store is lowenough (ie 120575 lt 1199053) she can lower the wholesale pricewith increasing consumersrsquo disutility but when consumersrsquodisutility of buying from Internet store is relatively larger (ie120575 gt 1199053) she should raise the wholesale price with increasingconsumersrsquo disutility

Proposition 22 Given that the dominant retailerrsquos bargainingpower we obtain the following results about the manufacturerrsquosretail price at her Internet store under MD-channel and M-channel

(1) If 120575 lt 1199053 when 120573 isin (0 23) then 120597119901MD119898

120597120575 =

(2 minus 3120573)4120573 gt 0 120597119901M119898120597120575 = minus1120573 lt 0 but when 120573 isin

(23 1) then 120597119901MD119898

120597120575 = (2 minus 3120573)4120573 lt 0 120597119901M119898120597120575 =

minus1120573 lt 0(2) If 120575 gt 1199053 when 120573 isin (0 23) then 120597119901

MD119898

120597120575 =

120597119901M119898120597120575 gt 0 but when 120573 isin (23 1) then 120597119901MD

119898120597120575 =

120597119901M119898120597120575 lt 0

Proposition 22 indicates that themanufacturer should setthe retail prices at her Internet store differentially across the

8 Mathematical Problems in Engineering

MD-channel and M-channel and raise or lower the prices inthe light of consumersrsquo disutility of buying the product fromInternet store More specifically if the consumersrsquo disutilityof buying from Internet store is low enough (ie 120575 lt 1199053)the manufacturer can raise the retail price at her Internetstore with increasing consumersrsquo disutility of buying fromInternet store when the dominant retailerrsquos bargaining poweris relatively small (ie 120573 lt 23) and the dominant retailerdoes not open Internet store However if the dominantretailer also opens an Internet store the manufacturer shouldlower the retail price at her Internet store so as to attractconsumers to buy the product from her Internet store On thecontrary if the consumersrsquo disutility of buying from Internetstore is relatively larger (ie 120575 gt 1199053) and the dominantretailer also opens an Internet store then the manufacturershould set the same price with the dominant retailerrsquos andadjust the price following the dominant retailer

Proposition 23 Given that the dominant retailerrsquos bargainingpower we obtain the following results about dominant retailerrsquosretail price under RD-channel MD-channel and M-channel

(1) If 120575 lt 1199053 then 120597119901RD119903120597120575 = minus1 lt 0 120597119901MD

119903120597120575 = 12120573 gt

0 and 120597119901M119903120597120575 = minus1120573 lt 0

(2) If 120575 gt 1199053 then 120597119901RD119903120597120575 = minus1 lt 0 120597119901

MD119903

120597120575 =

12120573 gt 0 and 120597119901M119903120597120575 = 12120573 gt 0

Proposition 23 indicates that no matter when the con-sumersrsquo disutility of buying from Internet store is small orlarger the dominant retailer should lower the retail price withincreasing consumersrsquo disutility buying from Internet store inthe RD-channel but in the MD-channel he always raises theretail price with increasing consumersrsquo disutility Howeverin the M-channel when consumersrsquo disutility buying fromInternet store is low enough (ie 120575 lt 1199053) he should lowerthe price with increasing consumersrsquo disutility but whenconsumersrsquo disutility is relatively larger (ie 120575 gt 1199053) he canset the price same as the price in the MD-channel and raisethe price with increasing consumersrsquo disutility

6 Numerical Examples

In this section we present numerical examples to illustratethe theoretical results about impacts of consumersrsquo disutilityof buying from Internet store on the manufacturer anddominant retailerrsquos pricing policies with different bargainingpower for the dominant retailerrsquos among RD-channel MD-channel and M-channel which are summarized in Figures2ndash11 where 119881 = 14 119905 = 6 120575 isin (0 6) and 120573 = 02 120573 = 08The parametersrsquo values satisfy the assumptions in Section 3 inorder to make the models feasible and meaningful

Comparing Figure 2 with Figure 3 we can observe thatwhen the dominant retailerrsquos bargaining power is relativelysmall (ie 120573 = 02) both of them can increase prices asincreasing consumersrsquo disutility of purchasing from Internetstore in MD-channel However when the dominant retailerrsquosbargaining power is relatively larger (ie 120573 = 08) themanufacturer has no choice but to lower the retail price soas to attract consumers to buy the product from her Internet

0 1 2 3 4 5 612

14

16

18

20

22

24

26

28

30

wMD

pMDm

pMDr

120575

Figure 2 Impacts of 120575 on prices in the MD-channel when 120573 = 02

0 1 2 3 4 5 60

1

2

3

4

5

6

7

8

wMD

pMDm

pMDr

120575

Figure 3 Impacts of 120575 on prices in the MD-channel when 120573 = 08

store In addition Figures 2 and 3 show that when consumersrsquodisutility buying from Internet store is low enough (ie 120575 lt

2) the manufacturer can set her retail price to be larger thanthe dominant retailerrsquos However when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2)the manufacturer can set her retail price to be lower than thedominant retailerrsquos

Figures 4 and 5 show that when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)both the manufacturer and dominant retailer should lowerprices to increase consumersrsquo disutility buying from Internet

Mathematical Problems in Engineering 9

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

wM

pMm

pMr

Figure 4 Impacts of 120575 on prices in the M-channel when 120573 = 02

0 1 2 3 4 5 61

2

3

4

5

6

7

8

120575

wM

pMm

pMr

Figure 5 Impacts of 120575 on prices in the M-channel when 120573 = 08

store It is noted that the rate of change of manufacturerrsquosretail price with respect to consumersrsquo disutility buying fromInternet store is equal to that of dominant retailerrsquos retailprice However when consumersrsquo disutility buying fromInternet store is relatively larger (ie 120575 gt 2) if the dominantretailerrsquos bargaining power is relatively small (ie 120573 =

02) the manufacturer can raise retail price following thedominant retailer as increasing consumersrsquo disutility buyingfrom Internet store if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 = 08) the manufacturershould cut down the retail price in her Internet store withincreasing consumersrsquo disutility

0 1 2 3 4 5 66

8

10

12

14

16

18

20

22

24

wMD

wRD

wM

120575

Figure 6 The wholesale prices in different channels when 120573 = 02

0 1 2 3 4 5 605

1

15

2

25

3

120575

wMD

wRD

wM

Figure 7 The wholesale prices in different channels when 120573 = 08

Figures 6 and 7 show that no matter whether thedominant retailerrsquos bargaining power is small or large themanufacturer can raise the wholesale price with increasingconsumersrsquo disutility buying from Internet store in the MD-channel but in the RD-channel the manufacturer shouldlower the wholesale price with increasing consumersrsquo disutil-ity However in the M-channel when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower the wholesale price withincreasing consumersrsquo disutility when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2) themanufacturer can raise the wholesale price with increasing

10 Mathematical Problems in Engineering

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

pMDm

pMm

Figure 8 Manufacturerrsquos retail prices in different channels when120573 = 02

0 1 2 3 4 5 645

5

55

6

65

7

75

120575

pMDm

pMm

Figure 9 Manufacturerrsquos retail prices in different channels when120573 = 08

consumersrsquo disutility and set the wholesale price the same asin the MD-channel

Figures 8 and 9 show that when the dominant retailerrsquosbargaining power is relatively small (ie 120573 = 02) inthe MD-channel the manufacturer can raise retail pricewith increasing consumersrsquo disutility buying from Internetstore but when the dominant retailerrsquos bargaining power isrelatively larger (ie 120573 = 08) the manufacturer should lowerretail price with increasing consumersrsquo disutility Howeverin the M-channel no matter whether the dominant retailerrsquosbargaining power is small or large when consumersrsquo disutility

0 1 2 3 4 5 65

10

15

20

25

30

120575

pRDr

pMDr

pMr

Figure 10 Dominant retailerrsquos prices in different channels when120573 =02

buying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower retail price with increasingconsumersrsquo disutility but when consumersrsquo disutility buyingfrom Internet store is relatively larger (ie 120575 gt 2) if thedominant retailerrsquos bargaining power is relatively small (ie120573 = 02) the manufacturer can raise retail price withincreasing consumersrsquo disutility buying from Internet storeif the dominant retailerrsquos bargaining power is relatively larger(ie 120573 = 08) themanufacturer should lower retail price withincreasing consumersrsquo disutility

Figures 10 and 11 show that no matter whether thedominant retailerrsquos bargaining power is small or larger healways lowers the retail price with increasing consumersrsquodisutility buying from Internet store in the RD-channel butin the MD-channel he always raises the retail price withincreasing consumersrsquo disutility However in the M-channelwhen consumersrsquo disutility buying from Internet store islow enough (ie 120575 lt 2) the dominant retailer shouldlower retail price with increasing consumersrsquo disutility butwhen consumersrsquo disutility is relatively larger (ie 120575 gt 2)the dominant retailer can raise retail price with increasingconsumersrsquo disutility buying from Internet store

7 Conclusions and Future Research

To investigate when the manufacturer and dominant retaileropen their own Internet stores with different setup costsand how set prices to ensure opening Internet stores areprofitable in a supply chain we first present the equilibriumoutcomes under four possible supply chain structures andthen discuss the strategic conditions for the manufacturerand dominant retailer when it is optimal to open an Internetstore In addition we analyze both playersrsquo pricing policies

Mathematical Problems in Engineering 11

0 1 2 3 4 5 62

4

6

8

10

12

14

120575

pMDr

pRDr

pMr

Figure 11 Dominant retailerrsquos prices in different channels when 120573 =08

after they open their Internet stores and discuss the impactsof the dominant retailerrsquos bargaining power and consumersrsquodisutility of purchasing a product from Internet store onthe manufacturer and dominant retailerrsquos pricing strategiesFinally we conduct numerical examples to illustrate thetheoretical results

We obtain some new results differing from those inthe literature We find that the optimal choices for themanufacturer and dominant retailer to open an Internetstore are largely determined by their respective setup costswhich are closely related to the dominant retailerrsquos bargainingpower and consumersrsquo disutility of buying from Internetstore It is worth mentioning that multichannel retailing forthe dominant retailer is not necessarily the best strategyIn other words if the dominant retailer opens an Internetstore the marketing plan for him to attract more consumersby charging a lower price is impossible to achieve and hecan induce the manufacturer to open an Internet store tocompetewith himOnlywhen the setup cost for the dominantretailer to open an Internet store is sufficiently low then he isprofitable

What is more we also find that the manufacturerrsquosoptimal price at her Internet store is not always being lowerthan the dominant retailerrsquos For example if the consumersrsquodisutility of buying from Internet store is sufficiently highthe manufacturer must provide strong price incentives forconsumers to purchase the product from the Internet store

Although this research provides new insights for themanufacturer and dominant retailer to open an Internetstore and set prices in a supply chain there are severaldirections that could be extended First this study assumedthat all information is known to the manufacturer anddominant retailer in our model However information couldbe asymmetric in the supply chain since both players haveprivate information about their own internal variable costs

for example the setup cost of opening an Internet storecustomersrsquo purchase patterns and search costsTherefore wecan explore the competitive equilibrium under asymmetricinformation settings Second we assume that consumersrsquodisutility of buy from Internet store is independent of theunit transportation cost which can be relaxed in the futureresearch Third trade credit is widely used in practice andhas important impact on supply chain management [39ndash41] In recent years trade credit has become one of themajor transactions between suppliers and retailers in a valuechain For example Wal-Mart Carrefour and GOME (alarge Chinese home appliance chain retailer) even delayedpayments to their suppliers for as long as one year [42]Hence it is worthy to understand how the trade creditaffects supply channel configuration together with pricingstrategies in the E-commerce market A final issue worthyof investigation is how different types of customers affectthe manufacturer and dominant retailerrsquos channel selectionstrategies We leave these questions for future research

Appendices

A Equilibrium Outcome ofthe Four Channel Structures

Proof of Lemma 6 (1) In the T-channel both the manufac-turer and dominant retailer do not open their Internet storesThere is only the dominant retailerrsquos physical store in themarket So the dominant retailer acts as a monopolist andoptimally charges a price 119881 minus 119905 such that the market isjust covered For the manufacturer given that the dominantretailerrsquos optimal retail price the optimal wholesale price is119908

T= (1 minus 120573)(119881 minus 119905) Since the manufacturer produces

the product at a constant unit (marginal) cost which isnormalized to zero and the market is just covered that is thesize of the market is one the profit for the manufacturer isprod

T119898= (1minus120573)(119881minus119905) Accordingly the profit for the dominant

retailer isprodT119903= 120573(119881 minus 119905)

(2) In RD-channel only the dominant retailer opens anInternet store (RIS) If a consumer locates at a distance fromphysical store (PS) he will get a net utility of by purchasingthe product from PS and a net utility of by purchasing theproduct from RIS To ensure the full market coverage thedominant retailer charges the monopoly price 119881 minus 120575 acrosshis two stores and sells the product to all consumers Forthe manufacturer given the dominant retailerrsquos optimal retailprice the optimal wholesale price is 119908RD

= (1 minus 120573)(119881 minus 120575)Since the manufacturer produces the product at a constantunit (marginal) cost which is normalized to zero and 119905 thesize of the market is one the profits for the manufacturer anddominant retailer are prodRD

119898= (1 minus 120573)(119881 minus 120575) and prod

RD119903

=

120573(119881 minus 120575) respectively(3) In MD-channel the manufacturer opens an Internet

store but dominant retailer does not So consumers canhave convenient access to the product through the dominantretailerrsquos physical store (PS) at price 119901

119903or the manufacturerrsquos

Internet store (MIS) at price 119901119898 their decision about which

store to buy revolves around the comparison of their net

12 Mathematical Problems in Engineering

utility derived fromPS119880PS = 119881minus119901119903minus119905119909 and119880MIS = 119881minus119901119898minus120575by buying the product from MIS Therefore the marginalconsumers are located at 119909 = (119901

119898minus 119901119903+ 120575)119905 So the profit

functions for the manufacturer and dominant retailer can bewritten as

prod

119898

= 119908[

(119901119898minus 119901119903+ 120575)

119905

] + 119901119898[

(119901119903minus 119901119898+ 119905 minus 120575)

119905

] minus 119865119898

(A1)

prod

119903

= (119901119903minus 119908) [

(119901119898minus 119901119903+ 120575)

119905

] (A2)

Under the assumption proposed in Section 3 the dom-inant retailer is the price leader and the manufacturer isthe follower As before the game is solved backwards Inthis market we firstly need to calculate the manufacturerrsquosoptimal price given any dominant retailerrsquos price

Themanufacturerrsquos reaction function can be derived fromthe first-order condition

120597prod119898

120597119901119898

=

[(2 minus 120573) 119901119903minus 2119901119898+ 119905 minus 120575]

119905

= 0

that is 119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A3)

Substituting (A3) into (A2) we get

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

(A4)

Taking the first-order derivative of (A4) with respect to119901119903and letting the derivative be zero we have

119901MD119903

=

(119905 + 120575)

2120573

(A5)

Given the wholesale price bargaining process we canobtain the manufacturerrsquos optimal wholesale price 119908MD

=

(1 minus 120573)(119905 + 120575)2120573 and substituting (A5) into (A3) we getthe manufacturerrsquos optimal retail price

119901MD119898

=

(2 + 120573) 119905 + (2 minus 3120573) 120575

4120573

(A6)

Substituting (A5) and (A6) into (A1) and (A2) wecan obtain the equilibrium profits for the manufacturers anddominant retailer respectively

MDprod

119898

=

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus 119865119898

MDprod

119903

=

(119905 + 120575)2

8119905

(A7)

Proof of Lemma 7 In the M-channel both the manufacturerand dominant retailer simultaneously open their own Inter-net stores then customers are able to purchase a product

either from the dominant retailerrsquos physical store (PS) or fromthe alternative Internet stores (MISRIS) They can get a netutility of 119880PS = 119881 minus 119901

119903minus 119905119909 by buying the product from PS

and a net utility of 119880MIS = 119881 minus 119901119898minus 120575 by buying the product

fromMIS and a net utility of119880RIS = 119881minus 119901119903minus 120575 by buying the

product from RISAccording to the basicmodel we know that the dominant

retailer firstmakes pricing decision as the price leader and themanufacturer is the follower If the dominant retailer chargesa price higher than the manufacturerrsquos price (119901

119903gt 119901119898) then

no consumer will buy the product from his Internet storeUnder this condition the dominant retailer makes no sale inhis Internet store and makes a profit of minus119865

119903 Therefore the

demand functions for the manufacturerrsquos Internet store anddominant retailerrsquos physical store are given respectively asfollows

119863MIS =(119901119903minus 119901119898+ 119905 minus 120575)

119905

(A8)

119863PS =(119901119898minus 119901119903+ 120575)

119905

(A9)

Hence the manufacturerrsquos profit function can be written as

prod

119898

=

[119908 (119901119898minus 119901119903+ 120575) + 119901

119898(119901119903minus 119901119898+ 119905 minus 120575)]

119905

minus 119865119898

(A10)

From the first-order condition we have

119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A11)

Given the condition of 119901119903gt 119901119898 this implies that 119901

119903gt (119905 minus

120575)120573 However when 119901119903le (119905 minus 120575)120573 and 119901

119903gt 119901119898 we always

have 120597prodM119898120597119901119898= [(2 minus 120573)119901

119903minus 2119901119898+ 119905 minus 120575]119905 gt 0

Therefore the manufacturer optimally sets its price at119901119898= 119901119903 and her optimal pricing schedule is as follows

119901119898=

119901119903 119901

119903le

119905 minus 120575

120572

(2 minus 120573) 119901119903+ 119905 minus 120575

2

119901119903gt

119905 minus 120575

120572

(A12)

Given the manufacturerrsquos pricing schedule the dominantretailerrsquos profit is given as follows

prod

119903

=

(119901119903minus 119908)

120575

119905

minus 119865119903 119901

119903le

119905 minus 120575

120573

(119901119903minus 119908)

119905 + 120575 minus 120573119901119903

2119905

minus 119865119903 119901119903gt

119905 minus 120575

120573

(A13)

Under the condition of 119901119903gt (119905 minus 120575)120573 the dominant

retailerrsquos profit is

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

minus 119865119903 (A14)

Taking the first-order derivative of (A14) with respect to 119901119903

and letting the derivative be zero we have 119901M119903= (119905 + 120575)2120573

Mathematical Problems in Engineering 13

Submitting it into (A11) we get the manufacturerrsquos optimalprice in her Internet store 119901M

119898= [(2 + 120573)119905 + (2 minus 3120573)120575]4120573

Hence the manufacturer and dominant retailerrsquos optimalprofits are prodM

119898= (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus 119865119898

andprodM119903= (119905 + 120575)

2

8119905 minus 119865119903 respectively

According to the previous assumption 119901119903gt (119905 minus 120575)120573

which implies that (119905 + 120575)2120573 gt (119905 minus 120575)120573 120575must satisfy 120575 gt1199053 However when 120575 lt 1199053 we always have

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](minus)

gt 0

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](+)

lt 0 (A15)

So the dominant retailerrsquos optimal retail price in the M-channel is 119901M

119903= (119905 minus 120575)120573 Therefore the manufacturer and

dominant retailerrsquos optimal profits areprodM119898= (119905 minus 120575)120573 minus [(119905 minus

120575)120575]119905 minus 119865119898andprodM

119903= [(119905 minus 120575)120575]119905 minus 119865

119903 respectively

B Strategic Conditions forOpening an Internet Store

Proofs of Proposition 8 and Corollary 9 From Lemma 6 weanalyse the equilibrium profits for the dominant retailerbetween the T-channel and RD-channel and note that onlywhen 119865

119903lt 120573(119905 minus 120575) then prodRD

119903gt prod

T119903 This implies that as

long as the setup cost of opening an Internet store satisfies119865119903

lt 120573(119905 minus 120575) ≜ 1198611 it is always optimal to open an

Internet store for the dominant retailer In addition we notethat 120597119861

1120597120575 = minus120573 lt 0 So the dominant retailerrsquos strategic

motive for opening an Internet store would be weakened byincreasing consumersrsquo disutility of purchasing a product fromInternet store

Proofs of Proposition 10 and Corollary 11 From Lemma 6 weanalyse the equilibrium profits for the manufacturer betweenthe T-channel and MD-channel and note that only when thesetup cost of opening an Internet store satisfies 119865

119898lt (119905 +

120575)2120573+[(119905minus120575)2

minus12119905120575]16119905minus(1minus120573)(119881minus119905) ≜ 1198612 thenprodMD

119898gt

prodT119898 In addition we note that 120597119861

2120597120575 = [4119905 minus 120573(7119905 minus 120575)]8120573119905

and find when 0 lt 120573 lt 4119905(7119905 minus 120575) then 1205971198612120597120575 gt 0 and

when 4119905(7119905 minus 120575) lt 120573 lt 1 then 1205971198612120597120575 lt 0

Proofs of Proposition 12 and Corollary 13 FromLemmas 6 and7 we analyse the equilibriumprofits for themanufacturer anddominant retailer between the T-channel andM-channel wenote that under the condition of 120575 lt 1199053 only when the setupcosts of opening an Internet store for the manufacturer anddominant retailer simultaneously satisfy

119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198613

119865119903lt

[(119905 minus 120575) 120575]

119905

minus 120573 (119881 minus 119905) ≜ 1198614

(B1)

thenMprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B2)

Similarly under the condition of 120575 gt 1199053 only when thesetup costs of opening an Internet store for the manufacturerand dominant retailer simultaneously satisfy

119865119898lt

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198615

119865119903lt

(119905 + 120575)2

8119905

minus 120573 (119881 minus 119905) ≜ 1198616

(B3)

then

Mprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B4)

In addition we note that both 1205971198613120597120575 = minus[119905 + 120573(119905 minus

2120575)]120573119905 lt 0 and 1205971198614120597120575 = (119905 minus 2120575)119905 gt 0 are held under

the condition of 120575 lt 1199053 Furthermore under the conditionof 120575 gt 1199053 we also find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198615120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

5120597120575 lt 0

1205971198616120597120575 = 2(119905 + 120575)8119905 gt 0

Proofs of Proposition 14 and Corollary 15 From Lemmas 6and 7 we analyse the manufacturerrsquos equilibrium profits inthe RD-channel and M-channel we note that under thecondition of 120575 lt 1199053 only when the setup cost of opening anInternet store for her satisfies 119865

119898lt (119905 minus 120575)120573 minus [(119905 minus 120575)120575]119905 minus

(1 minus 120573)(119881 minus 120575) ≜ 1198617 thenprodM

119898gt prod

RD119898 In addition we find

1205971198617120597120575 = minus[(1 + 120573

2

)119905 minus 2120573120575]120573119905 lt 0But under the condition of 120575 gt 1199053 only when the setup

cost of opening an Internet store for her satisfies 119865119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 120575) ≜ 1198618 then

prodM119898gt prod

RD119898 In addition 120597119861

8120597120575 = [120573(119905+120575)+4119905(1minus2120573

2

)]8120573119905

we find that when 0 lt 120573 lt [(119905 + 120575) + radic(119905 + 120575)2

+ 1281199052]16119905

then 1205971198618120597120575 gt 0 andwhen [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905 lt

120573 lt 1 then 1205971198618120597120575 lt 0

Proofs of Proposition 16 From Lemmas 6 and 7 we analysethe dominant retailerrsquos equilibriumprofits in theMD-channeland M-channel and note that when 120575 lt 1199053 then prod

M119903minus

prodMD119903

= minus(119905 minus 3120575)2

8119905 minus 119865119903lt 0 and when 120575 gt 1199053

then prodM119903minus prod

MD119903

= minus119865119903lt 0 These imply that when the

manufacturer has operated an Internet store the best choicefor dominant retailer is not to open an Internet store

Proofs of Proposition 17 and Corollary 18 From Lemmas 6and 7 we analyse the dominant retailerrsquos equilibrium profitsin the MD-channel and M-channel and note that under thecondition of 120575 lt 1199053 thenprodM

119898minus prod

MD119898

= [8119905(119905 minus 3120575) minus 120573[(119905 +

120575)2

minus 161205752

]8119905]16120573119905 This implies that the manufacturer willopen her Internet store when the dominant retailer opens an

14 Mathematical Problems in Engineering

Internet store and the setup costs of opening an Internet storefor her satisfies

1198619≜

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

lt 119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

≜ 11986110

(B5)

In addition we find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198619120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

9120597120575 lt 0

and 12059711986110120597120575 = minus[119905 + 120573(119905 minus 2120575)]120573119905 lt 0

C The ManufacturerDominantRetailers Pricing Policies

Proof of Proposition 19 In the MD-channel we respectivelydifferentiate between119901MD

119898and119901MD

119903with respect to 120573 and find

that 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0 For any given120573 differentiating between 119901MD

119898and 119901MD

119903with respect to 120575 we

have 120597119901MD119903

120597120575 = 12120573 gt 0 and 120597119901MD119898

120597120575 = (2 minus 3120573)4120573and if 120573 isin (0 23) then 120597119901MD

119898120597120575 gt 0 if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 In addition we find that 119901MD119898

minus 119901MD119903

= (119905 minus

3120575)4 it is obvious that when 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

when 120575 = 1199053 then 119901MD

119898= 119901

MD119903

and when 120575 gt 1199053 then119901MD119898

lt 119901MD119903

Proof of Proposition 20 In the M-channel we respectivelydifferentiate between 119901M

119898and 119901M

119903with respect to 120573 and find

that when 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0

and when 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 For any given 120573 we respectively differentiate between 119901M119898

and 119901M119903with respect to 120575 and find that when 120575 lt 1199053 then

120597119901M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0 when 120575 gt 1199053 then

120597119901M119898120597120575 = (2 minus 3120573)4120573 and 120597119901M

119903120597120575 = 12120573 gt 0

It is easy to note that when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0

but when 120573 isin (23 1) then 120597119901M119898120597120575 lt 0

Proof of Proposition 21 From Lemmas 6 and 7 we note that120597119908

RD120597120575 = minus(1 minus 120573) lt 0 and 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0In addition if 120575 lt 1199053 then 120597119908M

120597120575 = minus(1 minus 120573)120573 lt 0 if120575 gt 1199053 then 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0

Proof of Proposition 22 From the proofs of Propositions 19and 20 we note that when 120575 lt 1199053 if 120573 isin (0 23) then120597119901

MD119898

120597120575 gt 0 120597119901M119898120597120575 lt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 120597119901M119898120597120575 lt 0 when 120575 gt 1199053 if 120573 isin (0 23)

then 120597119901MD119898

120597120575 = 120597119901M119898120597120575 gt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 = 120597119901M119898120597120575 lt 0

Proof of Proposition 23 From Lemmas 6 and 7 we note that120597119901

RD119903120597120575 = minus1 lt 0 and 120597119901MD

119903120597120575 = 12120572 gt 0 In addition if

120575 lt 1199053 then 120597119901M119903120597120575 = minus1120572 lt 0 if 120575 gt 1199053 then 120597119901M

119903120597120575 =

12120572 gt 0

Abbreviations

UK The consumerrsquos utility of purchasing theproduct from K storeK isin PSRISMIS

119881 The value of consumers willing to payfor the product

120575 The consumersrsquo disutility of purchasingthe product from Internet store(MISRIS)

119905 The per unit transportation cost ofpurchasing the product from physicalstore (PS)

120573 The dominant retailerrsquos bargainingpower in the distribution channel

119908j The manufacturerrsquos wholesale price in

the j-channel j isin TRDMDM

119901j119903 The dominant retailerrsquos price in the

j-channel j isin TRDMDM

119901j119898 The manufacturerrsquos price in the

j-channel j isin MDM

119865119898119865119903 The setup cost of opening an Internetstore by the manufacturerdominantretailer

Πj119898Πj119903 The manufacturerdominant retailerrsquosprofit in the j-channelj isin TRDMDM

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been supported by theNational Natural Sci-ence Foundation of China (71271225) Chongqingrsquos NaturalScience Foundation (cstc2012jjA1404) and the Open Fund ofChongqing Key Laboratory of Logistics (CQKLL12001)

References

[1] L Hsiao and Y-J Chen ldquoStrategic motive for introducinginternet channels in a supply chainrdquo Production and OperationsManagement vol 23 no 1 pp 36ndash47 2014

[2] I Geyskens K Gielens and M G Dekimpe ldquoThe marketvaluation of Internet channel additionsrdquo Journal of Marketingvol 66 no 2 pp 102ndash119 2002

[3] 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

[4] S-H Chun and J-C Kim ldquoPricing strategies in B2C electroniccommerce analytical and empirical approachesrdquo Decision Sup-port Systems vol 40 no 2 pp 375ndash388 2005

[5] S K Mukhopadhyay X Zhu and X Yue ldquoOptimal contractdesign for mixed channels under information asymmetryrdquoProduction and Operations Management vol 17 no 6 pp 641ndash650 2008

Mathematical Problems in Engineering 15

[6] G S Cai ldquoChannel selection and coordination in dual-channelsupply chainsrdquo Journal of Retailing vol 86 no 1 pp 22ndash36 2010

[7] K Takahashi T Aoi D Hirotani and K Morikawa ldquoInventorycontrol in a two-echelon dual-channel supply chain with setupof production and deliveryrdquo International Journal of ProductionEconomics vol 133 no 1 pp 403ndash415 2011

[8] D W Carlton and J A Chevalier ldquoFree riding and salesstrategies for the Internetrdquo Journal of Industrial Economics vol49 no 4 pp 441ndash461 2001

[9] K D Antia M Bergen and S Dutta ldquoCompeting with graymarketsrdquoMIT SloanManagement Review vol 46 no 1 pp 63ndash69 2004

[10] J Shin ldquoHow does free riding on customer service affectcompetitionrdquo Marketing Science vol 26 no 4 pp 488ndash5032007

[11] G Iyer and J M Villas-Boas ldquoA bargaining theory of distribu-tion channelsrdquo Journal of Marketing Research vol 40 no 1 pp80ndash100 2003

[12] A Dukes and Y Liu ldquoIn-store media and distribution channelcoordinationrdquoMarketing Science vol 29 no 1 pp 94ndash107 2010

[13] H Ahn I Duenyas and R Zhang ldquoPrice competition betweenretailers and manufacturer-owned storesrdquoWorking Paper Uni-versity of California at Berkeley 2002

[14] K Cattani W Gilland H S Heese and J SwaminathanldquoBoiling frogs pricing strategies for a manufacturer addinga direct channel that competes with the traditional channelrdquoProduction and Operations Management vol 15 no 1 pp 40ndash56 2006

[15] K-Y Chen M Kaya and O Ozer ldquoDual sales channel man-agement with service competitionrdquo Manufacturing and ServiceOperations Management vol 10 no 4 pp 654ndash675 2008

[16] G Hua S Wang and T C E Cheng ldquoPrice and lead timedecisions in dual-channel supply chainsrdquo European Journal ofOperational Research vol 205 no 1 pp 113ndash126 2010

[17] W S Yoo andE Lee ldquoInternet channel entry a strategic analysisof mixed channel structuresrdquo Marketing Science vol 30 no 1pp 29ndash41 2011

[18] Y Xiong W Yan K Fernandes Z-K Xiong and N GuoldquoldquoBricks vs clicksrdquo the impact of manufacturer encroachmentwith a dealer leasing and selling of durable goodsrdquo EuropeanJournal of Operational Research vol 217 no 1 pp 75ndash83 2012

[19] Q Lu and N Liu ldquoPricing games of mixed conventional ande-commerce distribution channelsrdquo Computers and IndustrialEngineering vol 64 no 1 pp 122ndash132 2013

[20] Q Xu Z Liu and B Shen ldquoThe impact of price comparisonservice on pricing strategy in a dual-channel supply chainrdquoMathematical Problems in Engineering vol 2013 Article ID613528 13 pages 2013

[21] C A Ingene and M E Parry ldquoChannel coordination whenretailers competerdquoMarketing Science vol 14 no 4 pp 360ndash3771995

[22] 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

[23] J Raju and Z J Zhang ldquoChannel coordination in the presenceof a dominant retailerrdquoMarketing Science vol 24 no 2 pp 254ndash262 2005

[24] K L Webb and C J Lambe ldquoInternal multi-channel conflictan exploratory investigation and conceptual frameworkrdquo Indus-trial Marketing Management vol 36 no 1 pp 29ndash43 2007

[25] S K Mukhopadhyay D-Q Yao and X Yue ldquoInformationsharing of value-adding retailer in a mixed channel hi-techsupply chainrdquo Journal of Business Research vol 61 no 9 pp950ndash958 2008

[26] R Yan ldquoManaging channel coordination in a multi-channelmanufacturer-retailer supply chainrdquo Industrial Marketing Man-agement vol 40 no 4 pp 636ndash642 2011

[27] E Cao YMa CWan andM Lai ldquoContracting with asymmet-ric cost information in a dual-channel supply chainrdquoOperationsResearch Letters vol 41 no 4 pp 410ndash414 2013

[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] Y Liu S Gupta and Z J Zhang ldquoNote on self-restraint as anonline entry-deterrence strategyrdquoManagement Science vol 52no 11 pp 1799ndash1809 2006

[30] Z Cheng and B R Nault ldquoInternet channel entry retailcoverage and entry cost advantagerdquo Information Technology andManagement vol 8 no 2 pp 111ndash132 2007

[31] X Zhang ldquoRetailersrsquo multichannel and price advertising strate-giesrdquoMarketing Science vol 28 no 6 pp 1080ndash1094 2009

[32] W Huang and J M Swaminathan ldquoIntroduction of a secondchannel implications for pricing and profitsrdquo European Journalof Operational Research vol 194 no 1 pp 258ndash279 2009

[33] H Hotelling ldquoStability in competitionrdquo The Economic Journalvol 39 no 153 pp 41ndash57 1929

[34] J Zhang ldquoThe perils of behavior-based personalizationrdquo Mar-keting Science vol 30 no 1 pp 170ndash186 2011

[35] T Kabiraj and C Lee ldquoLicensing contracts in hotelling struc-turerdquoTheoretical Economics Letters vol 1 no 3 pp 57ndash62 2011

[36] HWang andTNariu ldquoDistribution channelmanagement in aninternet age equilibrium and social welfarerdquo Journal of IndustryCompetition and Trade vol 12 no 3 pp 285ndash298 2012

[37] M Lijesen ldquoHotellingrsquos webshoprdquo Journal of Economics vol 109no 2 pp 193ndash200 2013

[38] R Gulati and J Garino ldquoGet the right mix of bricks amp clicksrdquoHarvard Business Review vol 78 no 3 pp 107ndash214 2000

[39] K-J Chung S-D Lin and H M Srivastava ldquoThe completesolution procedures for the mathematical analysis of somefamilies of optimal inventorymodels with order-size dependenttrade credit and deterministic and constant demandrdquo AppliedMathematics and Computation vol 219 no 1 pp 142ndash157 2012

[40] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels under conditional trade credit in a supply chain systemrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 24 pp10036ndash10052 2013

[41] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels for deteriorating items in the discounted cash-flowsapproach under conditional trade credit and cash discount ina supply chain systemrdquo Applied Mathematics and InformationSciences vol 8 no 5 pp 2103ndash2111 2014

[42] J Luo and Q Zhang ldquoTrade credit a new mechanism tocoordinate supply chainrdquo Operations Research Letters vol 40no 5 pp 378ndash384 2012

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Mathematical Problems in Engineering

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Mathematical Problems in Engineering 3

R

PS

M

(a) T-channel

M

R

PS RIS

(b) RD-channel

M

R

PS MIS

(c) MD-channel

M

R

PS RIS MIS

(d) M-channel

Figure 1 The supply chain configuration of scenarios T- RD- MD- and M-channels

our study we note that the dominant retailerrsquos bargainingpower plays a critical role in influencing equilibrium pricesand profits in the distribution system as well as the strategicconditions for the manufacturer and dominant retailer toopen an Internet store

3 Model Fundamentals

Consider a two-echelon supply chain consisting of onemanufacturer denoted by M (referred to as ldquosherdquo) and onedominant retailer with a physical store in a monopolist mar-ket denoted by R (referred to as ldquoherdquo) who sells the productsof the manufacturer to the consumers With the prevailingpopularity of consumers purchasing products online theyhave to redesign their distribution channel structures Basedon marketing cases about the manufacturerrsquos direct channelstrategy and the dominant retailerrsquos multichannel retailingactivities we assume that each of them is able to commitwhether to open an Internet store is faced with differentsetup costs Since the manufacturer and dominant retailermay open the Internet stores successfully or not there are 4possible channel structures

Case (A) Both of them do not open their Internet storesdenoted by T-channel

Case (B) The manufacturer does not open an Internet storebut dominant retailer opens an Internet store denoted by RD-channel

Case (C) The manufacturer opens an Internet store butdominant retailer does not and is denoted by MD-channel

Case (D) Both of them open their Internet stores simultane-ously denoted by M-channel

Figure 1 depicts 4 possible cases For convenience letPS denotes the dominant retailerrsquos physical store MISthe manufacturer-owned Internet store RIS the dominantretailer-owned Internet store

Parameters and decision variablesrsquo notations used in thepaper are listed in Abbreviations section

Before establishing themodels we give some assumptionsrelated to this study as follows

Assumption 1 The manufacturer produces the product at aconstant unit (marginal) cost which is normalized to zero andsells product to the dominant retailer with a wholesale price119908

j= (1 minus 120573)119901

j119903in the j-channel which is derived by means of

the bargaining process where 119901j119903is the retail price charged by

the dominant retailer in the j-channel and the value of 120573 isin

(0 1) denotes his bargaining power The wholesale price thatis determined in the supply chain by a negotiation process issimilar to the previous researches such as [11 12]

Assumption 2 The dominant retailer acts as a Stackelbergprice leader in the distribution channel and his physicalstore has located at the left end point of a Hotelling linearcity bounded between zero and one as seen in the previousliterature [29 33ndash37] Without loss of generality we assumethat the size of the market is one and consumers areuniformly distributed over the line of the city with a unittravel cost (119905 gt 0) for traveling to the dominant retailerrsquosphysical store to shop and each consumer buys at most oneunit of the product

Assumption 3 The dominant retailer sets the same priceacross his physical store and Internet store In marketingpractice some dominant retailers such as Circuit CityTiffany Gap and Staples fully integrate their offline andonline operations which can make consumer not figure outwhether it is cheaper to purchase from its physical storesand Internet stores In fact this assumption is similar to[29 31 38]

Assumption 4 The value of consumers willing to pay for theproduct is sufficiently large (119881 gt 119905) so as to ensure thefull market coverage Otherwise the dominant retailer neveropens a physical store to serve consumers

Assumption 5 If a consumer chooses to purchase the productfrom the Internet stores (MIS or RIS) the purchasing incursa unit disutility (120575 gt 0) To ensure that at least one of themanufacturers and the dominant retailer has an incentive to

4 Mathematical Problems in Engineering

Table 1

Mrsquos wholesale price MISrsquos price PSRISrsquos price Mrsquos profit Rrsquos profitT-channel (1 minus 120573)(119881 minus 119905) NA 119881 minus 119905 (1 minus 120573)(119881 minus 119905) 120573(119881 minus 119905)

RD-channel (1 minus 120573)(119881 minus 120575) NA 119881 minus 120575 (1 minus 120573)(119881 minus 120575) 120573(119881 minus 120575) minus 119865119903

MD-channel(1 minus 120573)(119905 + 120575)

2120573

(2 + 120573)119905 + (2 minus 3120573)120575

4120573

119905 + 120575

2120573

119905 + 120575

2120573

+

(119905 minus 120575)2

minus 12119905120575

16119905

minus 119865119898

(119905 + 120575)2

8119905

Table 2

Mrsquos wholesale price MISrsquos price PSRISrsquos price Mrsquos profit Rrsquos profit

120575 lt

119905

3

(1 minus 120573)(119905 minus 120575)

120573

119905 minus 120575

120573

119905 minus 120575

120573

119905 minus 120575

120573

minus

(119905 minus 120575)120575

119905

minus 119865119898

(119905 minus 120575)120575

119905

minus 119865119903

120575 gt

119905

3

(1 minus 120573)(119905 + 120575)

2120573

(2 + 120573)119905 + (2 minus 3120573)120575

4120573

119905 + 120575

2120573

119905 + 120575

2120573

+

(119905 minus 120575)2

minus 12119905120575

16119905

minus 119865119898

(119905 + 120575)2

8119905

minus 119865119903

open an Internet store let 120575 lt 119905 in our study which is similarto previous studies [3 14 17]

Consumersrsquo disutility 120575 capturing various factors makesonline shopping inconvenient such as quality uncertainty(eg the inability to touch and feel) discomfort with onlinesecurity waiting time until delivery and shipping charge

Based on the above assumptions it is clear that for aconsumer located at 119909 isin [0 1] he will get utilities 119880PS =

119881minus119901119903minus 119905119909 when purchasing the product from the dominant

retailerrsquos physical store and 119880MIS = 119881 minus 119901119898minus 120575 when

purchasing the product from the manufacturerrsquos Internetstore and 119880RIS = 119881 minus 119901

119903minus 120575 when purchasing the product

from the dominant retailerrsquos Internet store

4 Equilibrium Outcomes and StrategicConditions for Opening an Internet Store

In this section we first present the equilibrium outcomesamong the different channel structures and then discussthe strategic conditions for the manufacturer and dominantretailer to open their Internet stores The equilibrium out-comes are given by the following Lemmas 6 and 7 and theproofs are provided in Appendix A

41 Equilibrium Outcomes

Lemma 6 In the T-channel MD-channel and RD-channelthe equilibrium prices and profits for the manufacturer anddominant retailer can be summarized as shown in Table 1

Lemma7 In theM-channel the equilibriumprices and profitsfor manufacturer and dominant retailer can be summarized asshown in Table 2

From Lemmas 6 and 7 we observe that no matter themanufacturer and dominant retailer open an Internet storewill affect the supply chain structure and equilibrium pricesand profits in different ways Let T-channel be a benchmarkwe note that the dominant retailer should lower retail priceonly when his Internet store in the market and when thesetup cost of opening an Internet store 119865

119903lt 120573(119905 minus 120575) then

he can get more profit than that of not opening an Internetstore In addition we find that when the manufacturer anddominant retailer open their Internet stores simultaneouslyif consumersrsquo disutility of purchasing a product from Internetstore is low enough (ie 120575 lt 1199053) the manufacturer can setthe retail price at her Internet store same to the dominantretailerrsquos retail price However if consumersrsquo disutility ofpurchasing a product from Internet store is relatively larger(ie 120575 gt 1199053) the equilibrium prices are same to the caseof the manufacturer only open an Internet store that isMD-channel Furthermore the manufacturerrsquos profit doesnot change but the dominant retailerrsquos profit decreasesTherefore we will discuss the strategic conditions for themanufacturer and dominant retailer to open an Internetstore according to the equilibrium profits among the differentchannel structures

42 Strategic Conditions for Opening an Internet Store Nowas one of the critical problems to obtain the strategic con-ditions for the manufacturer and dominant retailer to openan Internet store we compare the equilibrium profits in RD-channel MD-channel and M-channel to the equilibriumprofits in T-channel and compare the equilibrium profitsin M-channel to the equilibrium profits in RD-channeland MD-channel respectively The following propositionsand corollaries summarize the strategic conditions and itsimplications The proofs are given in Appendix B

Proposition 8 Suppose that themanufacturer has not openedan Internet store when the setup cost of opening an Internetstore by the dominant retailer 119865

119903lt 120573(119905 minus 120575) he can begin to

open an Internet store

Proposition 8 implies that under the condition of themanufacturer has not opened an Internet store onlywhen thesetup cost of opening an Internet store is relatively small thedominant retailer will getmore profit than that of not openingan Internet store Otherwise his profit will decrease due tocostly setup cost

Obviously an immediate consequence of above proposi-tions is the following corollary

Mathematical Problems in Engineering 5

Corollary 9 If the manufacturer has not opened an Internetstore the dominant retailerrsquos strategic motive for opening anInternet store would be weakened by increasing consumersrsquodisutility of purchasing a product from Internet store

Proposition 10 Suppose that the dominant retailer has notopened an Internet store when the setup cost of opening anInternet store by the manufacturer 119865

119898lt (119905 + 120575)2120573 + [(119905 minus

120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905) she can begin to open anInternet store

Proposition 10 implies that under the condition of thedominant retailer has not opened an Internet store onlywhenthe setup cost of opening an Internet store is relatively smallthemanufacturer will getmore profit than that of not openingan Internet store Otherwise her profit will decrease due tocostly setup cost

Based on Proposition 10 we have the following corollary

Corollary 11 If the dominant retailer has not opened anInternet store and his bargaining power is relatively small (ie120573 lt 4119905(7119905 minus 120575)) the manufacturerrsquos strategic motive foropening an Internet store would be strengthened by increasingconsumersrsquo disutility of purchasing a product from Internetstore Otherwise her strategic motive would be weakened

Proposition 12 There are two choices for the manufacturerand dominant retailer to open their Internet stores simultane-ously which are summarized as follows

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) and the setupcosts of opening an Internet store by the manufacturerand dominant retailer meet 119865

119898lt (119905 minus 120575)120573 minus (119905 minus

120575)120575119905 minus (1 minus 120573)(119881 minus 119905) and 119865119903lt (119905 minus 120575)120575119905 minus 120573(119881 minus 119905)

respectively both of them can open their own Internetstores simultaneously

(2) If consumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) andthe setup costs of opening an Internet store by themanufacturer and dominant retailer meet 119865

119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905) and119865119903lt (119905 + 120575)

2

8119905 minus 120573(119881 minus 119905) respectively both of themcan open their own Internet stores simultaneously

Proposition 12 implies that consumersrsquo disutility of pur-chasing a product from Internet store plays an importantrole for opening Internet stores simultaneously by the man-ufacturer and dominant retailer And only when the setupcosts of opening Internet stores by them are relatively smallrespectively then both will get more profit than that of notopening Internet stores Otherwise their profits will decreasedue to costly setup costs

It should be noted that the upper bounds of 119865119898and 119865119903are

related to 120575 for a given 120573 in Proposition 12 so we have thefollowing corollary

Corollary 13 If both the manufacturer and dominant retailerhave not operated their Internet stores then

(1) when consumersrsquo disutility of purchasing a productfrom Internet store is low enough (ie 120575 lt 1199053) themanufacturerrsquos strategic motive for opening an Internetstore would be weakened by increasing consumersrsquodisutility of purchasing a product from Internet storebut the dominant retailerrsquos strategic motive for openingan Internet store would be strengthened

(2) when consumersrsquo disutility of purchasing a productfrom Internet store is relatively larger (ie 120575 gt 1199053)the dominant retailerrsquos strategic motive for opening anInternet store would be strengthened by increasing con-sumersrsquo disutility of purchasing a product from Internetstore For the manufacturer only if the dominantretailerrsquos bargaining power is relatively small (ie 120573 lt

4119905(7119905minus120575)) her strategicmotive for opening an Internetstore would be strengthened by increasing consumersrsquodisutility of purchasing a product from Internet storeOtherwise her strategic motive would be weakened

Proposition 14 Suppose that the dominant retailer has oper-ated an Internet store themanufacturer has two choices to openan Internet store which are summarized as follows

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) and the setupcost of opening an Internet store by the manufacturer119865119898lt (119905 minus 120575)120573 minus (119905 minus 120575)120575119905 minus (1 minus 120573)(119881 minus 120575) she can

also open an Internet store(2) If consumersrsquo disutility of purchasing a product from

Internet store is relatively larger (ie 120575 gt 1199053) andthe setup cost of opening an Internet store by themanufacturer 119865

119898lt (119905+120575)2120573+[(119905minus120575)

2

minus12119905120575]16119905minus

(1 minus 120573)(119881 minus 120575) she can also open an Internet store

Proposition 14 implies that under the condition of thedominant retailer has operated an Internet store consumersrsquodisutility of purchasing a product from Internet store alsoplays an important role in opening an Internet store by themanufacturer And only when the setup cost of opening anInternet store is relatively small then the manufacturer willget more profit than that of not opening an Internet storeOtherwise her profit will decrease due to costly set-up cost

Based on Proposition 14 we have the following corollary

Corollary 15 If the dominant retailer has operated an Internetstore then

(1) when consumersrsquo disutility of purchasing a productfrom Internet store is low enough (ie 120575 lt 1199053) themanufacturerrsquos strategic motive for opening an Internetstore would be weakened by increasing consumersrsquodisutility of purchasing a product from Internet store

(2) when consumersrsquo disutility of purchasing a productfrom Internet store is relatively larger (ie 120575 gt 1199053) andonly if the dominant retailerrsquos bargaining power is rela-tively small (ie 120573 lt [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905)the manufacturerrsquos strategic motive for opening anInternet store would be strengthened by increasing

6 Mathematical Problems in Engineering

consumersrsquo disutility of purchasing a product fromInternet store Otherwise her strategic motive would beweakened

Proposition 16 Suppose that the manufacturer has operatedan Internet store the best choice for dominant retailer is not toopen an Internet store

Proposition 16 implies that under the condition of themanufacturer has operated an Internet store regardless ofconsumersrsquo disutility of purchasing a product from Internetstore is small or larger it is best for the dominant retailer notto open an Internet store Otherwise his profit will decreasedue to costly setup cost or the manufacturerrsquos low pricestrategy that attract more consumers to buy the product fromher Internet store

Proposition 17 Suppose that the manufacturer has notopened an Internet store if consumersrsquo disutility of purchasinga product from Internet store is low enough (ie 120575 lt 1199053) andthe setup cost of opening an Internet store for the manufactureris intermediate 119865

119898isin [(119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 (119905 minus

120575)120573 minus (119905 minus 120575)120575119905] the dominant retailer opening an Internetstore can lead to the well-known contagion-like effect

Proposition 17 implies that under the condition of themanufacturer has not opened an Internet store when con-sumersrsquo disutility of purchasing a product from Internet storeis relatively small and the set-up cost of opening an Internetstore for the manufacturer is intermediate the dominantretailerrsquos Internet store entry may induce the manufacturerto open her own Internet store competing with him

FromProposition 17 we observe that the upper and lowerbounds of 119865

119898are related to 120575 for a given 120573 so we have the

following corollary

Corollary 18 When consumersrsquo disutility of purchasing aproduct from Internet store is low enough (ie 120575 lt 1199053) ifthe dominant retailerrsquos bargaining power is relatively small (ie120573 lt 4119905(7119905minus120575)) the contagion-like effect would be expanded byincreasing consumersrsquo disutility of purchasing a product fromInternet store However if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 gt 4119905(7119905 minus 120575)) the contagion-like effect would be diminished

Based on aforementioned propositions we now showwhen do the manufacturer and dominant retailer open theirown Internet stores to a traditional supply chain and how dothey set prices after opening Internet stores in Table 3

5 Analytical Results onBoth Playersrsquo Pricing Policies

From Lemmas 6 and 7 we know that the T-channel andRD-channel are monopoly settings So the dominant retailercharges the optimal monopoly price and sells the productto all consumers However under the MD-channel and M-channel the manufacturer and dominant retailer engage in

price competition To investigate the impacts of the dom-inant retailerrsquos bargaining power and consumersrsquo disutilityof purchasing a product from Internet store on the manu-facturer and dominant retailerrsquos pricing strategies we obtainthe following propositions and the proofs are provided inAppendix C

Proposition 19 Suppose that only the manufacturer can openan Internet store then

(1) 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0(2) 120597119901MD

119903120597120575 = 12120573 gt 0 and 120597119901MD

119898120597120575 = (2 minus 3120573)4120573

and if 120573 isin (0 23) then 120597119901MD119898

120597120575 gt 0 if 120573 isin (23 1)then 120597119901MD

119898120597120575 lt 0

(3) if 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

if 120575 = 1199053 then 119901MD119898

=

119901MD119903

and if 120575 gt 1199053 then 119901MD119898

lt 119901MD119903

Proposition 19 indicates that when the manufacturer canopen an Internet store

(1) she should also lower the price to induce consumersto purchase the product from her Internet store asthe increasing dominant retailerrsquos bargaining powerotherwise the dominant retailer will also provideprice incentives for consumers to buy the productfrom his physical store

(2) if the dominant retailerrsquos bargaining power is rela-tively small (ie 120573 lt 23) she should raise the pricein her Internet store with increasing consumersrsquo disu-tility However if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 gt 23) she should cutdown the price in her Internet store with increasingconsumersrsquo disutility

(3) if consumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) shemust provide strong price incentives for consumersto purchase the product from her Internet storeotherwise her profits will cut down owing to someconsumers buying the product from the dominantretailerrsquos physical store on the contrary the domi-nant retailer will provide strong price incentives forconsumers to purchase the product from his physicalstore when consumersrsquo disutility of purchasing aproduct from Internet store is low enough (ie 120575 lt

1199053) then the manufacturerrsquos retail price is higherthan the dominant retailerrsquos If and only if consumersrsquodisutility of purchasing a product from Internet storesatisfies 120575 = 1199053 the manufacturer can set her retailprice to be equal to the dominant retailerrsquos

Proposition 20 Suppose that both the manufacturer anddominant retailer can open their Internet stores simultaneouslythen

(1) If 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0120597119901

M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0

(2) If 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 120597119901M119898120597120575 = (2 minus 3120573)4120573 120597119901M

119903120597120575 = 12120573 gt 0 and

Mathematical Problems in Engineering 7

Table 3 Strategic conditions for opening Internet stores to T-channel and pricing policies

Strategic conditions M and Rrsquos activities Pricing policiesM has not opened an Internet store and119865119903lt 120573(119905 minus 120575)

R can open an Internet store Monopoly pricing

R has not opened an Internet store and119865119898lt (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905)

M can open an Internet store

When 120575 lt 1199053then 119901MD

119898gt 119901

MD119903

When 120575 = 1199053then 119901MD

119898= 119901

MD119903

When 120575 gt 1199053then 119901MD

119898lt 119901

MD119903

When 120575 lt 1199053 119865119903lt (119905 minus 120575)120575119905 minus 120573(119881 minus 119905) and

119865119898lt (119905 minus 120575)120573 minus (119905 minus 120575)120575119905 minus (1 minus 120573)(119881 minus 119905)

Both M and R can open their Internet stores simultaneously119901M119898= 119901

M119903

When 120575 gt 1199053 119865119903lt (119905 + 120575)

2

8119905 minus 120573(119881 minus 119905) and119865119898lt (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905)

119901M119898lt 119901

M119903

when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0 but when 120573 isin

(23 1) then 120597119901M119898120597120575 lt 0

(3) If 120575 le 3119905 then 119901M119898= 119901

M119903 if 120575 gt 1199053 then 119901M

119898lt 119901

M119903

Proposition 20 indicates when both the manufacturerand dominant retailer can open their Internet stores simul-taneously

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) bothof them can set same price and lower prices as theincreasing consumersrsquo disutility On the contrary ifconsumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) themanufacturer must provide lower price incentivesthan the dominant retailer which may induce con-sumers to purchase the product from her Internetstore It should be pointed out that when the dom-inant retailerrsquos bargaining power is relatively small(ie 120573 lt 23) the manufacturerrsquos price increaseswith increasing consumersrsquo disutility but when thedominant retailerrsquos bargaining power is relativelylarger (ie 120573 gt 23) the manufacturerrsquos retail pricedecreases with increasing consumersrsquo disutility

(2) When consumersrsquo disutility of purchasing a prod-uct from Internet store is low enough (ie 120575 lt

1199053) the dominant retailerrsquos price decreases reducewith increasing consumersrsquo disutility but when con-sumersrsquo disutility of purchasing a product from Inter-net store is relatively larger (ie 120575 gt 1199053) thedominant retailerrsquos price decreases with increasingconsumersrsquo disutility Speaking frankly that is thedominant retailerrsquos smart pricing strategiesThe dom-inant retailer will raise the retail price when mostof consumers with a large disutility of purchasing aproduct from Internet store buy the product from hisphysical store and lower the retail price when mostof consumers with a small disutility of purchasing aproduct from Internet store buy the product from themanufacturerrsquos Internet store

Proposition 21 Given that the dominant retailerrsquos bargainingpower we obtain the following results about the manufacturerrsquoswholesale price under RD-channel MD-channel and M-channel

(1) 120597119908RD120597120575 = minus(1 minus 120573) lt 0

(2) 120597119908MD120597120575 = (1 minus 120573)2120573 gt 0

(3) if 120575 lt 1199053 then 120597119908M120597120575 = minus(1 minus 120573)120573 lt 0 if 120575 gt 1199053

then 120597119908M120597120575 = (1 minus 120573)2120573 gt 0

Proposition 21 indicates that the manufacturer should setthe wholesale prices differentially across the RD-channelMD-channel andM-channel and raise or lower thewholesaleprices in the light of consumersrsquo disutility of buying theproduct from Internet store More specifically the man-ufacturer can lower the wholesale price with increasingconsumersrsquo disutility of buying the product from Internetstore in the RD-channel but in theMD-channel she can raisethe wholesale price with increasing consumersrsquo disutility ofbuying from Internet store However in theM-channel whenthe consumersrsquo disutility of buying from Internet store is lowenough (ie 120575 lt 1199053) she can lower the wholesale pricewith increasing consumersrsquo disutility but when consumersrsquodisutility of buying from Internet store is relatively larger (ie120575 gt 1199053) she should raise the wholesale price with increasingconsumersrsquo disutility

Proposition 22 Given that the dominant retailerrsquos bargainingpower we obtain the following results about the manufacturerrsquosretail price at her Internet store under MD-channel and M-channel

(1) If 120575 lt 1199053 when 120573 isin (0 23) then 120597119901MD119898

120597120575 =

(2 minus 3120573)4120573 gt 0 120597119901M119898120597120575 = minus1120573 lt 0 but when 120573 isin

(23 1) then 120597119901MD119898

120597120575 = (2 minus 3120573)4120573 lt 0 120597119901M119898120597120575 =

minus1120573 lt 0(2) If 120575 gt 1199053 when 120573 isin (0 23) then 120597119901

MD119898

120597120575 =

120597119901M119898120597120575 gt 0 but when 120573 isin (23 1) then 120597119901MD

119898120597120575 =

120597119901M119898120597120575 lt 0

Proposition 22 indicates that themanufacturer should setthe retail prices at her Internet store differentially across the

8 Mathematical Problems in Engineering

MD-channel and M-channel and raise or lower the prices inthe light of consumersrsquo disutility of buying the product fromInternet store More specifically if the consumersrsquo disutilityof buying from Internet store is low enough (ie 120575 lt 1199053)the manufacturer can raise the retail price at her Internetstore with increasing consumersrsquo disutility of buying fromInternet store when the dominant retailerrsquos bargaining poweris relatively small (ie 120573 lt 23) and the dominant retailerdoes not open Internet store However if the dominantretailer also opens an Internet store the manufacturer shouldlower the retail price at her Internet store so as to attractconsumers to buy the product from her Internet store On thecontrary if the consumersrsquo disutility of buying from Internetstore is relatively larger (ie 120575 gt 1199053) and the dominantretailer also opens an Internet store then the manufacturershould set the same price with the dominant retailerrsquos andadjust the price following the dominant retailer

Proposition 23 Given that the dominant retailerrsquos bargainingpower we obtain the following results about dominant retailerrsquosretail price under RD-channel MD-channel and M-channel

(1) If 120575 lt 1199053 then 120597119901RD119903120597120575 = minus1 lt 0 120597119901MD

119903120597120575 = 12120573 gt

0 and 120597119901M119903120597120575 = minus1120573 lt 0

(2) If 120575 gt 1199053 then 120597119901RD119903120597120575 = minus1 lt 0 120597119901

MD119903

120597120575 =

12120573 gt 0 and 120597119901M119903120597120575 = 12120573 gt 0

Proposition 23 indicates that no matter when the con-sumersrsquo disutility of buying from Internet store is small orlarger the dominant retailer should lower the retail price withincreasing consumersrsquo disutility buying from Internet store inthe RD-channel but in the MD-channel he always raises theretail price with increasing consumersrsquo disutility Howeverin the M-channel when consumersrsquo disutility buying fromInternet store is low enough (ie 120575 lt 1199053) he should lowerthe price with increasing consumersrsquo disutility but whenconsumersrsquo disutility is relatively larger (ie 120575 gt 1199053) he canset the price same as the price in the MD-channel and raisethe price with increasing consumersrsquo disutility

6 Numerical Examples

In this section we present numerical examples to illustratethe theoretical results about impacts of consumersrsquo disutilityof buying from Internet store on the manufacturer anddominant retailerrsquos pricing policies with different bargainingpower for the dominant retailerrsquos among RD-channel MD-channel and M-channel which are summarized in Figures2ndash11 where 119881 = 14 119905 = 6 120575 isin (0 6) and 120573 = 02 120573 = 08The parametersrsquo values satisfy the assumptions in Section 3 inorder to make the models feasible and meaningful

Comparing Figure 2 with Figure 3 we can observe thatwhen the dominant retailerrsquos bargaining power is relativelysmall (ie 120573 = 02) both of them can increase prices asincreasing consumersrsquo disutility of purchasing from Internetstore in MD-channel However when the dominant retailerrsquosbargaining power is relatively larger (ie 120573 = 08) themanufacturer has no choice but to lower the retail price soas to attract consumers to buy the product from her Internet

0 1 2 3 4 5 612

14

16

18

20

22

24

26

28

30

wMD

pMDm

pMDr

120575

Figure 2 Impacts of 120575 on prices in the MD-channel when 120573 = 02

0 1 2 3 4 5 60

1

2

3

4

5

6

7

8

wMD

pMDm

pMDr

120575

Figure 3 Impacts of 120575 on prices in the MD-channel when 120573 = 08

store In addition Figures 2 and 3 show that when consumersrsquodisutility buying from Internet store is low enough (ie 120575 lt

2) the manufacturer can set her retail price to be larger thanthe dominant retailerrsquos However when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2)the manufacturer can set her retail price to be lower than thedominant retailerrsquos

Figures 4 and 5 show that when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)both the manufacturer and dominant retailer should lowerprices to increase consumersrsquo disutility buying from Internet

Mathematical Problems in Engineering 9

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

wM

pMm

pMr

Figure 4 Impacts of 120575 on prices in the M-channel when 120573 = 02

0 1 2 3 4 5 61

2

3

4

5

6

7

8

120575

wM

pMm

pMr

Figure 5 Impacts of 120575 on prices in the M-channel when 120573 = 08

store It is noted that the rate of change of manufacturerrsquosretail price with respect to consumersrsquo disutility buying fromInternet store is equal to that of dominant retailerrsquos retailprice However when consumersrsquo disutility buying fromInternet store is relatively larger (ie 120575 gt 2) if the dominantretailerrsquos bargaining power is relatively small (ie 120573 =

02) the manufacturer can raise retail price following thedominant retailer as increasing consumersrsquo disutility buyingfrom Internet store if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 = 08) the manufacturershould cut down the retail price in her Internet store withincreasing consumersrsquo disutility

0 1 2 3 4 5 66

8

10

12

14

16

18

20

22

24

wMD

wRD

wM

120575

Figure 6 The wholesale prices in different channels when 120573 = 02

0 1 2 3 4 5 605

1

15

2

25

3

120575

wMD

wRD

wM

Figure 7 The wholesale prices in different channels when 120573 = 08

Figures 6 and 7 show that no matter whether thedominant retailerrsquos bargaining power is small or large themanufacturer can raise the wholesale price with increasingconsumersrsquo disutility buying from Internet store in the MD-channel but in the RD-channel the manufacturer shouldlower the wholesale price with increasing consumersrsquo disutil-ity However in the M-channel when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower the wholesale price withincreasing consumersrsquo disutility when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2) themanufacturer can raise the wholesale price with increasing

10 Mathematical Problems in Engineering

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

pMDm

pMm

Figure 8 Manufacturerrsquos retail prices in different channels when120573 = 02

0 1 2 3 4 5 645

5

55

6

65

7

75

120575

pMDm

pMm

Figure 9 Manufacturerrsquos retail prices in different channels when120573 = 08

consumersrsquo disutility and set the wholesale price the same asin the MD-channel

Figures 8 and 9 show that when the dominant retailerrsquosbargaining power is relatively small (ie 120573 = 02) inthe MD-channel the manufacturer can raise retail pricewith increasing consumersrsquo disutility buying from Internetstore but when the dominant retailerrsquos bargaining power isrelatively larger (ie 120573 = 08) the manufacturer should lowerretail price with increasing consumersrsquo disutility Howeverin the M-channel no matter whether the dominant retailerrsquosbargaining power is small or large when consumersrsquo disutility

0 1 2 3 4 5 65

10

15

20

25

30

120575

pRDr

pMDr

pMr

Figure 10 Dominant retailerrsquos prices in different channels when120573 =02

buying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower retail price with increasingconsumersrsquo disutility but when consumersrsquo disutility buyingfrom Internet store is relatively larger (ie 120575 gt 2) if thedominant retailerrsquos bargaining power is relatively small (ie120573 = 02) the manufacturer can raise retail price withincreasing consumersrsquo disutility buying from Internet storeif the dominant retailerrsquos bargaining power is relatively larger(ie 120573 = 08) themanufacturer should lower retail price withincreasing consumersrsquo disutility

Figures 10 and 11 show that no matter whether thedominant retailerrsquos bargaining power is small or larger healways lowers the retail price with increasing consumersrsquodisutility buying from Internet store in the RD-channel butin the MD-channel he always raises the retail price withincreasing consumersrsquo disutility However in the M-channelwhen consumersrsquo disutility buying from Internet store islow enough (ie 120575 lt 2) the dominant retailer shouldlower retail price with increasing consumersrsquo disutility butwhen consumersrsquo disutility is relatively larger (ie 120575 gt 2)the dominant retailer can raise retail price with increasingconsumersrsquo disutility buying from Internet store

7 Conclusions and Future Research

To investigate when the manufacturer and dominant retaileropen their own Internet stores with different setup costsand how set prices to ensure opening Internet stores areprofitable in a supply chain we first present the equilibriumoutcomes under four possible supply chain structures andthen discuss the strategic conditions for the manufacturerand dominant retailer when it is optimal to open an Internetstore In addition we analyze both playersrsquo pricing policies

Mathematical Problems in Engineering 11

0 1 2 3 4 5 62

4

6

8

10

12

14

120575

pMDr

pRDr

pMr

Figure 11 Dominant retailerrsquos prices in different channels when 120573 =08

after they open their Internet stores and discuss the impactsof the dominant retailerrsquos bargaining power and consumersrsquodisutility of purchasing a product from Internet store onthe manufacturer and dominant retailerrsquos pricing strategiesFinally we conduct numerical examples to illustrate thetheoretical results

We obtain some new results differing from those inthe literature We find that the optimal choices for themanufacturer and dominant retailer to open an Internetstore are largely determined by their respective setup costswhich are closely related to the dominant retailerrsquos bargainingpower and consumersrsquo disutility of buying from Internetstore It is worth mentioning that multichannel retailing forthe dominant retailer is not necessarily the best strategyIn other words if the dominant retailer opens an Internetstore the marketing plan for him to attract more consumersby charging a lower price is impossible to achieve and hecan induce the manufacturer to open an Internet store tocompetewith himOnlywhen the setup cost for the dominantretailer to open an Internet store is sufficiently low then he isprofitable

What is more we also find that the manufacturerrsquosoptimal price at her Internet store is not always being lowerthan the dominant retailerrsquos For example if the consumersrsquodisutility of buying from Internet store is sufficiently highthe manufacturer must provide strong price incentives forconsumers to purchase the product from the Internet store

Although this research provides new insights for themanufacturer and dominant retailer to open an Internetstore and set prices in a supply chain there are severaldirections that could be extended First this study assumedthat all information is known to the manufacturer anddominant retailer in our model However information couldbe asymmetric in the supply chain since both players haveprivate information about their own internal variable costs

for example the setup cost of opening an Internet storecustomersrsquo purchase patterns and search costsTherefore wecan explore the competitive equilibrium under asymmetricinformation settings Second we assume that consumersrsquodisutility of buy from Internet store is independent of theunit transportation cost which can be relaxed in the futureresearch Third trade credit is widely used in practice andhas important impact on supply chain management [39ndash41] In recent years trade credit has become one of themajor transactions between suppliers and retailers in a valuechain For example Wal-Mart Carrefour and GOME (alarge Chinese home appliance chain retailer) even delayedpayments to their suppliers for as long as one year [42]Hence it is worthy to understand how the trade creditaffects supply channel configuration together with pricingstrategies in the E-commerce market A final issue worthyof investigation is how different types of customers affectthe manufacturer and dominant retailerrsquos channel selectionstrategies We leave these questions for future research

Appendices

A Equilibrium Outcome ofthe Four Channel Structures

Proof of Lemma 6 (1) In the T-channel both the manufac-turer and dominant retailer do not open their Internet storesThere is only the dominant retailerrsquos physical store in themarket So the dominant retailer acts as a monopolist andoptimally charges a price 119881 minus 119905 such that the market isjust covered For the manufacturer given that the dominantretailerrsquos optimal retail price the optimal wholesale price is119908

T= (1 minus 120573)(119881 minus 119905) Since the manufacturer produces

the product at a constant unit (marginal) cost which isnormalized to zero and the market is just covered that is thesize of the market is one the profit for the manufacturer isprod

T119898= (1minus120573)(119881minus119905) Accordingly the profit for the dominant

retailer isprodT119903= 120573(119881 minus 119905)

(2) In RD-channel only the dominant retailer opens anInternet store (RIS) If a consumer locates at a distance fromphysical store (PS) he will get a net utility of by purchasingthe product from PS and a net utility of by purchasing theproduct from RIS To ensure the full market coverage thedominant retailer charges the monopoly price 119881 minus 120575 acrosshis two stores and sells the product to all consumers Forthe manufacturer given the dominant retailerrsquos optimal retailprice the optimal wholesale price is 119908RD

= (1 minus 120573)(119881 minus 120575)Since the manufacturer produces the product at a constantunit (marginal) cost which is normalized to zero and 119905 thesize of the market is one the profits for the manufacturer anddominant retailer are prodRD

119898= (1 minus 120573)(119881 minus 120575) and prod

RD119903

=

120573(119881 minus 120575) respectively(3) In MD-channel the manufacturer opens an Internet

store but dominant retailer does not So consumers canhave convenient access to the product through the dominantretailerrsquos physical store (PS) at price 119901

119903or the manufacturerrsquos

Internet store (MIS) at price 119901119898 their decision about which

store to buy revolves around the comparison of their net

12 Mathematical Problems in Engineering

utility derived fromPS119880PS = 119881minus119901119903minus119905119909 and119880MIS = 119881minus119901119898minus120575by buying the product from MIS Therefore the marginalconsumers are located at 119909 = (119901

119898minus 119901119903+ 120575)119905 So the profit

functions for the manufacturer and dominant retailer can bewritten as

prod

119898

= 119908[

(119901119898minus 119901119903+ 120575)

119905

] + 119901119898[

(119901119903minus 119901119898+ 119905 minus 120575)

119905

] minus 119865119898

(A1)

prod

119903

= (119901119903minus 119908) [

(119901119898minus 119901119903+ 120575)

119905

] (A2)

Under the assumption proposed in Section 3 the dom-inant retailer is the price leader and the manufacturer isthe follower As before the game is solved backwards Inthis market we firstly need to calculate the manufacturerrsquosoptimal price given any dominant retailerrsquos price

Themanufacturerrsquos reaction function can be derived fromthe first-order condition

120597prod119898

120597119901119898

=

[(2 minus 120573) 119901119903minus 2119901119898+ 119905 minus 120575]

119905

= 0

that is 119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A3)

Substituting (A3) into (A2) we get

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

(A4)

Taking the first-order derivative of (A4) with respect to119901119903and letting the derivative be zero we have

119901MD119903

=

(119905 + 120575)

2120573

(A5)

Given the wholesale price bargaining process we canobtain the manufacturerrsquos optimal wholesale price 119908MD

=

(1 minus 120573)(119905 + 120575)2120573 and substituting (A5) into (A3) we getthe manufacturerrsquos optimal retail price

119901MD119898

=

(2 + 120573) 119905 + (2 minus 3120573) 120575

4120573

(A6)

Substituting (A5) and (A6) into (A1) and (A2) wecan obtain the equilibrium profits for the manufacturers anddominant retailer respectively

MDprod

119898

=

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus 119865119898

MDprod

119903

=

(119905 + 120575)2

8119905

(A7)

Proof of Lemma 7 In the M-channel both the manufacturerand dominant retailer simultaneously open their own Inter-net stores then customers are able to purchase a product

either from the dominant retailerrsquos physical store (PS) or fromthe alternative Internet stores (MISRIS) They can get a netutility of 119880PS = 119881 minus 119901

119903minus 119905119909 by buying the product from PS

and a net utility of 119880MIS = 119881 minus 119901119898minus 120575 by buying the product

fromMIS and a net utility of119880RIS = 119881minus 119901119903minus 120575 by buying the

product from RISAccording to the basicmodel we know that the dominant

retailer firstmakes pricing decision as the price leader and themanufacturer is the follower If the dominant retailer chargesa price higher than the manufacturerrsquos price (119901

119903gt 119901119898) then

no consumer will buy the product from his Internet storeUnder this condition the dominant retailer makes no sale inhis Internet store and makes a profit of minus119865

119903 Therefore the

demand functions for the manufacturerrsquos Internet store anddominant retailerrsquos physical store are given respectively asfollows

119863MIS =(119901119903minus 119901119898+ 119905 minus 120575)

119905

(A8)

119863PS =(119901119898minus 119901119903+ 120575)

119905

(A9)

Hence the manufacturerrsquos profit function can be written as

prod

119898

=

[119908 (119901119898minus 119901119903+ 120575) + 119901

119898(119901119903minus 119901119898+ 119905 minus 120575)]

119905

minus 119865119898

(A10)

From the first-order condition we have

119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A11)

Given the condition of 119901119903gt 119901119898 this implies that 119901

119903gt (119905 minus

120575)120573 However when 119901119903le (119905 minus 120575)120573 and 119901

119903gt 119901119898 we always

have 120597prodM119898120597119901119898= [(2 minus 120573)119901

119903minus 2119901119898+ 119905 minus 120575]119905 gt 0

Therefore the manufacturer optimally sets its price at119901119898= 119901119903 and her optimal pricing schedule is as follows

119901119898=

119901119903 119901

119903le

119905 minus 120575

120572

(2 minus 120573) 119901119903+ 119905 minus 120575

2

119901119903gt

119905 minus 120575

120572

(A12)

Given the manufacturerrsquos pricing schedule the dominantretailerrsquos profit is given as follows

prod

119903

=

(119901119903minus 119908)

120575

119905

minus 119865119903 119901

119903le

119905 minus 120575

120573

(119901119903minus 119908)

119905 + 120575 minus 120573119901119903

2119905

minus 119865119903 119901119903gt

119905 minus 120575

120573

(A13)

Under the condition of 119901119903gt (119905 minus 120575)120573 the dominant

retailerrsquos profit is

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

minus 119865119903 (A14)

Taking the first-order derivative of (A14) with respect to 119901119903

and letting the derivative be zero we have 119901M119903= (119905 + 120575)2120573

Mathematical Problems in Engineering 13

Submitting it into (A11) we get the manufacturerrsquos optimalprice in her Internet store 119901M

119898= [(2 + 120573)119905 + (2 minus 3120573)120575]4120573

Hence the manufacturer and dominant retailerrsquos optimalprofits are prodM

119898= (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus 119865119898

andprodM119903= (119905 + 120575)

2

8119905 minus 119865119903 respectively

According to the previous assumption 119901119903gt (119905 minus 120575)120573

which implies that (119905 + 120575)2120573 gt (119905 minus 120575)120573 120575must satisfy 120575 gt1199053 However when 120575 lt 1199053 we always have

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](minus)

gt 0

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](+)

lt 0 (A15)

So the dominant retailerrsquos optimal retail price in the M-channel is 119901M

119903= (119905 minus 120575)120573 Therefore the manufacturer and

dominant retailerrsquos optimal profits areprodM119898= (119905 minus 120575)120573 minus [(119905 minus

120575)120575]119905 minus 119865119898andprodM

119903= [(119905 minus 120575)120575]119905 minus 119865

119903 respectively

B Strategic Conditions forOpening an Internet Store

Proofs of Proposition 8 and Corollary 9 From Lemma 6 weanalyse the equilibrium profits for the dominant retailerbetween the T-channel and RD-channel and note that onlywhen 119865

119903lt 120573(119905 minus 120575) then prodRD

119903gt prod

T119903 This implies that as

long as the setup cost of opening an Internet store satisfies119865119903

lt 120573(119905 minus 120575) ≜ 1198611 it is always optimal to open an

Internet store for the dominant retailer In addition we notethat 120597119861

1120597120575 = minus120573 lt 0 So the dominant retailerrsquos strategic

motive for opening an Internet store would be weakened byincreasing consumersrsquo disutility of purchasing a product fromInternet store

Proofs of Proposition 10 and Corollary 11 From Lemma 6 weanalyse the equilibrium profits for the manufacturer betweenthe T-channel and MD-channel and note that only when thesetup cost of opening an Internet store satisfies 119865

119898lt (119905 +

120575)2120573+[(119905minus120575)2

minus12119905120575]16119905minus(1minus120573)(119881minus119905) ≜ 1198612 thenprodMD

119898gt

prodT119898 In addition we note that 120597119861

2120597120575 = [4119905 minus 120573(7119905 minus 120575)]8120573119905

and find when 0 lt 120573 lt 4119905(7119905 minus 120575) then 1205971198612120597120575 gt 0 and

when 4119905(7119905 minus 120575) lt 120573 lt 1 then 1205971198612120597120575 lt 0

Proofs of Proposition 12 and Corollary 13 FromLemmas 6 and7 we analyse the equilibriumprofits for themanufacturer anddominant retailer between the T-channel andM-channel wenote that under the condition of 120575 lt 1199053 only when the setupcosts of opening an Internet store for the manufacturer anddominant retailer simultaneously satisfy

119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198613

119865119903lt

[(119905 minus 120575) 120575]

119905

minus 120573 (119881 minus 119905) ≜ 1198614

(B1)

thenMprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B2)

Similarly under the condition of 120575 gt 1199053 only when thesetup costs of opening an Internet store for the manufacturerand dominant retailer simultaneously satisfy

119865119898lt

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198615

119865119903lt

(119905 + 120575)2

8119905

minus 120573 (119881 minus 119905) ≜ 1198616

(B3)

then

Mprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B4)

In addition we note that both 1205971198613120597120575 = minus[119905 + 120573(119905 minus

2120575)]120573119905 lt 0 and 1205971198614120597120575 = (119905 minus 2120575)119905 gt 0 are held under

the condition of 120575 lt 1199053 Furthermore under the conditionof 120575 gt 1199053 we also find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198615120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

5120597120575 lt 0

1205971198616120597120575 = 2(119905 + 120575)8119905 gt 0

Proofs of Proposition 14 and Corollary 15 From Lemmas 6and 7 we analyse the manufacturerrsquos equilibrium profits inthe RD-channel and M-channel we note that under thecondition of 120575 lt 1199053 only when the setup cost of opening anInternet store for her satisfies 119865

119898lt (119905 minus 120575)120573 minus [(119905 minus 120575)120575]119905 minus

(1 minus 120573)(119881 minus 120575) ≜ 1198617 thenprodM

119898gt prod

RD119898 In addition we find

1205971198617120597120575 = minus[(1 + 120573

2

)119905 minus 2120573120575]120573119905 lt 0But under the condition of 120575 gt 1199053 only when the setup

cost of opening an Internet store for her satisfies 119865119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 120575) ≜ 1198618 then

prodM119898gt prod

RD119898 In addition 120597119861

8120597120575 = [120573(119905+120575)+4119905(1minus2120573

2

)]8120573119905

we find that when 0 lt 120573 lt [(119905 + 120575) + radic(119905 + 120575)2

+ 1281199052]16119905

then 1205971198618120597120575 gt 0 andwhen [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905 lt

120573 lt 1 then 1205971198618120597120575 lt 0

Proofs of Proposition 16 From Lemmas 6 and 7 we analysethe dominant retailerrsquos equilibriumprofits in theMD-channeland M-channel and note that when 120575 lt 1199053 then prod

M119903minus

prodMD119903

= minus(119905 minus 3120575)2

8119905 minus 119865119903lt 0 and when 120575 gt 1199053

then prodM119903minus prod

MD119903

= minus119865119903lt 0 These imply that when the

manufacturer has operated an Internet store the best choicefor dominant retailer is not to open an Internet store

Proofs of Proposition 17 and Corollary 18 From Lemmas 6and 7 we analyse the dominant retailerrsquos equilibrium profitsin the MD-channel and M-channel and note that under thecondition of 120575 lt 1199053 thenprodM

119898minus prod

MD119898

= [8119905(119905 minus 3120575) minus 120573[(119905 +

120575)2

minus 161205752

]8119905]16120573119905 This implies that the manufacturer willopen her Internet store when the dominant retailer opens an

14 Mathematical Problems in Engineering

Internet store and the setup costs of opening an Internet storefor her satisfies

1198619≜

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

lt 119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

≜ 11986110

(B5)

In addition we find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198619120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

9120597120575 lt 0

and 12059711986110120597120575 = minus[119905 + 120573(119905 minus 2120575)]120573119905 lt 0

C The ManufacturerDominantRetailers Pricing Policies

Proof of Proposition 19 In the MD-channel we respectivelydifferentiate between119901MD

119898and119901MD

119903with respect to 120573 and find

that 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0 For any given120573 differentiating between 119901MD

119898and 119901MD

119903with respect to 120575 we

have 120597119901MD119903

120597120575 = 12120573 gt 0 and 120597119901MD119898

120597120575 = (2 minus 3120573)4120573and if 120573 isin (0 23) then 120597119901MD

119898120597120575 gt 0 if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 In addition we find that 119901MD119898

minus 119901MD119903

= (119905 minus

3120575)4 it is obvious that when 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

when 120575 = 1199053 then 119901MD

119898= 119901

MD119903

and when 120575 gt 1199053 then119901MD119898

lt 119901MD119903

Proof of Proposition 20 In the M-channel we respectivelydifferentiate between 119901M

119898and 119901M

119903with respect to 120573 and find

that when 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0

and when 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 For any given 120573 we respectively differentiate between 119901M119898

and 119901M119903with respect to 120575 and find that when 120575 lt 1199053 then

120597119901M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0 when 120575 gt 1199053 then

120597119901M119898120597120575 = (2 minus 3120573)4120573 and 120597119901M

119903120597120575 = 12120573 gt 0

It is easy to note that when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0

but when 120573 isin (23 1) then 120597119901M119898120597120575 lt 0

Proof of Proposition 21 From Lemmas 6 and 7 we note that120597119908

RD120597120575 = minus(1 minus 120573) lt 0 and 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0In addition if 120575 lt 1199053 then 120597119908M

120597120575 = minus(1 minus 120573)120573 lt 0 if120575 gt 1199053 then 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0

Proof of Proposition 22 From the proofs of Propositions 19and 20 we note that when 120575 lt 1199053 if 120573 isin (0 23) then120597119901

MD119898

120597120575 gt 0 120597119901M119898120597120575 lt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 120597119901M119898120597120575 lt 0 when 120575 gt 1199053 if 120573 isin (0 23)

then 120597119901MD119898

120597120575 = 120597119901M119898120597120575 gt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 = 120597119901M119898120597120575 lt 0

Proof of Proposition 23 From Lemmas 6 and 7 we note that120597119901

RD119903120597120575 = minus1 lt 0 and 120597119901MD

119903120597120575 = 12120572 gt 0 In addition if

120575 lt 1199053 then 120597119901M119903120597120575 = minus1120572 lt 0 if 120575 gt 1199053 then 120597119901M

119903120597120575 =

12120572 gt 0

Abbreviations

UK The consumerrsquos utility of purchasing theproduct from K storeK isin PSRISMIS

119881 The value of consumers willing to payfor the product

120575 The consumersrsquo disutility of purchasingthe product from Internet store(MISRIS)

119905 The per unit transportation cost ofpurchasing the product from physicalstore (PS)

120573 The dominant retailerrsquos bargainingpower in the distribution channel

119908j The manufacturerrsquos wholesale price in

the j-channel j isin TRDMDM

119901j119903 The dominant retailerrsquos price in the

j-channel j isin TRDMDM

119901j119898 The manufacturerrsquos price in the

j-channel j isin MDM

119865119898119865119903 The setup cost of opening an Internetstore by the manufacturerdominantretailer

Πj119898Πj119903 The manufacturerdominant retailerrsquosprofit in the j-channelj isin TRDMDM

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been supported by theNational Natural Sci-ence Foundation of China (71271225) Chongqingrsquos NaturalScience Foundation (cstc2012jjA1404) and the Open Fund ofChongqing Key Laboratory of Logistics (CQKLL12001)

References

[1] L Hsiao and Y-J Chen ldquoStrategic motive for introducinginternet channels in a supply chainrdquo Production and OperationsManagement vol 23 no 1 pp 36ndash47 2014

[2] I Geyskens K Gielens and M G Dekimpe ldquoThe marketvaluation of Internet channel additionsrdquo Journal of Marketingvol 66 no 2 pp 102ndash119 2002

[3] 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

[4] S-H Chun and J-C Kim ldquoPricing strategies in B2C electroniccommerce analytical and empirical approachesrdquo Decision Sup-port Systems vol 40 no 2 pp 375ndash388 2005

[5] S K Mukhopadhyay X Zhu and X Yue ldquoOptimal contractdesign for mixed channels under information asymmetryrdquoProduction and Operations Management vol 17 no 6 pp 641ndash650 2008

Mathematical Problems in Engineering 15

[6] G S Cai ldquoChannel selection and coordination in dual-channelsupply chainsrdquo Journal of Retailing vol 86 no 1 pp 22ndash36 2010

[7] K Takahashi T Aoi D Hirotani and K Morikawa ldquoInventorycontrol in a two-echelon dual-channel supply chain with setupof production and deliveryrdquo International Journal of ProductionEconomics vol 133 no 1 pp 403ndash415 2011

[8] D W Carlton and J A Chevalier ldquoFree riding and salesstrategies for the Internetrdquo Journal of Industrial Economics vol49 no 4 pp 441ndash461 2001

[9] K D Antia M Bergen and S Dutta ldquoCompeting with graymarketsrdquoMIT SloanManagement Review vol 46 no 1 pp 63ndash69 2004

[10] J Shin ldquoHow does free riding on customer service affectcompetitionrdquo Marketing Science vol 26 no 4 pp 488ndash5032007

[11] G Iyer and J M Villas-Boas ldquoA bargaining theory of distribu-tion channelsrdquo Journal of Marketing Research vol 40 no 1 pp80ndash100 2003

[12] A Dukes and Y Liu ldquoIn-store media and distribution channelcoordinationrdquoMarketing Science vol 29 no 1 pp 94ndash107 2010

[13] H Ahn I Duenyas and R Zhang ldquoPrice competition betweenretailers and manufacturer-owned storesrdquoWorking Paper Uni-versity of California at Berkeley 2002

[14] K Cattani W Gilland H S Heese and J SwaminathanldquoBoiling frogs pricing strategies for a manufacturer addinga direct channel that competes with the traditional channelrdquoProduction and Operations Management vol 15 no 1 pp 40ndash56 2006

[15] K-Y Chen M Kaya and O Ozer ldquoDual sales channel man-agement with service competitionrdquo Manufacturing and ServiceOperations Management vol 10 no 4 pp 654ndash675 2008

[16] G Hua S Wang and T C E Cheng ldquoPrice and lead timedecisions in dual-channel supply chainsrdquo European Journal ofOperational Research vol 205 no 1 pp 113ndash126 2010

[17] W S Yoo andE Lee ldquoInternet channel entry a strategic analysisof mixed channel structuresrdquo Marketing Science vol 30 no 1pp 29ndash41 2011

[18] Y Xiong W Yan K Fernandes Z-K Xiong and N GuoldquoldquoBricks vs clicksrdquo the impact of manufacturer encroachmentwith a dealer leasing and selling of durable goodsrdquo EuropeanJournal of Operational Research vol 217 no 1 pp 75ndash83 2012

[19] Q Lu and N Liu ldquoPricing games of mixed conventional ande-commerce distribution channelsrdquo Computers and IndustrialEngineering vol 64 no 1 pp 122ndash132 2013

[20] Q Xu Z Liu and B Shen ldquoThe impact of price comparisonservice on pricing strategy in a dual-channel supply chainrdquoMathematical Problems in Engineering vol 2013 Article ID613528 13 pages 2013

[21] C A Ingene and M E Parry ldquoChannel coordination whenretailers competerdquoMarketing Science vol 14 no 4 pp 360ndash3771995

[22] 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

[23] J Raju and Z J Zhang ldquoChannel coordination in the presenceof a dominant retailerrdquoMarketing Science vol 24 no 2 pp 254ndash262 2005

[24] K L Webb and C J Lambe ldquoInternal multi-channel conflictan exploratory investigation and conceptual frameworkrdquo Indus-trial Marketing Management vol 36 no 1 pp 29ndash43 2007

[25] S K Mukhopadhyay D-Q Yao and X Yue ldquoInformationsharing of value-adding retailer in a mixed channel hi-techsupply chainrdquo Journal of Business Research vol 61 no 9 pp950ndash958 2008

[26] R Yan ldquoManaging channel coordination in a multi-channelmanufacturer-retailer supply chainrdquo Industrial Marketing Man-agement vol 40 no 4 pp 636ndash642 2011

[27] E Cao YMa CWan andM Lai ldquoContracting with asymmet-ric cost information in a dual-channel supply chainrdquoOperationsResearch Letters vol 41 no 4 pp 410ndash414 2013

[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] Y Liu S Gupta and Z J Zhang ldquoNote on self-restraint as anonline entry-deterrence strategyrdquoManagement Science vol 52no 11 pp 1799ndash1809 2006

[30] Z Cheng and B R Nault ldquoInternet channel entry retailcoverage and entry cost advantagerdquo Information Technology andManagement vol 8 no 2 pp 111ndash132 2007

[31] X Zhang ldquoRetailersrsquo multichannel and price advertising strate-giesrdquoMarketing Science vol 28 no 6 pp 1080ndash1094 2009

[32] W Huang and J M Swaminathan ldquoIntroduction of a secondchannel implications for pricing and profitsrdquo European Journalof Operational Research vol 194 no 1 pp 258ndash279 2009

[33] H Hotelling ldquoStability in competitionrdquo The Economic Journalvol 39 no 153 pp 41ndash57 1929

[34] J Zhang ldquoThe perils of behavior-based personalizationrdquo Mar-keting Science vol 30 no 1 pp 170ndash186 2011

[35] T Kabiraj and C Lee ldquoLicensing contracts in hotelling struc-turerdquoTheoretical Economics Letters vol 1 no 3 pp 57ndash62 2011

[36] HWang andTNariu ldquoDistribution channelmanagement in aninternet age equilibrium and social welfarerdquo Journal of IndustryCompetition and Trade vol 12 no 3 pp 285ndash298 2012

[37] M Lijesen ldquoHotellingrsquos webshoprdquo Journal of Economics vol 109no 2 pp 193ndash200 2013

[38] R Gulati and J Garino ldquoGet the right mix of bricks amp clicksrdquoHarvard Business Review vol 78 no 3 pp 107ndash214 2000

[39] K-J Chung S-D Lin and H M Srivastava ldquoThe completesolution procedures for the mathematical analysis of somefamilies of optimal inventorymodels with order-size dependenttrade credit and deterministic and constant demandrdquo AppliedMathematics and Computation vol 219 no 1 pp 142ndash157 2012

[40] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels under conditional trade credit in a supply chain systemrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 24 pp10036ndash10052 2013

[41] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels for deteriorating items in the discounted cash-flowsapproach under conditional trade credit and cash discount ina supply chain systemrdquo Applied Mathematics and InformationSciences vol 8 no 5 pp 2103ndash2111 2014

[42] J Luo and Q Zhang ldquoTrade credit a new mechanism tocoordinate supply chainrdquo Operations Research Letters vol 40no 5 pp 378ndash384 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

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Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

Table 1

Mrsquos wholesale price MISrsquos price PSRISrsquos price Mrsquos profit Rrsquos profitT-channel (1 minus 120573)(119881 minus 119905) NA 119881 minus 119905 (1 minus 120573)(119881 minus 119905) 120573(119881 minus 119905)

RD-channel (1 minus 120573)(119881 minus 120575) NA 119881 minus 120575 (1 minus 120573)(119881 minus 120575) 120573(119881 minus 120575) minus 119865119903

MD-channel(1 minus 120573)(119905 + 120575)

2120573

(2 + 120573)119905 + (2 minus 3120573)120575

4120573

119905 + 120575

2120573

119905 + 120575

2120573

+

(119905 minus 120575)2

minus 12119905120575

16119905

minus 119865119898

(119905 + 120575)2

8119905

Table 2

Mrsquos wholesale price MISrsquos price PSRISrsquos price Mrsquos profit Rrsquos profit

120575 lt

119905

3

(1 minus 120573)(119905 minus 120575)

120573

119905 minus 120575

120573

119905 minus 120575

120573

119905 minus 120575

120573

minus

(119905 minus 120575)120575

119905

minus 119865119898

(119905 minus 120575)120575

119905

minus 119865119903

120575 gt

119905

3

(1 minus 120573)(119905 + 120575)

2120573

(2 + 120573)119905 + (2 minus 3120573)120575

4120573

119905 + 120575

2120573

119905 + 120575

2120573

+

(119905 minus 120575)2

minus 12119905120575

16119905

minus 119865119898

(119905 + 120575)2

8119905

minus 119865119903

open an Internet store let 120575 lt 119905 in our study which is similarto previous studies [3 14 17]

Consumersrsquo disutility 120575 capturing various factors makesonline shopping inconvenient such as quality uncertainty(eg the inability to touch and feel) discomfort with onlinesecurity waiting time until delivery and shipping charge

Based on the above assumptions it is clear that for aconsumer located at 119909 isin [0 1] he will get utilities 119880PS =

119881minus119901119903minus 119905119909 when purchasing the product from the dominant

retailerrsquos physical store and 119880MIS = 119881 minus 119901119898minus 120575 when

purchasing the product from the manufacturerrsquos Internetstore and 119880RIS = 119881 minus 119901

119903minus 120575 when purchasing the product

from the dominant retailerrsquos Internet store

4 Equilibrium Outcomes and StrategicConditions for Opening an Internet Store

In this section we first present the equilibrium outcomesamong the different channel structures and then discussthe strategic conditions for the manufacturer and dominantretailer to open their Internet stores The equilibrium out-comes are given by the following Lemmas 6 and 7 and theproofs are provided in Appendix A

41 Equilibrium Outcomes

Lemma 6 In the T-channel MD-channel and RD-channelthe equilibrium prices and profits for the manufacturer anddominant retailer can be summarized as shown in Table 1

Lemma7 In theM-channel the equilibriumprices and profitsfor manufacturer and dominant retailer can be summarized asshown in Table 2

From Lemmas 6 and 7 we observe that no matter themanufacturer and dominant retailer open an Internet storewill affect the supply chain structure and equilibrium pricesand profits in different ways Let T-channel be a benchmarkwe note that the dominant retailer should lower retail priceonly when his Internet store in the market and when thesetup cost of opening an Internet store 119865

119903lt 120573(119905 minus 120575) then

he can get more profit than that of not opening an Internetstore In addition we find that when the manufacturer anddominant retailer open their Internet stores simultaneouslyif consumersrsquo disutility of purchasing a product from Internetstore is low enough (ie 120575 lt 1199053) the manufacturer can setthe retail price at her Internet store same to the dominantretailerrsquos retail price However if consumersrsquo disutility ofpurchasing a product from Internet store is relatively larger(ie 120575 gt 1199053) the equilibrium prices are same to the caseof the manufacturer only open an Internet store that isMD-channel Furthermore the manufacturerrsquos profit doesnot change but the dominant retailerrsquos profit decreasesTherefore we will discuss the strategic conditions for themanufacturer and dominant retailer to open an Internetstore according to the equilibrium profits among the differentchannel structures

42 Strategic Conditions for Opening an Internet Store Nowas one of the critical problems to obtain the strategic con-ditions for the manufacturer and dominant retailer to openan Internet store we compare the equilibrium profits in RD-channel MD-channel and M-channel to the equilibriumprofits in T-channel and compare the equilibrium profitsin M-channel to the equilibrium profits in RD-channeland MD-channel respectively The following propositionsand corollaries summarize the strategic conditions and itsimplications The proofs are given in Appendix B

Proposition 8 Suppose that themanufacturer has not openedan Internet store when the setup cost of opening an Internetstore by the dominant retailer 119865

119903lt 120573(119905 minus 120575) he can begin to

open an Internet store

Proposition 8 implies that under the condition of themanufacturer has not opened an Internet store onlywhen thesetup cost of opening an Internet store is relatively small thedominant retailer will getmore profit than that of not openingan Internet store Otherwise his profit will decrease due tocostly setup cost

Obviously an immediate consequence of above proposi-tions is the following corollary

Mathematical Problems in Engineering 5

Corollary 9 If the manufacturer has not opened an Internetstore the dominant retailerrsquos strategic motive for opening anInternet store would be weakened by increasing consumersrsquodisutility of purchasing a product from Internet store

Proposition 10 Suppose that the dominant retailer has notopened an Internet store when the setup cost of opening anInternet store by the manufacturer 119865

119898lt (119905 + 120575)2120573 + [(119905 minus

120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905) she can begin to open anInternet store

Proposition 10 implies that under the condition of thedominant retailer has not opened an Internet store onlywhenthe setup cost of opening an Internet store is relatively smallthemanufacturer will getmore profit than that of not openingan Internet store Otherwise her profit will decrease due tocostly setup cost

Based on Proposition 10 we have the following corollary

Corollary 11 If the dominant retailer has not opened anInternet store and his bargaining power is relatively small (ie120573 lt 4119905(7119905 minus 120575)) the manufacturerrsquos strategic motive foropening an Internet store would be strengthened by increasingconsumersrsquo disutility of purchasing a product from Internetstore Otherwise her strategic motive would be weakened

Proposition 12 There are two choices for the manufacturerand dominant retailer to open their Internet stores simultane-ously which are summarized as follows

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) and the setupcosts of opening an Internet store by the manufacturerand dominant retailer meet 119865

119898lt (119905 minus 120575)120573 minus (119905 minus

120575)120575119905 minus (1 minus 120573)(119881 minus 119905) and 119865119903lt (119905 minus 120575)120575119905 minus 120573(119881 minus 119905)

respectively both of them can open their own Internetstores simultaneously

(2) If consumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) andthe setup costs of opening an Internet store by themanufacturer and dominant retailer meet 119865

119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905) and119865119903lt (119905 + 120575)

2

8119905 minus 120573(119881 minus 119905) respectively both of themcan open their own Internet stores simultaneously

Proposition 12 implies that consumersrsquo disutility of pur-chasing a product from Internet store plays an importantrole for opening Internet stores simultaneously by the man-ufacturer and dominant retailer And only when the setupcosts of opening Internet stores by them are relatively smallrespectively then both will get more profit than that of notopening Internet stores Otherwise their profits will decreasedue to costly setup costs

It should be noted that the upper bounds of 119865119898and 119865119903are

related to 120575 for a given 120573 in Proposition 12 so we have thefollowing corollary

Corollary 13 If both the manufacturer and dominant retailerhave not operated their Internet stores then

(1) when consumersrsquo disutility of purchasing a productfrom Internet store is low enough (ie 120575 lt 1199053) themanufacturerrsquos strategic motive for opening an Internetstore would be weakened by increasing consumersrsquodisutility of purchasing a product from Internet storebut the dominant retailerrsquos strategic motive for openingan Internet store would be strengthened

(2) when consumersrsquo disutility of purchasing a productfrom Internet store is relatively larger (ie 120575 gt 1199053)the dominant retailerrsquos strategic motive for opening anInternet store would be strengthened by increasing con-sumersrsquo disutility of purchasing a product from Internetstore For the manufacturer only if the dominantretailerrsquos bargaining power is relatively small (ie 120573 lt

4119905(7119905minus120575)) her strategicmotive for opening an Internetstore would be strengthened by increasing consumersrsquodisutility of purchasing a product from Internet storeOtherwise her strategic motive would be weakened

Proposition 14 Suppose that the dominant retailer has oper-ated an Internet store themanufacturer has two choices to openan Internet store which are summarized as follows

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) and the setupcost of opening an Internet store by the manufacturer119865119898lt (119905 minus 120575)120573 minus (119905 minus 120575)120575119905 minus (1 minus 120573)(119881 minus 120575) she can

also open an Internet store(2) If consumersrsquo disutility of purchasing a product from

Internet store is relatively larger (ie 120575 gt 1199053) andthe setup cost of opening an Internet store by themanufacturer 119865

119898lt (119905+120575)2120573+[(119905minus120575)

2

minus12119905120575]16119905minus

(1 minus 120573)(119881 minus 120575) she can also open an Internet store

Proposition 14 implies that under the condition of thedominant retailer has operated an Internet store consumersrsquodisutility of purchasing a product from Internet store alsoplays an important role in opening an Internet store by themanufacturer And only when the setup cost of opening anInternet store is relatively small then the manufacturer willget more profit than that of not opening an Internet storeOtherwise her profit will decrease due to costly set-up cost

Based on Proposition 14 we have the following corollary

Corollary 15 If the dominant retailer has operated an Internetstore then

(1) when consumersrsquo disutility of purchasing a productfrom Internet store is low enough (ie 120575 lt 1199053) themanufacturerrsquos strategic motive for opening an Internetstore would be weakened by increasing consumersrsquodisutility of purchasing a product from Internet store

(2) when consumersrsquo disutility of purchasing a productfrom Internet store is relatively larger (ie 120575 gt 1199053) andonly if the dominant retailerrsquos bargaining power is rela-tively small (ie 120573 lt [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905)the manufacturerrsquos strategic motive for opening anInternet store would be strengthened by increasing

6 Mathematical Problems in Engineering

consumersrsquo disutility of purchasing a product fromInternet store Otherwise her strategic motive would beweakened

Proposition 16 Suppose that the manufacturer has operatedan Internet store the best choice for dominant retailer is not toopen an Internet store

Proposition 16 implies that under the condition of themanufacturer has operated an Internet store regardless ofconsumersrsquo disutility of purchasing a product from Internetstore is small or larger it is best for the dominant retailer notto open an Internet store Otherwise his profit will decreasedue to costly setup cost or the manufacturerrsquos low pricestrategy that attract more consumers to buy the product fromher Internet store

Proposition 17 Suppose that the manufacturer has notopened an Internet store if consumersrsquo disutility of purchasinga product from Internet store is low enough (ie 120575 lt 1199053) andthe setup cost of opening an Internet store for the manufactureris intermediate 119865

119898isin [(119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 (119905 minus

120575)120573 minus (119905 minus 120575)120575119905] the dominant retailer opening an Internetstore can lead to the well-known contagion-like effect

Proposition 17 implies that under the condition of themanufacturer has not opened an Internet store when con-sumersrsquo disutility of purchasing a product from Internet storeis relatively small and the set-up cost of opening an Internetstore for the manufacturer is intermediate the dominantretailerrsquos Internet store entry may induce the manufacturerto open her own Internet store competing with him

FromProposition 17 we observe that the upper and lowerbounds of 119865

119898are related to 120575 for a given 120573 so we have the

following corollary

Corollary 18 When consumersrsquo disutility of purchasing aproduct from Internet store is low enough (ie 120575 lt 1199053) ifthe dominant retailerrsquos bargaining power is relatively small (ie120573 lt 4119905(7119905minus120575)) the contagion-like effect would be expanded byincreasing consumersrsquo disutility of purchasing a product fromInternet store However if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 gt 4119905(7119905 minus 120575)) the contagion-like effect would be diminished

Based on aforementioned propositions we now showwhen do the manufacturer and dominant retailer open theirown Internet stores to a traditional supply chain and how dothey set prices after opening Internet stores in Table 3

5 Analytical Results onBoth Playersrsquo Pricing Policies

From Lemmas 6 and 7 we know that the T-channel andRD-channel are monopoly settings So the dominant retailercharges the optimal monopoly price and sells the productto all consumers However under the MD-channel and M-channel the manufacturer and dominant retailer engage in

price competition To investigate the impacts of the dom-inant retailerrsquos bargaining power and consumersrsquo disutilityof purchasing a product from Internet store on the manu-facturer and dominant retailerrsquos pricing strategies we obtainthe following propositions and the proofs are provided inAppendix C

Proposition 19 Suppose that only the manufacturer can openan Internet store then

(1) 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0(2) 120597119901MD

119903120597120575 = 12120573 gt 0 and 120597119901MD

119898120597120575 = (2 minus 3120573)4120573

and if 120573 isin (0 23) then 120597119901MD119898

120597120575 gt 0 if 120573 isin (23 1)then 120597119901MD

119898120597120575 lt 0

(3) if 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

if 120575 = 1199053 then 119901MD119898

=

119901MD119903

and if 120575 gt 1199053 then 119901MD119898

lt 119901MD119903

Proposition 19 indicates that when the manufacturer canopen an Internet store

(1) she should also lower the price to induce consumersto purchase the product from her Internet store asthe increasing dominant retailerrsquos bargaining powerotherwise the dominant retailer will also provideprice incentives for consumers to buy the productfrom his physical store

(2) if the dominant retailerrsquos bargaining power is rela-tively small (ie 120573 lt 23) she should raise the pricein her Internet store with increasing consumersrsquo disu-tility However if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 gt 23) she should cutdown the price in her Internet store with increasingconsumersrsquo disutility

(3) if consumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) shemust provide strong price incentives for consumersto purchase the product from her Internet storeotherwise her profits will cut down owing to someconsumers buying the product from the dominantretailerrsquos physical store on the contrary the domi-nant retailer will provide strong price incentives forconsumers to purchase the product from his physicalstore when consumersrsquo disutility of purchasing aproduct from Internet store is low enough (ie 120575 lt

1199053) then the manufacturerrsquos retail price is higherthan the dominant retailerrsquos If and only if consumersrsquodisutility of purchasing a product from Internet storesatisfies 120575 = 1199053 the manufacturer can set her retailprice to be equal to the dominant retailerrsquos

Proposition 20 Suppose that both the manufacturer anddominant retailer can open their Internet stores simultaneouslythen

(1) If 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0120597119901

M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0

(2) If 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 120597119901M119898120597120575 = (2 minus 3120573)4120573 120597119901M

119903120597120575 = 12120573 gt 0 and

Mathematical Problems in Engineering 7

Table 3 Strategic conditions for opening Internet stores to T-channel and pricing policies

Strategic conditions M and Rrsquos activities Pricing policiesM has not opened an Internet store and119865119903lt 120573(119905 minus 120575)

R can open an Internet store Monopoly pricing

R has not opened an Internet store and119865119898lt (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905)

M can open an Internet store

When 120575 lt 1199053then 119901MD

119898gt 119901

MD119903

When 120575 = 1199053then 119901MD

119898= 119901

MD119903

When 120575 gt 1199053then 119901MD

119898lt 119901

MD119903

When 120575 lt 1199053 119865119903lt (119905 minus 120575)120575119905 minus 120573(119881 minus 119905) and

119865119898lt (119905 minus 120575)120573 minus (119905 minus 120575)120575119905 minus (1 minus 120573)(119881 minus 119905)

Both M and R can open their Internet stores simultaneously119901M119898= 119901

M119903

When 120575 gt 1199053 119865119903lt (119905 + 120575)

2

8119905 minus 120573(119881 minus 119905) and119865119898lt (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905)

119901M119898lt 119901

M119903

when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0 but when 120573 isin

(23 1) then 120597119901M119898120597120575 lt 0

(3) If 120575 le 3119905 then 119901M119898= 119901

M119903 if 120575 gt 1199053 then 119901M

119898lt 119901

M119903

Proposition 20 indicates when both the manufacturerand dominant retailer can open their Internet stores simul-taneously

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) bothof them can set same price and lower prices as theincreasing consumersrsquo disutility On the contrary ifconsumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) themanufacturer must provide lower price incentivesthan the dominant retailer which may induce con-sumers to purchase the product from her Internetstore It should be pointed out that when the dom-inant retailerrsquos bargaining power is relatively small(ie 120573 lt 23) the manufacturerrsquos price increaseswith increasing consumersrsquo disutility but when thedominant retailerrsquos bargaining power is relativelylarger (ie 120573 gt 23) the manufacturerrsquos retail pricedecreases with increasing consumersrsquo disutility

(2) When consumersrsquo disutility of purchasing a prod-uct from Internet store is low enough (ie 120575 lt

1199053) the dominant retailerrsquos price decreases reducewith increasing consumersrsquo disutility but when con-sumersrsquo disutility of purchasing a product from Inter-net store is relatively larger (ie 120575 gt 1199053) thedominant retailerrsquos price decreases with increasingconsumersrsquo disutility Speaking frankly that is thedominant retailerrsquos smart pricing strategiesThe dom-inant retailer will raise the retail price when mostof consumers with a large disutility of purchasing aproduct from Internet store buy the product from hisphysical store and lower the retail price when mostof consumers with a small disutility of purchasing aproduct from Internet store buy the product from themanufacturerrsquos Internet store

Proposition 21 Given that the dominant retailerrsquos bargainingpower we obtain the following results about the manufacturerrsquoswholesale price under RD-channel MD-channel and M-channel

(1) 120597119908RD120597120575 = minus(1 minus 120573) lt 0

(2) 120597119908MD120597120575 = (1 minus 120573)2120573 gt 0

(3) if 120575 lt 1199053 then 120597119908M120597120575 = minus(1 minus 120573)120573 lt 0 if 120575 gt 1199053

then 120597119908M120597120575 = (1 minus 120573)2120573 gt 0

Proposition 21 indicates that the manufacturer should setthe wholesale prices differentially across the RD-channelMD-channel andM-channel and raise or lower thewholesaleprices in the light of consumersrsquo disutility of buying theproduct from Internet store More specifically the man-ufacturer can lower the wholesale price with increasingconsumersrsquo disutility of buying the product from Internetstore in the RD-channel but in theMD-channel she can raisethe wholesale price with increasing consumersrsquo disutility ofbuying from Internet store However in theM-channel whenthe consumersrsquo disutility of buying from Internet store is lowenough (ie 120575 lt 1199053) she can lower the wholesale pricewith increasing consumersrsquo disutility but when consumersrsquodisutility of buying from Internet store is relatively larger (ie120575 gt 1199053) she should raise the wholesale price with increasingconsumersrsquo disutility

Proposition 22 Given that the dominant retailerrsquos bargainingpower we obtain the following results about the manufacturerrsquosretail price at her Internet store under MD-channel and M-channel

(1) If 120575 lt 1199053 when 120573 isin (0 23) then 120597119901MD119898

120597120575 =

(2 minus 3120573)4120573 gt 0 120597119901M119898120597120575 = minus1120573 lt 0 but when 120573 isin

(23 1) then 120597119901MD119898

120597120575 = (2 minus 3120573)4120573 lt 0 120597119901M119898120597120575 =

minus1120573 lt 0(2) If 120575 gt 1199053 when 120573 isin (0 23) then 120597119901

MD119898

120597120575 =

120597119901M119898120597120575 gt 0 but when 120573 isin (23 1) then 120597119901MD

119898120597120575 =

120597119901M119898120597120575 lt 0

Proposition 22 indicates that themanufacturer should setthe retail prices at her Internet store differentially across the

8 Mathematical Problems in Engineering

MD-channel and M-channel and raise or lower the prices inthe light of consumersrsquo disutility of buying the product fromInternet store More specifically if the consumersrsquo disutilityof buying from Internet store is low enough (ie 120575 lt 1199053)the manufacturer can raise the retail price at her Internetstore with increasing consumersrsquo disutility of buying fromInternet store when the dominant retailerrsquos bargaining poweris relatively small (ie 120573 lt 23) and the dominant retailerdoes not open Internet store However if the dominantretailer also opens an Internet store the manufacturer shouldlower the retail price at her Internet store so as to attractconsumers to buy the product from her Internet store On thecontrary if the consumersrsquo disutility of buying from Internetstore is relatively larger (ie 120575 gt 1199053) and the dominantretailer also opens an Internet store then the manufacturershould set the same price with the dominant retailerrsquos andadjust the price following the dominant retailer

Proposition 23 Given that the dominant retailerrsquos bargainingpower we obtain the following results about dominant retailerrsquosretail price under RD-channel MD-channel and M-channel

(1) If 120575 lt 1199053 then 120597119901RD119903120597120575 = minus1 lt 0 120597119901MD

119903120597120575 = 12120573 gt

0 and 120597119901M119903120597120575 = minus1120573 lt 0

(2) If 120575 gt 1199053 then 120597119901RD119903120597120575 = minus1 lt 0 120597119901

MD119903

120597120575 =

12120573 gt 0 and 120597119901M119903120597120575 = 12120573 gt 0

Proposition 23 indicates that no matter when the con-sumersrsquo disutility of buying from Internet store is small orlarger the dominant retailer should lower the retail price withincreasing consumersrsquo disutility buying from Internet store inthe RD-channel but in the MD-channel he always raises theretail price with increasing consumersrsquo disutility Howeverin the M-channel when consumersrsquo disutility buying fromInternet store is low enough (ie 120575 lt 1199053) he should lowerthe price with increasing consumersrsquo disutility but whenconsumersrsquo disutility is relatively larger (ie 120575 gt 1199053) he canset the price same as the price in the MD-channel and raisethe price with increasing consumersrsquo disutility

6 Numerical Examples

In this section we present numerical examples to illustratethe theoretical results about impacts of consumersrsquo disutilityof buying from Internet store on the manufacturer anddominant retailerrsquos pricing policies with different bargainingpower for the dominant retailerrsquos among RD-channel MD-channel and M-channel which are summarized in Figures2ndash11 where 119881 = 14 119905 = 6 120575 isin (0 6) and 120573 = 02 120573 = 08The parametersrsquo values satisfy the assumptions in Section 3 inorder to make the models feasible and meaningful

Comparing Figure 2 with Figure 3 we can observe thatwhen the dominant retailerrsquos bargaining power is relativelysmall (ie 120573 = 02) both of them can increase prices asincreasing consumersrsquo disutility of purchasing from Internetstore in MD-channel However when the dominant retailerrsquosbargaining power is relatively larger (ie 120573 = 08) themanufacturer has no choice but to lower the retail price soas to attract consumers to buy the product from her Internet

0 1 2 3 4 5 612

14

16

18

20

22

24

26

28

30

wMD

pMDm

pMDr

120575

Figure 2 Impacts of 120575 on prices in the MD-channel when 120573 = 02

0 1 2 3 4 5 60

1

2

3

4

5

6

7

8

wMD

pMDm

pMDr

120575

Figure 3 Impacts of 120575 on prices in the MD-channel when 120573 = 08

store In addition Figures 2 and 3 show that when consumersrsquodisutility buying from Internet store is low enough (ie 120575 lt

2) the manufacturer can set her retail price to be larger thanthe dominant retailerrsquos However when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2)the manufacturer can set her retail price to be lower than thedominant retailerrsquos

Figures 4 and 5 show that when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)both the manufacturer and dominant retailer should lowerprices to increase consumersrsquo disutility buying from Internet

Mathematical Problems in Engineering 9

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

wM

pMm

pMr

Figure 4 Impacts of 120575 on prices in the M-channel when 120573 = 02

0 1 2 3 4 5 61

2

3

4

5

6

7

8

120575

wM

pMm

pMr

Figure 5 Impacts of 120575 on prices in the M-channel when 120573 = 08

store It is noted that the rate of change of manufacturerrsquosretail price with respect to consumersrsquo disutility buying fromInternet store is equal to that of dominant retailerrsquos retailprice However when consumersrsquo disutility buying fromInternet store is relatively larger (ie 120575 gt 2) if the dominantretailerrsquos bargaining power is relatively small (ie 120573 =

02) the manufacturer can raise retail price following thedominant retailer as increasing consumersrsquo disutility buyingfrom Internet store if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 = 08) the manufacturershould cut down the retail price in her Internet store withincreasing consumersrsquo disutility

0 1 2 3 4 5 66

8

10

12

14

16

18

20

22

24

wMD

wRD

wM

120575

Figure 6 The wholesale prices in different channels when 120573 = 02

0 1 2 3 4 5 605

1

15

2

25

3

120575

wMD

wRD

wM

Figure 7 The wholesale prices in different channels when 120573 = 08

Figures 6 and 7 show that no matter whether thedominant retailerrsquos bargaining power is small or large themanufacturer can raise the wholesale price with increasingconsumersrsquo disutility buying from Internet store in the MD-channel but in the RD-channel the manufacturer shouldlower the wholesale price with increasing consumersrsquo disutil-ity However in the M-channel when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower the wholesale price withincreasing consumersrsquo disutility when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2) themanufacturer can raise the wholesale price with increasing

10 Mathematical Problems in Engineering

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

pMDm

pMm

Figure 8 Manufacturerrsquos retail prices in different channels when120573 = 02

0 1 2 3 4 5 645

5

55

6

65

7

75

120575

pMDm

pMm

Figure 9 Manufacturerrsquos retail prices in different channels when120573 = 08

consumersrsquo disutility and set the wholesale price the same asin the MD-channel

Figures 8 and 9 show that when the dominant retailerrsquosbargaining power is relatively small (ie 120573 = 02) inthe MD-channel the manufacturer can raise retail pricewith increasing consumersrsquo disutility buying from Internetstore but when the dominant retailerrsquos bargaining power isrelatively larger (ie 120573 = 08) the manufacturer should lowerretail price with increasing consumersrsquo disutility Howeverin the M-channel no matter whether the dominant retailerrsquosbargaining power is small or large when consumersrsquo disutility

0 1 2 3 4 5 65

10

15

20

25

30

120575

pRDr

pMDr

pMr

Figure 10 Dominant retailerrsquos prices in different channels when120573 =02

buying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower retail price with increasingconsumersrsquo disutility but when consumersrsquo disutility buyingfrom Internet store is relatively larger (ie 120575 gt 2) if thedominant retailerrsquos bargaining power is relatively small (ie120573 = 02) the manufacturer can raise retail price withincreasing consumersrsquo disutility buying from Internet storeif the dominant retailerrsquos bargaining power is relatively larger(ie 120573 = 08) themanufacturer should lower retail price withincreasing consumersrsquo disutility

Figures 10 and 11 show that no matter whether thedominant retailerrsquos bargaining power is small or larger healways lowers the retail price with increasing consumersrsquodisutility buying from Internet store in the RD-channel butin the MD-channel he always raises the retail price withincreasing consumersrsquo disutility However in the M-channelwhen consumersrsquo disutility buying from Internet store islow enough (ie 120575 lt 2) the dominant retailer shouldlower retail price with increasing consumersrsquo disutility butwhen consumersrsquo disutility is relatively larger (ie 120575 gt 2)the dominant retailer can raise retail price with increasingconsumersrsquo disutility buying from Internet store

7 Conclusions and Future Research

To investigate when the manufacturer and dominant retaileropen their own Internet stores with different setup costsand how set prices to ensure opening Internet stores areprofitable in a supply chain we first present the equilibriumoutcomes under four possible supply chain structures andthen discuss the strategic conditions for the manufacturerand dominant retailer when it is optimal to open an Internetstore In addition we analyze both playersrsquo pricing policies

Mathematical Problems in Engineering 11

0 1 2 3 4 5 62

4

6

8

10

12

14

120575

pMDr

pRDr

pMr

Figure 11 Dominant retailerrsquos prices in different channels when 120573 =08

after they open their Internet stores and discuss the impactsof the dominant retailerrsquos bargaining power and consumersrsquodisutility of purchasing a product from Internet store onthe manufacturer and dominant retailerrsquos pricing strategiesFinally we conduct numerical examples to illustrate thetheoretical results

We obtain some new results differing from those inthe literature We find that the optimal choices for themanufacturer and dominant retailer to open an Internetstore are largely determined by their respective setup costswhich are closely related to the dominant retailerrsquos bargainingpower and consumersrsquo disutility of buying from Internetstore It is worth mentioning that multichannel retailing forthe dominant retailer is not necessarily the best strategyIn other words if the dominant retailer opens an Internetstore the marketing plan for him to attract more consumersby charging a lower price is impossible to achieve and hecan induce the manufacturer to open an Internet store tocompetewith himOnlywhen the setup cost for the dominantretailer to open an Internet store is sufficiently low then he isprofitable

What is more we also find that the manufacturerrsquosoptimal price at her Internet store is not always being lowerthan the dominant retailerrsquos For example if the consumersrsquodisutility of buying from Internet store is sufficiently highthe manufacturer must provide strong price incentives forconsumers to purchase the product from the Internet store

Although this research provides new insights for themanufacturer and dominant retailer to open an Internetstore and set prices in a supply chain there are severaldirections that could be extended First this study assumedthat all information is known to the manufacturer anddominant retailer in our model However information couldbe asymmetric in the supply chain since both players haveprivate information about their own internal variable costs

for example the setup cost of opening an Internet storecustomersrsquo purchase patterns and search costsTherefore wecan explore the competitive equilibrium under asymmetricinformation settings Second we assume that consumersrsquodisutility of buy from Internet store is independent of theunit transportation cost which can be relaxed in the futureresearch Third trade credit is widely used in practice andhas important impact on supply chain management [39ndash41] In recent years trade credit has become one of themajor transactions between suppliers and retailers in a valuechain For example Wal-Mart Carrefour and GOME (alarge Chinese home appliance chain retailer) even delayedpayments to their suppliers for as long as one year [42]Hence it is worthy to understand how the trade creditaffects supply channel configuration together with pricingstrategies in the E-commerce market A final issue worthyof investigation is how different types of customers affectthe manufacturer and dominant retailerrsquos channel selectionstrategies We leave these questions for future research

Appendices

A Equilibrium Outcome ofthe Four Channel Structures

Proof of Lemma 6 (1) In the T-channel both the manufac-turer and dominant retailer do not open their Internet storesThere is only the dominant retailerrsquos physical store in themarket So the dominant retailer acts as a monopolist andoptimally charges a price 119881 minus 119905 such that the market isjust covered For the manufacturer given that the dominantretailerrsquos optimal retail price the optimal wholesale price is119908

T= (1 minus 120573)(119881 minus 119905) Since the manufacturer produces

the product at a constant unit (marginal) cost which isnormalized to zero and the market is just covered that is thesize of the market is one the profit for the manufacturer isprod

T119898= (1minus120573)(119881minus119905) Accordingly the profit for the dominant

retailer isprodT119903= 120573(119881 minus 119905)

(2) In RD-channel only the dominant retailer opens anInternet store (RIS) If a consumer locates at a distance fromphysical store (PS) he will get a net utility of by purchasingthe product from PS and a net utility of by purchasing theproduct from RIS To ensure the full market coverage thedominant retailer charges the monopoly price 119881 minus 120575 acrosshis two stores and sells the product to all consumers Forthe manufacturer given the dominant retailerrsquos optimal retailprice the optimal wholesale price is 119908RD

= (1 minus 120573)(119881 minus 120575)Since the manufacturer produces the product at a constantunit (marginal) cost which is normalized to zero and 119905 thesize of the market is one the profits for the manufacturer anddominant retailer are prodRD

119898= (1 minus 120573)(119881 minus 120575) and prod

RD119903

=

120573(119881 minus 120575) respectively(3) In MD-channel the manufacturer opens an Internet

store but dominant retailer does not So consumers canhave convenient access to the product through the dominantretailerrsquos physical store (PS) at price 119901

119903or the manufacturerrsquos

Internet store (MIS) at price 119901119898 their decision about which

store to buy revolves around the comparison of their net

12 Mathematical Problems in Engineering

utility derived fromPS119880PS = 119881minus119901119903minus119905119909 and119880MIS = 119881minus119901119898minus120575by buying the product from MIS Therefore the marginalconsumers are located at 119909 = (119901

119898minus 119901119903+ 120575)119905 So the profit

functions for the manufacturer and dominant retailer can bewritten as

prod

119898

= 119908[

(119901119898minus 119901119903+ 120575)

119905

] + 119901119898[

(119901119903minus 119901119898+ 119905 minus 120575)

119905

] minus 119865119898

(A1)

prod

119903

= (119901119903minus 119908) [

(119901119898minus 119901119903+ 120575)

119905

] (A2)

Under the assumption proposed in Section 3 the dom-inant retailer is the price leader and the manufacturer isthe follower As before the game is solved backwards Inthis market we firstly need to calculate the manufacturerrsquosoptimal price given any dominant retailerrsquos price

Themanufacturerrsquos reaction function can be derived fromthe first-order condition

120597prod119898

120597119901119898

=

[(2 minus 120573) 119901119903minus 2119901119898+ 119905 minus 120575]

119905

= 0

that is 119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A3)

Substituting (A3) into (A2) we get

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

(A4)

Taking the first-order derivative of (A4) with respect to119901119903and letting the derivative be zero we have

119901MD119903

=

(119905 + 120575)

2120573

(A5)

Given the wholesale price bargaining process we canobtain the manufacturerrsquos optimal wholesale price 119908MD

=

(1 minus 120573)(119905 + 120575)2120573 and substituting (A5) into (A3) we getthe manufacturerrsquos optimal retail price

119901MD119898

=

(2 + 120573) 119905 + (2 minus 3120573) 120575

4120573

(A6)

Substituting (A5) and (A6) into (A1) and (A2) wecan obtain the equilibrium profits for the manufacturers anddominant retailer respectively

MDprod

119898

=

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus 119865119898

MDprod

119903

=

(119905 + 120575)2

8119905

(A7)

Proof of Lemma 7 In the M-channel both the manufacturerand dominant retailer simultaneously open their own Inter-net stores then customers are able to purchase a product

either from the dominant retailerrsquos physical store (PS) or fromthe alternative Internet stores (MISRIS) They can get a netutility of 119880PS = 119881 minus 119901

119903minus 119905119909 by buying the product from PS

and a net utility of 119880MIS = 119881 minus 119901119898minus 120575 by buying the product

fromMIS and a net utility of119880RIS = 119881minus 119901119903minus 120575 by buying the

product from RISAccording to the basicmodel we know that the dominant

retailer firstmakes pricing decision as the price leader and themanufacturer is the follower If the dominant retailer chargesa price higher than the manufacturerrsquos price (119901

119903gt 119901119898) then

no consumer will buy the product from his Internet storeUnder this condition the dominant retailer makes no sale inhis Internet store and makes a profit of minus119865

119903 Therefore the

demand functions for the manufacturerrsquos Internet store anddominant retailerrsquos physical store are given respectively asfollows

119863MIS =(119901119903minus 119901119898+ 119905 minus 120575)

119905

(A8)

119863PS =(119901119898minus 119901119903+ 120575)

119905

(A9)

Hence the manufacturerrsquos profit function can be written as

prod

119898

=

[119908 (119901119898minus 119901119903+ 120575) + 119901

119898(119901119903minus 119901119898+ 119905 minus 120575)]

119905

minus 119865119898

(A10)

From the first-order condition we have

119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A11)

Given the condition of 119901119903gt 119901119898 this implies that 119901

119903gt (119905 minus

120575)120573 However when 119901119903le (119905 minus 120575)120573 and 119901

119903gt 119901119898 we always

have 120597prodM119898120597119901119898= [(2 minus 120573)119901

119903minus 2119901119898+ 119905 minus 120575]119905 gt 0

Therefore the manufacturer optimally sets its price at119901119898= 119901119903 and her optimal pricing schedule is as follows

119901119898=

119901119903 119901

119903le

119905 minus 120575

120572

(2 minus 120573) 119901119903+ 119905 minus 120575

2

119901119903gt

119905 minus 120575

120572

(A12)

Given the manufacturerrsquos pricing schedule the dominantretailerrsquos profit is given as follows

prod

119903

=

(119901119903minus 119908)

120575

119905

minus 119865119903 119901

119903le

119905 minus 120575

120573

(119901119903minus 119908)

119905 + 120575 minus 120573119901119903

2119905

minus 119865119903 119901119903gt

119905 minus 120575

120573

(A13)

Under the condition of 119901119903gt (119905 minus 120575)120573 the dominant

retailerrsquos profit is

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

minus 119865119903 (A14)

Taking the first-order derivative of (A14) with respect to 119901119903

and letting the derivative be zero we have 119901M119903= (119905 + 120575)2120573

Mathematical Problems in Engineering 13

Submitting it into (A11) we get the manufacturerrsquos optimalprice in her Internet store 119901M

119898= [(2 + 120573)119905 + (2 minus 3120573)120575]4120573

Hence the manufacturer and dominant retailerrsquos optimalprofits are prodM

119898= (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus 119865119898

andprodM119903= (119905 + 120575)

2

8119905 minus 119865119903 respectively

According to the previous assumption 119901119903gt (119905 minus 120575)120573

which implies that (119905 + 120575)2120573 gt (119905 minus 120575)120573 120575must satisfy 120575 gt1199053 However when 120575 lt 1199053 we always have

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](minus)

gt 0

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](+)

lt 0 (A15)

So the dominant retailerrsquos optimal retail price in the M-channel is 119901M

119903= (119905 minus 120575)120573 Therefore the manufacturer and

dominant retailerrsquos optimal profits areprodM119898= (119905 minus 120575)120573 minus [(119905 minus

120575)120575]119905 minus 119865119898andprodM

119903= [(119905 minus 120575)120575]119905 minus 119865

119903 respectively

B Strategic Conditions forOpening an Internet Store

Proofs of Proposition 8 and Corollary 9 From Lemma 6 weanalyse the equilibrium profits for the dominant retailerbetween the T-channel and RD-channel and note that onlywhen 119865

119903lt 120573(119905 minus 120575) then prodRD

119903gt prod

T119903 This implies that as

long as the setup cost of opening an Internet store satisfies119865119903

lt 120573(119905 minus 120575) ≜ 1198611 it is always optimal to open an

Internet store for the dominant retailer In addition we notethat 120597119861

1120597120575 = minus120573 lt 0 So the dominant retailerrsquos strategic

motive for opening an Internet store would be weakened byincreasing consumersrsquo disutility of purchasing a product fromInternet store

Proofs of Proposition 10 and Corollary 11 From Lemma 6 weanalyse the equilibrium profits for the manufacturer betweenthe T-channel and MD-channel and note that only when thesetup cost of opening an Internet store satisfies 119865

119898lt (119905 +

120575)2120573+[(119905minus120575)2

minus12119905120575]16119905minus(1minus120573)(119881minus119905) ≜ 1198612 thenprodMD

119898gt

prodT119898 In addition we note that 120597119861

2120597120575 = [4119905 minus 120573(7119905 minus 120575)]8120573119905

and find when 0 lt 120573 lt 4119905(7119905 minus 120575) then 1205971198612120597120575 gt 0 and

when 4119905(7119905 minus 120575) lt 120573 lt 1 then 1205971198612120597120575 lt 0

Proofs of Proposition 12 and Corollary 13 FromLemmas 6 and7 we analyse the equilibriumprofits for themanufacturer anddominant retailer between the T-channel andM-channel wenote that under the condition of 120575 lt 1199053 only when the setupcosts of opening an Internet store for the manufacturer anddominant retailer simultaneously satisfy

119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198613

119865119903lt

[(119905 minus 120575) 120575]

119905

minus 120573 (119881 minus 119905) ≜ 1198614

(B1)

thenMprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B2)

Similarly under the condition of 120575 gt 1199053 only when thesetup costs of opening an Internet store for the manufacturerand dominant retailer simultaneously satisfy

119865119898lt

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198615

119865119903lt

(119905 + 120575)2

8119905

minus 120573 (119881 minus 119905) ≜ 1198616

(B3)

then

Mprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B4)

In addition we note that both 1205971198613120597120575 = minus[119905 + 120573(119905 minus

2120575)]120573119905 lt 0 and 1205971198614120597120575 = (119905 minus 2120575)119905 gt 0 are held under

the condition of 120575 lt 1199053 Furthermore under the conditionof 120575 gt 1199053 we also find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198615120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

5120597120575 lt 0

1205971198616120597120575 = 2(119905 + 120575)8119905 gt 0

Proofs of Proposition 14 and Corollary 15 From Lemmas 6and 7 we analyse the manufacturerrsquos equilibrium profits inthe RD-channel and M-channel we note that under thecondition of 120575 lt 1199053 only when the setup cost of opening anInternet store for her satisfies 119865

119898lt (119905 minus 120575)120573 minus [(119905 minus 120575)120575]119905 minus

(1 minus 120573)(119881 minus 120575) ≜ 1198617 thenprodM

119898gt prod

RD119898 In addition we find

1205971198617120597120575 = minus[(1 + 120573

2

)119905 minus 2120573120575]120573119905 lt 0But under the condition of 120575 gt 1199053 only when the setup

cost of opening an Internet store for her satisfies 119865119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 120575) ≜ 1198618 then

prodM119898gt prod

RD119898 In addition 120597119861

8120597120575 = [120573(119905+120575)+4119905(1minus2120573

2

)]8120573119905

we find that when 0 lt 120573 lt [(119905 + 120575) + radic(119905 + 120575)2

+ 1281199052]16119905

then 1205971198618120597120575 gt 0 andwhen [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905 lt

120573 lt 1 then 1205971198618120597120575 lt 0

Proofs of Proposition 16 From Lemmas 6 and 7 we analysethe dominant retailerrsquos equilibriumprofits in theMD-channeland M-channel and note that when 120575 lt 1199053 then prod

M119903minus

prodMD119903

= minus(119905 minus 3120575)2

8119905 minus 119865119903lt 0 and when 120575 gt 1199053

then prodM119903minus prod

MD119903

= minus119865119903lt 0 These imply that when the

manufacturer has operated an Internet store the best choicefor dominant retailer is not to open an Internet store

Proofs of Proposition 17 and Corollary 18 From Lemmas 6and 7 we analyse the dominant retailerrsquos equilibrium profitsin the MD-channel and M-channel and note that under thecondition of 120575 lt 1199053 thenprodM

119898minus prod

MD119898

= [8119905(119905 minus 3120575) minus 120573[(119905 +

120575)2

minus 161205752

]8119905]16120573119905 This implies that the manufacturer willopen her Internet store when the dominant retailer opens an

14 Mathematical Problems in Engineering

Internet store and the setup costs of opening an Internet storefor her satisfies

1198619≜

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

lt 119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

≜ 11986110

(B5)

In addition we find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198619120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

9120597120575 lt 0

and 12059711986110120597120575 = minus[119905 + 120573(119905 minus 2120575)]120573119905 lt 0

C The ManufacturerDominantRetailers Pricing Policies

Proof of Proposition 19 In the MD-channel we respectivelydifferentiate between119901MD

119898and119901MD

119903with respect to 120573 and find

that 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0 For any given120573 differentiating between 119901MD

119898and 119901MD

119903with respect to 120575 we

have 120597119901MD119903

120597120575 = 12120573 gt 0 and 120597119901MD119898

120597120575 = (2 minus 3120573)4120573and if 120573 isin (0 23) then 120597119901MD

119898120597120575 gt 0 if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 In addition we find that 119901MD119898

minus 119901MD119903

= (119905 minus

3120575)4 it is obvious that when 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

when 120575 = 1199053 then 119901MD

119898= 119901

MD119903

and when 120575 gt 1199053 then119901MD119898

lt 119901MD119903

Proof of Proposition 20 In the M-channel we respectivelydifferentiate between 119901M

119898and 119901M

119903with respect to 120573 and find

that when 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0

and when 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 For any given 120573 we respectively differentiate between 119901M119898

and 119901M119903with respect to 120575 and find that when 120575 lt 1199053 then

120597119901M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0 when 120575 gt 1199053 then

120597119901M119898120597120575 = (2 minus 3120573)4120573 and 120597119901M

119903120597120575 = 12120573 gt 0

It is easy to note that when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0

but when 120573 isin (23 1) then 120597119901M119898120597120575 lt 0

Proof of Proposition 21 From Lemmas 6 and 7 we note that120597119908

RD120597120575 = minus(1 minus 120573) lt 0 and 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0In addition if 120575 lt 1199053 then 120597119908M

120597120575 = minus(1 minus 120573)120573 lt 0 if120575 gt 1199053 then 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0

Proof of Proposition 22 From the proofs of Propositions 19and 20 we note that when 120575 lt 1199053 if 120573 isin (0 23) then120597119901

MD119898

120597120575 gt 0 120597119901M119898120597120575 lt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 120597119901M119898120597120575 lt 0 when 120575 gt 1199053 if 120573 isin (0 23)

then 120597119901MD119898

120597120575 = 120597119901M119898120597120575 gt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 = 120597119901M119898120597120575 lt 0

Proof of Proposition 23 From Lemmas 6 and 7 we note that120597119901

RD119903120597120575 = minus1 lt 0 and 120597119901MD

119903120597120575 = 12120572 gt 0 In addition if

120575 lt 1199053 then 120597119901M119903120597120575 = minus1120572 lt 0 if 120575 gt 1199053 then 120597119901M

119903120597120575 =

12120572 gt 0

Abbreviations

UK The consumerrsquos utility of purchasing theproduct from K storeK isin PSRISMIS

119881 The value of consumers willing to payfor the product

120575 The consumersrsquo disutility of purchasingthe product from Internet store(MISRIS)

119905 The per unit transportation cost ofpurchasing the product from physicalstore (PS)

120573 The dominant retailerrsquos bargainingpower in the distribution channel

119908j The manufacturerrsquos wholesale price in

the j-channel j isin TRDMDM

119901j119903 The dominant retailerrsquos price in the

j-channel j isin TRDMDM

119901j119898 The manufacturerrsquos price in the

j-channel j isin MDM

119865119898119865119903 The setup cost of opening an Internetstore by the manufacturerdominantretailer

Πj119898Πj119903 The manufacturerdominant retailerrsquosprofit in the j-channelj isin TRDMDM

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been supported by theNational Natural Sci-ence Foundation of China (71271225) Chongqingrsquos NaturalScience Foundation (cstc2012jjA1404) and the Open Fund ofChongqing Key Laboratory of Logistics (CQKLL12001)

References

[1] L Hsiao and Y-J Chen ldquoStrategic motive for introducinginternet channels in a supply chainrdquo Production and OperationsManagement vol 23 no 1 pp 36ndash47 2014

[2] I Geyskens K Gielens and M G Dekimpe ldquoThe marketvaluation of Internet channel additionsrdquo Journal of Marketingvol 66 no 2 pp 102ndash119 2002

[3] 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

[4] S-H Chun and J-C Kim ldquoPricing strategies in B2C electroniccommerce analytical and empirical approachesrdquo Decision Sup-port Systems vol 40 no 2 pp 375ndash388 2005

[5] S K Mukhopadhyay X Zhu and X Yue ldquoOptimal contractdesign for mixed channels under information asymmetryrdquoProduction and Operations Management vol 17 no 6 pp 641ndash650 2008

Mathematical Problems in Engineering 15

[6] G S Cai ldquoChannel selection and coordination in dual-channelsupply chainsrdquo Journal of Retailing vol 86 no 1 pp 22ndash36 2010

[7] K Takahashi T Aoi D Hirotani and K Morikawa ldquoInventorycontrol in a two-echelon dual-channel supply chain with setupof production and deliveryrdquo International Journal of ProductionEconomics vol 133 no 1 pp 403ndash415 2011

[8] D W Carlton and J A Chevalier ldquoFree riding and salesstrategies for the Internetrdquo Journal of Industrial Economics vol49 no 4 pp 441ndash461 2001

[9] K D Antia M Bergen and S Dutta ldquoCompeting with graymarketsrdquoMIT SloanManagement Review vol 46 no 1 pp 63ndash69 2004

[10] J Shin ldquoHow does free riding on customer service affectcompetitionrdquo Marketing Science vol 26 no 4 pp 488ndash5032007

[11] G Iyer and J M Villas-Boas ldquoA bargaining theory of distribu-tion channelsrdquo Journal of Marketing Research vol 40 no 1 pp80ndash100 2003

[12] A Dukes and Y Liu ldquoIn-store media and distribution channelcoordinationrdquoMarketing Science vol 29 no 1 pp 94ndash107 2010

[13] H Ahn I Duenyas and R Zhang ldquoPrice competition betweenretailers and manufacturer-owned storesrdquoWorking Paper Uni-versity of California at Berkeley 2002

[14] K Cattani W Gilland H S Heese and J SwaminathanldquoBoiling frogs pricing strategies for a manufacturer addinga direct channel that competes with the traditional channelrdquoProduction and Operations Management vol 15 no 1 pp 40ndash56 2006

[15] K-Y Chen M Kaya and O Ozer ldquoDual sales channel man-agement with service competitionrdquo Manufacturing and ServiceOperations Management vol 10 no 4 pp 654ndash675 2008

[16] G Hua S Wang and T C E Cheng ldquoPrice and lead timedecisions in dual-channel supply chainsrdquo European Journal ofOperational Research vol 205 no 1 pp 113ndash126 2010

[17] W S Yoo andE Lee ldquoInternet channel entry a strategic analysisof mixed channel structuresrdquo Marketing Science vol 30 no 1pp 29ndash41 2011

[18] Y Xiong W Yan K Fernandes Z-K Xiong and N GuoldquoldquoBricks vs clicksrdquo the impact of manufacturer encroachmentwith a dealer leasing and selling of durable goodsrdquo EuropeanJournal of Operational Research vol 217 no 1 pp 75ndash83 2012

[19] Q Lu and N Liu ldquoPricing games of mixed conventional ande-commerce distribution channelsrdquo Computers and IndustrialEngineering vol 64 no 1 pp 122ndash132 2013

[20] Q Xu Z Liu and B Shen ldquoThe impact of price comparisonservice on pricing strategy in a dual-channel supply chainrdquoMathematical Problems in Engineering vol 2013 Article ID613528 13 pages 2013

[21] C A Ingene and M E Parry ldquoChannel coordination whenretailers competerdquoMarketing Science vol 14 no 4 pp 360ndash3771995

[22] 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

[23] J Raju and Z J Zhang ldquoChannel coordination in the presenceof a dominant retailerrdquoMarketing Science vol 24 no 2 pp 254ndash262 2005

[24] K L Webb and C J Lambe ldquoInternal multi-channel conflictan exploratory investigation and conceptual frameworkrdquo Indus-trial Marketing Management vol 36 no 1 pp 29ndash43 2007

[25] S K Mukhopadhyay D-Q Yao and X Yue ldquoInformationsharing of value-adding retailer in a mixed channel hi-techsupply chainrdquo Journal of Business Research vol 61 no 9 pp950ndash958 2008

[26] R Yan ldquoManaging channel coordination in a multi-channelmanufacturer-retailer supply chainrdquo Industrial Marketing Man-agement vol 40 no 4 pp 636ndash642 2011

[27] E Cao YMa CWan andM Lai ldquoContracting with asymmet-ric cost information in a dual-channel supply chainrdquoOperationsResearch Letters vol 41 no 4 pp 410ndash414 2013

[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] Y Liu S Gupta and Z J Zhang ldquoNote on self-restraint as anonline entry-deterrence strategyrdquoManagement Science vol 52no 11 pp 1799ndash1809 2006

[30] Z Cheng and B R Nault ldquoInternet channel entry retailcoverage and entry cost advantagerdquo Information Technology andManagement vol 8 no 2 pp 111ndash132 2007

[31] X Zhang ldquoRetailersrsquo multichannel and price advertising strate-giesrdquoMarketing Science vol 28 no 6 pp 1080ndash1094 2009

[32] W Huang and J M Swaminathan ldquoIntroduction of a secondchannel implications for pricing and profitsrdquo European Journalof Operational Research vol 194 no 1 pp 258ndash279 2009

[33] H Hotelling ldquoStability in competitionrdquo The Economic Journalvol 39 no 153 pp 41ndash57 1929

[34] J Zhang ldquoThe perils of behavior-based personalizationrdquo Mar-keting Science vol 30 no 1 pp 170ndash186 2011

[35] T Kabiraj and C Lee ldquoLicensing contracts in hotelling struc-turerdquoTheoretical Economics Letters vol 1 no 3 pp 57ndash62 2011

[36] HWang andTNariu ldquoDistribution channelmanagement in aninternet age equilibrium and social welfarerdquo Journal of IndustryCompetition and Trade vol 12 no 3 pp 285ndash298 2012

[37] M Lijesen ldquoHotellingrsquos webshoprdquo Journal of Economics vol 109no 2 pp 193ndash200 2013

[38] R Gulati and J Garino ldquoGet the right mix of bricks amp clicksrdquoHarvard Business Review vol 78 no 3 pp 107ndash214 2000

[39] K-J Chung S-D Lin and H M Srivastava ldquoThe completesolution procedures for the mathematical analysis of somefamilies of optimal inventorymodels with order-size dependenttrade credit and deterministic and constant demandrdquo AppliedMathematics and Computation vol 219 no 1 pp 142ndash157 2012

[40] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels under conditional trade credit in a supply chain systemrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 24 pp10036ndash10052 2013

[41] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels for deteriorating items in the discounted cash-flowsapproach under conditional trade credit and cash discount ina supply chain systemrdquo Applied Mathematics and InformationSciences vol 8 no 5 pp 2103ndash2111 2014

[42] J Luo and Q Zhang ldquoTrade credit a new mechanism tocoordinate supply chainrdquo Operations Research Letters vol 40no 5 pp 378ndash384 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

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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

Mathematical Problems in Engineering 5

Corollary 9 If the manufacturer has not opened an Internetstore the dominant retailerrsquos strategic motive for opening anInternet store would be weakened by increasing consumersrsquodisutility of purchasing a product from Internet store

Proposition 10 Suppose that the dominant retailer has notopened an Internet store when the setup cost of opening anInternet store by the manufacturer 119865

119898lt (119905 + 120575)2120573 + [(119905 minus

120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905) she can begin to open anInternet store

Proposition 10 implies that under the condition of thedominant retailer has not opened an Internet store onlywhenthe setup cost of opening an Internet store is relatively smallthemanufacturer will getmore profit than that of not openingan Internet store Otherwise her profit will decrease due tocostly setup cost

Based on Proposition 10 we have the following corollary

Corollary 11 If the dominant retailer has not opened anInternet store and his bargaining power is relatively small (ie120573 lt 4119905(7119905 minus 120575)) the manufacturerrsquos strategic motive foropening an Internet store would be strengthened by increasingconsumersrsquo disutility of purchasing a product from Internetstore Otherwise her strategic motive would be weakened

Proposition 12 There are two choices for the manufacturerand dominant retailer to open their Internet stores simultane-ously which are summarized as follows

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) and the setupcosts of opening an Internet store by the manufacturerand dominant retailer meet 119865

119898lt (119905 minus 120575)120573 minus (119905 minus

120575)120575119905 minus (1 minus 120573)(119881 minus 119905) and 119865119903lt (119905 minus 120575)120575119905 minus 120573(119881 minus 119905)

respectively both of them can open their own Internetstores simultaneously

(2) If consumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) andthe setup costs of opening an Internet store by themanufacturer and dominant retailer meet 119865

119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905) and119865119903lt (119905 + 120575)

2

8119905 minus 120573(119881 minus 119905) respectively both of themcan open their own Internet stores simultaneously

Proposition 12 implies that consumersrsquo disutility of pur-chasing a product from Internet store plays an importantrole for opening Internet stores simultaneously by the man-ufacturer and dominant retailer And only when the setupcosts of opening Internet stores by them are relatively smallrespectively then both will get more profit than that of notopening Internet stores Otherwise their profits will decreasedue to costly setup costs

It should be noted that the upper bounds of 119865119898and 119865119903are

related to 120575 for a given 120573 in Proposition 12 so we have thefollowing corollary

Corollary 13 If both the manufacturer and dominant retailerhave not operated their Internet stores then

(1) when consumersrsquo disutility of purchasing a productfrom Internet store is low enough (ie 120575 lt 1199053) themanufacturerrsquos strategic motive for opening an Internetstore would be weakened by increasing consumersrsquodisutility of purchasing a product from Internet storebut the dominant retailerrsquos strategic motive for openingan Internet store would be strengthened

(2) when consumersrsquo disutility of purchasing a productfrom Internet store is relatively larger (ie 120575 gt 1199053)the dominant retailerrsquos strategic motive for opening anInternet store would be strengthened by increasing con-sumersrsquo disutility of purchasing a product from Internetstore For the manufacturer only if the dominantretailerrsquos bargaining power is relatively small (ie 120573 lt

4119905(7119905minus120575)) her strategicmotive for opening an Internetstore would be strengthened by increasing consumersrsquodisutility of purchasing a product from Internet storeOtherwise her strategic motive would be weakened

Proposition 14 Suppose that the dominant retailer has oper-ated an Internet store themanufacturer has two choices to openan Internet store which are summarized as follows

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) and the setupcost of opening an Internet store by the manufacturer119865119898lt (119905 minus 120575)120573 minus (119905 minus 120575)120575119905 minus (1 minus 120573)(119881 minus 120575) she can

also open an Internet store(2) If consumersrsquo disutility of purchasing a product from

Internet store is relatively larger (ie 120575 gt 1199053) andthe setup cost of opening an Internet store by themanufacturer 119865

119898lt (119905+120575)2120573+[(119905minus120575)

2

minus12119905120575]16119905minus

(1 minus 120573)(119881 minus 120575) she can also open an Internet store

Proposition 14 implies that under the condition of thedominant retailer has operated an Internet store consumersrsquodisutility of purchasing a product from Internet store alsoplays an important role in opening an Internet store by themanufacturer And only when the setup cost of opening anInternet store is relatively small then the manufacturer willget more profit than that of not opening an Internet storeOtherwise her profit will decrease due to costly set-up cost

Based on Proposition 14 we have the following corollary

Corollary 15 If the dominant retailer has operated an Internetstore then

(1) when consumersrsquo disutility of purchasing a productfrom Internet store is low enough (ie 120575 lt 1199053) themanufacturerrsquos strategic motive for opening an Internetstore would be weakened by increasing consumersrsquodisutility of purchasing a product from Internet store

(2) when consumersrsquo disutility of purchasing a productfrom Internet store is relatively larger (ie 120575 gt 1199053) andonly if the dominant retailerrsquos bargaining power is rela-tively small (ie 120573 lt [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905)the manufacturerrsquos strategic motive for opening anInternet store would be strengthened by increasing

6 Mathematical Problems in Engineering

consumersrsquo disutility of purchasing a product fromInternet store Otherwise her strategic motive would beweakened

Proposition 16 Suppose that the manufacturer has operatedan Internet store the best choice for dominant retailer is not toopen an Internet store

Proposition 16 implies that under the condition of themanufacturer has operated an Internet store regardless ofconsumersrsquo disutility of purchasing a product from Internetstore is small or larger it is best for the dominant retailer notto open an Internet store Otherwise his profit will decreasedue to costly setup cost or the manufacturerrsquos low pricestrategy that attract more consumers to buy the product fromher Internet store

Proposition 17 Suppose that the manufacturer has notopened an Internet store if consumersrsquo disutility of purchasinga product from Internet store is low enough (ie 120575 lt 1199053) andthe setup cost of opening an Internet store for the manufactureris intermediate 119865

119898isin [(119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 (119905 minus

120575)120573 minus (119905 minus 120575)120575119905] the dominant retailer opening an Internetstore can lead to the well-known contagion-like effect

Proposition 17 implies that under the condition of themanufacturer has not opened an Internet store when con-sumersrsquo disutility of purchasing a product from Internet storeis relatively small and the set-up cost of opening an Internetstore for the manufacturer is intermediate the dominantretailerrsquos Internet store entry may induce the manufacturerto open her own Internet store competing with him

FromProposition 17 we observe that the upper and lowerbounds of 119865

119898are related to 120575 for a given 120573 so we have the

following corollary

Corollary 18 When consumersrsquo disutility of purchasing aproduct from Internet store is low enough (ie 120575 lt 1199053) ifthe dominant retailerrsquos bargaining power is relatively small (ie120573 lt 4119905(7119905minus120575)) the contagion-like effect would be expanded byincreasing consumersrsquo disutility of purchasing a product fromInternet store However if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 gt 4119905(7119905 minus 120575)) the contagion-like effect would be diminished

Based on aforementioned propositions we now showwhen do the manufacturer and dominant retailer open theirown Internet stores to a traditional supply chain and how dothey set prices after opening Internet stores in Table 3

5 Analytical Results onBoth Playersrsquo Pricing Policies

From Lemmas 6 and 7 we know that the T-channel andRD-channel are monopoly settings So the dominant retailercharges the optimal monopoly price and sells the productto all consumers However under the MD-channel and M-channel the manufacturer and dominant retailer engage in

price competition To investigate the impacts of the dom-inant retailerrsquos bargaining power and consumersrsquo disutilityof purchasing a product from Internet store on the manu-facturer and dominant retailerrsquos pricing strategies we obtainthe following propositions and the proofs are provided inAppendix C

Proposition 19 Suppose that only the manufacturer can openan Internet store then

(1) 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0(2) 120597119901MD

119903120597120575 = 12120573 gt 0 and 120597119901MD

119898120597120575 = (2 minus 3120573)4120573

and if 120573 isin (0 23) then 120597119901MD119898

120597120575 gt 0 if 120573 isin (23 1)then 120597119901MD

119898120597120575 lt 0

(3) if 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

if 120575 = 1199053 then 119901MD119898

=

119901MD119903

and if 120575 gt 1199053 then 119901MD119898

lt 119901MD119903

Proposition 19 indicates that when the manufacturer canopen an Internet store

(1) she should also lower the price to induce consumersto purchase the product from her Internet store asthe increasing dominant retailerrsquos bargaining powerotherwise the dominant retailer will also provideprice incentives for consumers to buy the productfrom his physical store

(2) if the dominant retailerrsquos bargaining power is rela-tively small (ie 120573 lt 23) she should raise the pricein her Internet store with increasing consumersrsquo disu-tility However if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 gt 23) she should cutdown the price in her Internet store with increasingconsumersrsquo disutility

(3) if consumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) shemust provide strong price incentives for consumersto purchase the product from her Internet storeotherwise her profits will cut down owing to someconsumers buying the product from the dominantretailerrsquos physical store on the contrary the domi-nant retailer will provide strong price incentives forconsumers to purchase the product from his physicalstore when consumersrsquo disutility of purchasing aproduct from Internet store is low enough (ie 120575 lt

1199053) then the manufacturerrsquos retail price is higherthan the dominant retailerrsquos If and only if consumersrsquodisutility of purchasing a product from Internet storesatisfies 120575 = 1199053 the manufacturer can set her retailprice to be equal to the dominant retailerrsquos

Proposition 20 Suppose that both the manufacturer anddominant retailer can open their Internet stores simultaneouslythen

(1) If 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0120597119901

M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0

(2) If 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 120597119901M119898120597120575 = (2 minus 3120573)4120573 120597119901M

119903120597120575 = 12120573 gt 0 and

Mathematical Problems in Engineering 7

Table 3 Strategic conditions for opening Internet stores to T-channel and pricing policies

Strategic conditions M and Rrsquos activities Pricing policiesM has not opened an Internet store and119865119903lt 120573(119905 minus 120575)

R can open an Internet store Monopoly pricing

R has not opened an Internet store and119865119898lt (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905)

M can open an Internet store

When 120575 lt 1199053then 119901MD

119898gt 119901

MD119903

When 120575 = 1199053then 119901MD

119898= 119901

MD119903

When 120575 gt 1199053then 119901MD

119898lt 119901

MD119903

When 120575 lt 1199053 119865119903lt (119905 minus 120575)120575119905 minus 120573(119881 minus 119905) and

119865119898lt (119905 minus 120575)120573 minus (119905 minus 120575)120575119905 minus (1 minus 120573)(119881 minus 119905)

Both M and R can open their Internet stores simultaneously119901M119898= 119901

M119903

When 120575 gt 1199053 119865119903lt (119905 + 120575)

2

8119905 minus 120573(119881 minus 119905) and119865119898lt (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905)

119901M119898lt 119901

M119903

when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0 but when 120573 isin

(23 1) then 120597119901M119898120597120575 lt 0

(3) If 120575 le 3119905 then 119901M119898= 119901

M119903 if 120575 gt 1199053 then 119901M

119898lt 119901

M119903

Proposition 20 indicates when both the manufacturerand dominant retailer can open their Internet stores simul-taneously

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) bothof them can set same price and lower prices as theincreasing consumersrsquo disutility On the contrary ifconsumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) themanufacturer must provide lower price incentivesthan the dominant retailer which may induce con-sumers to purchase the product from her Internetstore It should be pointed out that when the dom-inant retailerrsquos bargaining power is relatively small(ie 120573 lt 23) the manufacturerrsquos price increaseswith increasing consumersrsquo disutility but when thedominant retailerrsquos bargaining power is relativelylarger (ie 120573 gt 23) the manufacturerrsquos retail pricedecreases with increasing consumersrsquo disutility

(2) When consumersrsquo disutility of purchasing a prod-uct from Internet store is low enough (ie 120575 lt

1199053) the dominant retailerrsquos price decreases reducewith increasing consumersrsquo disutility but when con-sumersrsquo disutility of purchasing a product from Inter-net store is relatively larger (ie 120575 gt 1199053) thedominant retailerrsquos price decreases with increasingconsumersrsquo disutility Speaking frankly that is thedominant retailerrsquos smart pricing strategiesThe dom-inant retailer will raise the retail price when mostof consumers with a large disutility of purchasing aproduct from Internet store buy the product from hisphysical store and lower the retail price when mostof consumers with a small disutility of purchasing aproduct from Internet store buy the product from themanufacturerrsquos Internet store

Proposition 21 Given that the dominant retailerrsquos bargainingpower we obtain the following results about the manufacturerrsquoswholesale price under RD-channel MD-channel and M-channel

(1) 120597119908RD120597120575 = minus(1 minus 120573) lt 0

(2) 120597119908MD120597120575 = (1 minus 120573)2120573 gt 0

(3) if 120575 lt 1199053 then 120597119908M120597120575 = minus(1 minus 120573)120573 lt 0 if 120575 gt 1199053

then 120597119908M120597120575 = (1 minus 120573)2120573 gt 0

Proposition 21 indicates that the manufacturer should setthe wholesale prices differentially across the RD-channelMD-channel andM-channel and raise or lower thewholesaleprices in the light of consumersrsquo disutility of buying theproduct from Internet store More specifically the man-ufacturer can lower the wholesale price with increasingconsumersrsquo disutility of buying the product from Internetstore in the RD-channel but in theMD-channel she can raisethe wholesale price with increasing consumersrsquo disutility ofbuying from Internet store However in theM-channel whenthe consumersrsquo disutility of buying from Internet store is lowenough (ie 120575 lt 1199053) she can lower the wholesale pricewith increasing consumersrsquo disutility but when consumersrsquodisutility of buying from Internet store is relatively larger (ie120575 gt 1199053) she should raise the wholesale price with increasingconsumersrsquo disutility

Proposition 22 Given that the dominant retailerrsquos bargainingpower we obtain the following results about the manufacturerrsquosretail price at her Internet store under MD-channel and M-channel

(1) If 120575 lt 1199053 when 120573 isin (0 23) then 120597119901MD119898

120597120575 =

(2 minus 3120573)4120573 gt 0 120597119901M119898120597120575 = minus1120573 lt 0 but when 120573 isin

(23 1) then 120597119901MD119898

120597120575 = (2 minus 3120573)4120573 lt 0 120597119901M119898120597120575 =

minus1120573 lt 0(2) If 120575 gt 1199053 when 120573 isin (0 23) then 120597119901

MD119898

120597120575 =

120597119901M119898120597120575 gt 0 but when 120573 isin (23 1) then 120597119901MD

119898120597120575 =

120597119901M119898120597120575 lt 0

Proposition 22 indicates that themanufacturer should setthe retail prices at her Internet store differentially across the

8 Mathematical Problems in Engineering

MD-channel and M-channel and raise or lower the prices inthe light of consumersrsquo disutility of buying the product fromInternet store More specifically if the consumersrsquo disutilityof buying from Internet store is low enough (ie 120575 lt 1199053)the manufacturer can raise the retail price at her Internetstore with increasing consumersrsquo disutility of buying fromInternet store when the dominant retailerrsquos bargaining poweris relatively small (ie 120573 lt 23) and the dominant retailerdoes not open Internet store However if the dominantretailer also opens an Internet store the manufacturer shouldlower the retail price at her Internet store so as to attractconsumers to buy the product from her Internet store On thecontrary if the consumersrsquo disutility of buying from Internetstore is relatively larger (ie 120575 gt 1199053) and the dominantretailer also opens an Internet store then the manufacturershould set the same price with the dominant retailerrsquos andadjust the price following the dominant retailer

Proposition 23 Given that the dominant retailerrsquos bargainingpower we obtain the following results about dominant retailerrsquosretail price under RD-channel MD-channel and M-channel

(1) If 120575 lt 1199053 then 120597119901RD119903120597120575 = minus1 lt 0 120597119901MD

119903120597120575 = 12120573 gt

0 and 120597119901M119903120597120575 = minus1120573 lt 0

(2) If 120575 gt 1199053 then 120597119901RD119903120597120575 = minus1 lt 0 120597119901

MD119903

120597120575 =

12120573 gt 0 and 120597119901M119903120597120575 = 12120573 gt 0

Proposition 23 indicates that no matter when the con-sumersrsquo disutility of buying from Internet store is small orlarger the dominant retailer should lower the retail price withincreasing consumersrsquo disutility buying from Internet store inthe RD-channel but in the MD-channel he always raises theretail price with increasing consumersrsquo disutility Howeverin the M-channel when consumersrsquo disutility buying fromInternet store is low enough (ie 120575 lt 1199053) he should lowerthe price with increasing consumersrsquo disutility but whenconsumersrsquo disutility is relatively larger (ie 120575 gt 1199053) he canset the price same as the price in the MD-channel and raisethe price with increasing consumersrsquo disutility

6 Numerical Examples

In this section we present numerical examples to illustratethe theoretical results about impacts of consumersrsquo disutilityof buying from Internet store on the manufacturer anddominant retailerrsquos pricing policies with different bargainingpower for the dominant retailerrsquos among RD-channel MD-channel and M-channel which are summarized in Figures2ndash11 where 119881 = 14 119905 = 6 120575 isin (0 6) and 120573 = 02 120573 = 08The parametersrsquo values satisfy the assumptions in Section 3 inorder to make the models feasible and meaningful

Comparing Figure 2 with Figure 3 we can observe thatwhen the dominant retailerrsquos bargaining power is relativelysmall (ie 120573 = 02) both of them can increase prices asincreasing consumersrsquo disutility of purchasing from Internetstore in MD-channel However when the dominant retailerrsquosbargaining power is relatively larger (ie 120573 = 08) themanufacturer has no choice but to lower the retail price soas to attract consumers to buy the product from her Internet

0 1 2 3 4 5 612

14

16

18

20

22

24

26

28

30

wMD

pMDm

pMDr

120575

Figure 2 Impacts of 120575 on prices in the MD-channel when 120573 = 02

0 1 2 3 4 5 60

1

2

3

4

5

6

7

8

wMD

pMDm

pMDr

120575

Figure 3 Impacts of 120575 on prices in the MD-channel when 120573 = 08

store In addition Figures 2 and 3 show that when consumersrsquodisutility buying from Internet store is low enough (ie 120575 lt

2) the manufacturer can set her retail price to be larger thanthe dominant retailerrsquos However when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2)the manufacturer can set her retail price to be lower than thedominant retailerrsquos

Figures 4 and 5 show that when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)both the manufacturer and dominant retailer should lowerprices to increase consumersrsquo disutility buying from Internet

Mathematical Problems in Engineering 9

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

wM

pMm

pMr

Figure 4 Impacts of 120575 on prices in the M-channel when 120573 = 02

0 1 2 3 4 5 61

2

3

4

5

6

7

8

120575

wM

pMm

pMr

Figure 5 Impacts of 120575 on prices in the M-channel when 120573 = 08

store It is noted that the rate of change of manufacturerrsquosretail price with respect to consumersrsquo disutility buying fromInternet store is equal to that of dominant retailerrsquos retailprice However when consumersrsquo disutility buying fromInternet store is relatively larger (ie 120575 gt 2) if the dominantretailerrsquos bargaining power is relatively small (ie 120573 =

02) the manufacturer can raise retail price following thedominant retailer as increasing consumersrsquo disutility buyingfrom Internet store if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 = 08) the manufacturershould cut down the retail price in her Internet store withincreasing consumersrsquo disutility

0 1 2 3 4 5 66

8

10

12

14

16

18

20

22

24

wMD

wRD

wM

120575

Figure 6 The wholesale prices in different channels when 120573 = 02

0 1 2 3 4 5 605

1

15

2

25

3

120575

wMD

wRD

wM

Figure 7 The wholesale prices in different channels when 120573 = 08

Figures 6 and 7 show that no matter whether thedominant retailerrsquos bargaining power is small or large themanufacturer can raise the wholesale price with increasingconsumersrsquo disutility buying from Internet store in the MD-channel but in the RD-channel the manufacturer shouldlower the wholesale price with increasing consumersrsquo disutil-ity However in the M-channel when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower the wholesale price withincreasing consumersrsquo disutility when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2) themanufacturer can raise the wholesale price with increasing

10 Mathematical Problems in Engineering

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

pMDm

pMm

Figure 8 Manufacturerrsquos retail prices in different channels when120573 = 02

0 1 2 3 4 5 645

5

55

6

65

7

75

120575

pMDm

pMm

Figure 9 Manufacturerrsquos retail prices in different channels when120573 = 08

consumersrsquo disutility and set the wholesale price the same asin the MD-channel

Figures 8 and 9 show that when the dominant retailerrsquosbargaining power is relatively small (ie 120573 = 02) inthe MD-channel the manufacturer can raise retail pricewith increasing consumersrsquo disutility buying from Internetstore but when the dominant retailerrsquos bargaining power isrelatively larger (ie 120573 = 08) the manufacturer should lowerretail price with increasing consumersrsquo disutility Howeverin the M-channel no matter whether the dominant retailerrsquosbargaining power is small or large when consumersrsquo disutility

0 1 2 3 4 5 65

10

15

20

25

30

120575

pRDr

pMDr

pMr

Figure 10 Dominant retailerrsquos prices in different channels when120573 =02

buying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower retail price with increasingconsumersrsquo disutility but when consumersrsquo disutility buyingfrom Internet store is relatively larger (ie 120575 gt 2) if thedominant retailerrsquos bargaining power is relatively small (ie120573 = 02) the manufacturer can raise retail price withincreasing consumersrsquo disutility buying from Internet storeif the dominant retailerrsquos bargaining power is relatively larger(ie 120573 = 08) themanufacturer should lower retail price withincreasing consumersrsquo disutility

Figures 10 and 11 show that no matter whether thedominant retailerrsquos bargaining power is small or larger healways lowers the retail price with increasing consumersrsquodisutility buying from Internet store in the RD-channel butin the MD-channel he always raises the retail price withincreasing consumersrsquo disutility However in the M-channelwhen consumersrsquo disutility buying from Internet store islow enough (ie 120575 lt 2) the dominant retailer shouldlower retail price with increasing consumersrsquo disutility butwhen consumersrsquo disutility is relatively larger (ie 120575 gt 2)the dominant retailer can raise retail price with increasingconsumersrsquo disutility buying from Internet store

7 Conclusions and Future Research

To investigate when the manufacturer and dominant retaileropen their own Internet stores with different setup costsand how set prices to ensure opening Internet stores areprofitable in a supply chain we first present the equilibriumoutcomes under four possible supply chain structures andthen discuss the strategic conditions for the manufacturerand dominant retailer when it is optimal to open an Internetstore In addition we analyze both playersrsquo pricing policies

Mathematical Problems in Engineering 11

0 1 2 3 4 5 62

4

6

8

10

12

14

120575

pMDr

pRDr

pMr

Figure 11 Dominant retailerrsquos prices in different channels when 120573 =08

after they open their Internet stores and discuss the impactsof the dominant retailerrsquos bargaining power and consumersrsquodisutility of purchasing a product from Internet store onthe manufacturer and dominant retailerrsquos pricing strategiesFinally we conduct numerical examples to illustrate thetheoretical results

We obtain some new results differing from those inthe literature We find that the optimal choices for themanufacturer and dominant retailer to open an Internetstore are largely determined by their respective setup costswhich are closely related to the dominant retailerrsquos bargainingpower and consumersrsquo disutility of buying from Internetstore It is worth mentioning that multichannel retailing forthe dominant retailer is not necessarily the best strategyIn other words if the dominant retailer opens an Internetstore the marketing plan for him to attract more consumersby charging a lower price is impossible to achieve and hecan induce the manufacturer to open an Internet store tocompetewith himOnlywhen the setup cost for the dominantretailer to open an Internet store is sufficiently low then he isprofitable

What is more we also find that the manufacturerrsquosoptimal price at her Internet store is not always being lowerthan the dominant retailerrsquos For example if the consumersrsquodisutility of buying from Internet store is sufficiently highthe manufacturer must provide strong price incentives forconsumers to purchase the product from the Internet store

Although this research provides new insights for themanufacturer and dominant retailer to open an Internetstore and set prices in a supply chain there are severaldirections that could be extended First this study assumedthat all information is known to the manufacturer anddominant retailer in our model However information couldbe asymmetric in the supply chain since both players haveprivate information about their own internal variable costs

for example the setup cost of opening an Internet storecustomersrsquo purchase patterns and search costsTherefore wecan explore the competitive equilibrium under asymmetricinformation settings Second we assume that consumersrsquodisutility of buy from Internet store is independent of theunit transportation cost which can be relaxed in the futureresearch Third trade credit is widely used in practice andhas important impact on supply chain management [39ndash41] In recent years trade credit has become one of themajor transactions between suppliers and retailers in a valuechain For example Wal-Mart Carrefour and GOME (alarge Chinese home appliance chain retailer) even delayedpayments to their suppliers for as long as one year [42]Hence it is worthy to understand how the trade creditaffects supply channel configuration together with pricingstrategies in the E-commerce market A final issue worthyof investigation is how different types of customers affectthe manufacturer and dominant retailerrsquos channel selectionstrategies We leave these questions for future research

Appendices

A Equilibrium Outcome ofthe Four Channel Structures

Proof of Lemma 6 (1) In the T-channel both the manufac-turer and dominant retailer do not open their Internet storesThere is only the dominant retailerrsquos physical store in themarket So the dominant retailer acts as a monopolist andoptimally charges a price 119881 minus 119905 such that the market isjust covered For the manufacturer given that the dominantretailerrsquos optimal retail price the optimal wholesale price is119908

T= (1 minus 120573)(119881 minus 119905) Since the manufacturer produces

the product at a constant unit (marginal) cost which isnormalized to zero and the market is just covered that is thesize of the market is one the profit for the manufacturer isprod

T119898= (1minus120573)(119881minus119905) Accordingly the profit for the dominant

retailer isprodT119903= 120573(119881 minus 119905)

(2) In RD-channel only the dominant retailer opens anInternet store (RIS) If a consumer locates at a distance fromphysical store (PS) he will get a net utility of by purchasingthe product from PS and a net utility of by purchasing theproduct from RIS To ensure the full market coverage thedominant retailer charges the monopoly price 119881 minus 120575 acrosshis two stores and sells the product to all consumers Forthe manufacturer given the dominant retailerrsquos optimal retailprice the optimal wholesale price is 119908RD

= (1 minus 120573)(119881 minus 120575)Since the manufacturer produces the product at a constantunit (marginal) cost which is normalized to zero and 119905 thesize of the market is one the profits for the manufacturer anddominant retailer are prodRD

119898= (1 minus 120573)(119881 minus 120575) and prod

RD119903

=

120573(119881 minus 120575) respectively(3) In MD-channel the manufacturer opens an Internet

store but dominant retailer does not So consumers canhave convenient access to the product through the dominantretailerrsquos physical store (PS) at price 119901

119903or the manufacturerrsquos

Internet store (MIS) at price 119901119898 their decision about which

store to buy revolves around the comparison of their net

12 Mathematical Problems in Engineering

utility derived fromPS119880PS = 119881minus119901119903minus119905119909 and119880MIS = 119881minus119901119898minus120575by buying the product from MIS Therefore the marginalconsumers are located at 119909 = (119901

119898minus 119901119903+ 120575)119905 So the profit

functions for the manufacturer and dominant retailer can bewritten as

prod

119898

= 119908[

(119901119898minus 119901119903+ 120575)

119905

] + 119901119898[

(119901119903minus 119901119898+ 119905 minus 120575)

119905

] minus 119865119898

(A1)

prod

119903

= (119901119903minus 119908) [

(119901119898minus 119901119903+ 120575)

119905

] (A2)

Under the assumption proposed in Section 3 the dom-inant retailer is the price leader and the manufacturer isthe follower As before the game is solved backwards Inthis market we firstly need to calculate the manufacturerrsquosoptimal price given any dominant retailerrsquos price

Themanufacturerrsquos reaction function can be derived fromthe first-order condition

120597prod119898

120597119901119898

=

[(2 minus 120573) 119901119903minus 2119901119898+ 119905 minus 120575]

119905

= 0

that is 119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A3)

Substituting (A3) into (A2) we get

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

(A4)

Taking the first-order derivative of (A4) with respect to119901119903and letting the derivative be zero we have

119901MD119903

=

(119905 + 120575)

2120573

(A5)

Given the wholesale price bargaining process we canobtain the manufacturerrsquos optimal wholesale price 119908MD

=

(1 minus 120573)(119905 + 120575)2120573 and substituting (A5) into (A3) we getthe manufacturerrsquos optimal retail price

119901MD119898

=

(2 + 120573) 119905 + (2 minus 3120573) 120575

4120573

(A6)

Substituting (A5) and (A6) into (A1) and (A2) wecan obtain the equilibrium profits for the manufacturers anddominant retailer respectively

MDprod

119898

=

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus 119865119898

MDprod

119903

=

(119905 + 120575)2

8119905

(A7)

Proof of Lemma 7 In the M-channel both the manufacturerand dominant retailer simultaneously open their own Inter-net stores then customers are able to purchase a product

either from the dominant retailerrsquos physical store (PS) or fromthe alternative Internet stores (MISRIS) They can get a netutility of 119880PS = 119881 minus 119901

119903minus 119905119909 by buying the product from PS

and a net utility of 119880MIS = 119881 minus 119901119898minus 120575 by buying the product

fromMIS and a net utility of119880RIS = 119881minus 119901119903minus 120575 by buying the

product from RISAccording to the basicmodel we know that the dominant

retailer firstmakes pricing decision as the price leader and themanufacturer is the follower If the dominant retailer chargesa price higher than the manufacturerrsquos price (119901

119903gt 119901119898) then

no consumer will buy the product from his Internet storeUnder this condition the dominant retailer makes no sale inhis Internet store and makes a profit of minus119865

119903 Therefore the

demand functions for the manufacturerrsquos Internet store anddominant retailerrsquos physical store are given respectively asfollows

119863MIS =(119901119903minus 119901119898+ 119905 minus 120575)

119905

(A8)

119863PS =(119901119898minus 119901119903+ 120575)

119905

(A9)

Hence the manufacturerrsquos profit function can be written as

prod

119898

=

[119908 (119901119898minus 119901119903+ 120575) + 119901

119898(119901119903minus 119901119898+ 119905 minus 120575)]

119905

minus 119865119898

(A10)

From the first-order condition we have

119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A11)

Given the condition of 119901119903gt 119901119898 this implies that 119901

119903gt (119905 minus

120575)120573 However when 119901119903le (119905 minus 120575)120573 and 119901

119903gt 119901119898 we always

have 120597prodM119898120597119901119898= [(2 minus 120573)119901

119903minus 2119901119898+ 119905 minus 120575]119905 gt 0

Therefore the manufacturer optimally sets its price at119901119898= 119901119903 and her optimal pricing schedule is as follows

119901119898=

119901119903 119901

119903le

119905 minus 120575

120572

(2 minus 120573) 119901119903+ 119905 minus 120575

2

119901119903gt

119905 minus 120575

120572

(A12)

Given the manufacturerrsquos pricing schedule the dominantretailerrsquos profit is given as follows

prod

119903

=

(119901119903minus 119908)

120575

119905

minus 119865119903 119901

119903le

119905 minus 120575

120573

(119901119903minus 119908)

119905 + 120575 minus 120573119901119903

2119905

minus 119865119903 119901119903gt

119905 minus 120575

120573

(A13)

Under the condition of 119901119903gt (119905 minus 120575)120573 the dominant

retailerrsquos profit is

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

minus 119865119903 (A14)

Taking the first-order derivative of (A14) with respect to 119901119903

and letting the derivative be zero we have 119901M119903= (119905 + 120575)2120573

Mathematical Problems in Engineering 13

Submitting it into (A11) we get the manufacturerrsquos optimalprice in her Internet store 119901M

119898= [(2 + 120573)119905 + (2 minus 3120573)120575]4120573

Hence the manufacturer and dominant retailerrsquos optimalprofits are prodM

119898= (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus 119865119898

andprodM119903= (119905 + 120575)

2

8119905 minus 119865119903 respectively

According to the previous assumption 119901119903gt (119905 minus 120575)120573

which implies that (119905 + 120575)2120573 gt (119905 minus 120575)120573 120575must satisfy 120575 gt1199053 However when 120575 lt 1199053 we always have

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](minus)

gt 0

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](+)

lt 0 (A15)

So the dominant retailerrsquos optimal retail price in the M-channel is 119901M

119903= (119905 minus 120575)120573 Therefore the manufacturer and

dominant retailerrsquos optimal profits areprodM119898= (119905 minus 120575)120573 minus [(119905 minus

120575)120575]119905 minus 119865119898andprodM

119903= [(119905 minus 120575)120575]119905 minus 119865

119903 respectively

B Strategic Conditions forOpening an Internet Store

Proofs of Proposition 8 and Corollary 9 From Lemma 6 weanalyse the equilibrium profits for the dominant retailerbetween the T-channel and RD-channel and note that onlywhen 119865

119903lt 120573(119905 minus 120575) then prodRD

119903gt prod

T119903 This implies that as

long as the setup cost of opening an Internet store satisfies119865119903

lt 120573(119905 minus 120575) ≜ 1198611 it is always optimal to open an

Internet store for the dominant retailer In addition we notethat 120597119861

1120597120575 = minus120573 lt 0 So the dominant retailerrsquos strategic

motive for opening an Internet store would be weakened byincreasing consumersrsquo disutility of purchasing a product fromInternet store

Proofs of Proposition 10 and Corollary 11 From Lemma 6 weanalyse the equilibrium profits for the manufacturer betweenthe T-channel and MD-channel and note that only when thesetup cost of opening an Internet store satisfies 119865

119898lt (119905 +

120575)2120573+[(119905minus120575)2

minus12119905120575]16119905minus(1minus120573)(119881minus119905) ≜ 1198612 thenprodMD

119898gt

prodT119898 In addition we note that 120597119861

2120597120575 = [4119905 minus 120573(7119905 minus 120575)]8120573119905

and find when 0 lt 120573 lt 4119905(7119905 minus 120575) then 1205971198612120597120575 gt 0 and

when 4119905(7119905 minus 120575) lt 120573 lt 1 then 1205971198612120597120575 lt 0

Proofs of Proposition 12 and Corollary 13 FromLemmas 6 and7 we analyse the equilibriumprofits for themanufacturer anddominant retailer between the T-channel andM-channel wenote that under the condition of 120575 lt 1199053 only when the setupcosts of opening an Internet store for the manufacturer anddominant retailer simultaneously satisfy

119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198613

119865119903lt

[(119905 minus 120575) 120575]

119905

minus 120573 (119881 minus 119905) ≜ 1198614

(B1)

thenMprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B2)

Similarly under the condition of 120575 gt 1199053 only when thesetup costs of opening an Internet store for the manufacturerand dominant retailer simultaneously satisfy

119865119898lt

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198615

119865119903lt

(119905 + 120575)2

8119905

minus 120573 (119881 minus 119905) ≜ 1198616

(B3)

then

Mprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B4)

In addition we note that both 1205971198613120597120575 = minus[119905 + 120573(119905 minus

2120575)]120573119905 lt 0 and 1205971198614120597120575 = (119905 minus 2120575)119905 gt 0 are held under

the condition of 120575 lt 1199053 Furthermore under the conditionof 120575 gt 1199053 we also find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198615120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

5120597120575 lt 0

1205971198616120597120575 = 2(119905 + 120575)8119905 gt 0

Proofs of Proposition 14 and Corollary 15 From Lemmas 6and 7 we analyse the manufacturerrsquos equilibrium profits inthe RD-channel and M-channel we note that under thecondition of 120575 lt 1199053 only when the setup cost of opening anInternet store for her satisfies 119865

119898lt (119905 minus 120575)120573 minus [(119905 minus 120575)120575]119905 minus

(1 minus 120573)(119881 minus 120575) ≜ 1198617 thenprodM

119898gt prod

RD119898 In addition we find

1205971198617120597120575 = minus[(1 + 120573

2

)119905 minus 2120573120575]120573119905 lt 0But under the condition of 120575 gt 1199053 only when the setup

cost of opening an Internet store for her satisfies 119865119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 120575) ≜ 1198618 then

prodM119898gt prod

RD119898 In addition 120597119861

8120597120575 = [120573(119905+120575)+4119905(1minus2120573

2

)]8120573119905

we find that when 0 lt 120573 lt [(119905 + 120575) + radic(119905 + 120575)2

+ 1281199052]16119905

then 1205971198618120597120575 gt 0 andwhen [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905 lt

120573 lt 1 then 1205971198618120597120575 lt 0

Proofs of Proposition 16 From Lemmas 6 and 7 we analysethe dominant retailerrsquos equilibriumprofits in theMD-channeland M-channel and note that when 120575 lt 1199053 then prod

M119903minus

prodMD119903

= minus(119905 minus 3120575)2

8119905 minus 119865119903lt 0 and when 120575 gt 1199053

then prodM119903minus prod

MD119903

= minus119865119903lt 0 These imply that when the

manufacturer has operated an Internet store the best choicefor dominant retailer is not to open an Internet store

Proofs of Proposition 17 and Corollary 18 From Lemmas 6and 7 we analyse the dominant retailerrsquos equilibrium profitsin the MD-channel and M-channel and note that under thecondition of 120575 lt 1199053 thenprodM

119898minus prod

MD119898

= [8119905(119905 minus 3120575) minus 120573[(119905 +

120575)2

minus 161205752

]8119905]16120573119905 This implies that the manufacturer willopen her Internet store when the dominant retailer opens an

14 Mathematical Problems in Engineering

Internet store and the setup costs of opening an Internet storefor her satisfies

1198619≜

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

lt 119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

≜ 11986110

(B5)

In addition we find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198619120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

9120597120575 lt 0

and 12059711986110120597120575 = minus[119905 + 120573(119905 minus 2120575)]120573119905 lt 0

C The ManufacturerDominantRetailers Pricing Policies

Proof of Proposition 19 In the MD-channel we respectivelydifferentiate between119901MD

119898and119901MD

119903with respect to 120573 and find

that 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0 For any given120573 differentiating between 119901MD

119898and 119901MD

119903with respect to 120575 we

have 120597119901MD119903

120597120575 = 12120573 gt 0 and 120597119901MD119898

120597120575 = (2 minus 3120573)4120573and if 120573 isin (0 23) then 120597119901MD

119898120597120575 gt 0 if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 In addition we find that 119901MD119898

minus 119901MD119903

= (119905 minus

3120575)4 it is obvious that when 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

when 120575 = 1199053 then 119901MD

119898= 119901

MD119903

and when 120575 gt 1199053 then119901MD119898

lt 119901MD119903

Proof of Proposition 20 In the M-channel we respectivelydifferentiate between 119901M

119898and 119901M

119903with respect to 120573 and find

that when 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0

and when 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 For any given 120573 we respectively differentiate between 119901M119898

and 119901M119903with respect to 120575 and find that when 120575 lt 1199053 then

120597119901M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0 when 120575 gt 1199053 then

120597119901M119898120597120575 = (2 minus 3120573)4120573 and 120597119901M

119903120597120575 = 12120573 gt 0

It is easy to note that when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0

but when 120573 isin (23 1) then 120597119901M119898120597120575 lt 0

Proof of Proposition 21 From Lemmas 6 and 7 we note that120597119908

RD120597120575 = minus(1 minus 120573) lt 0 and 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0In addition if 120575 lt 1199053 then 120597119908M

120597120575 = minus(1 minus 120573)120573 lt 0 if120575 gt 1199053 then 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0

Proof of Proposition 22 From the proofs of Propositions 19and 20 we note that when 120575 lt 1199053 if 120573 isin (0 23) then120597119901

MD119898

120597120575 gt 0 120597119901M119898120597120575 lt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 120597119901M119898120597120575 lt 0 when 120575 gt 1199053 if 120573 isin (0 23)

then 120597119901MD119898

120597120575 = 120597119901M119898120597120575 gt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 = 120597119901M119898120597120575 lt 0

Proof of Proposition 23 From Lemmas 6 and 7 we note that120597119901

RD119903120597120575 = minus1 lt 0 and 120597119901MD

119903120597120575 = 12120572 gt 0 In addition if

120575 lt 1199053 then 120597119901M119903120597120575 = minus1120572 lt 0 if 120575 gt 1199053 then 120597119901M

119903120597120575 =

12120572 gt 0

Abbreviations

UK The consumerrsquos utility of purchasing theproduct from K storeK isin PSRISMIS

119881 The value of consumers willing to payfor the product

120575 The consumersrsquo disutility of purchasingthe product from Internet store(MISRIS)

119905 The per unit transportation cost ofpurchasing the product from physicalstore (PS)

120573 The dominant retailerrsquos bargainingpower in the distribution channel

119908j The manufacturerrsquos wholesale price in

the j-channel j isin TRDMDM

119901j119903 The dominant retailerrsquos price in the

j-channel j isin TRDMDM

119901j119898 The manufacturerrsquos price in the

j-channel j isin MDM

119865119898119865119903 The setup cost of opening an Internetstore by the manufacturerdominantretailer

Πj119898Πj119903 The manufacturerdominant retailerrsquosprofit in the j-channelj isin TRDMDM

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been supported by theNational Natural Sci-ence Foundation of China (71271225) Chongqingrsquos NaturalScience Foundation (cstc2012jjA1404) and the Open Fund ofChongqing Key Laboratory of Logistics (CQKLL12001)

References

[1] L Hsiao and Y-J Chen ldquoStrategic motive for introducinginternet channels in a supply chainrdquo Production and OperationsManagement vol 23 no 1 pp 36ndash47 2014

[2] I Geyskens K Gielens and M G Dekimpe ldquoThe marketvaluation of Internet channel additionsrdquo Journal of Marketingvol 66 no 2 pp 102ndash119 2002

[3] 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

[4] S-H Chun and J-C Kim ldquoPricing strategies in B2C electroniccommerce analytical and empirical approachesrdquo Decision Sup-port Systems vol 40 no 2 pp 375ndash388 2005

[5] S K Mukhopadhyay X Zhu and X Yue ldquoOptimal contractdesign for mixed channels under information asymmetryrdquoProduction and Operations Management vol 17 no 6 pp 641ndash650 2008

Mathematical Problems in Engineering 15

[6] G S Cai ldquoChannel selection and coordination in dual-channelsupply chainsrdquo Journal of Retailing vol 86 no 1 pp 22ndash36 2010

[7] K Takahashi T Aoi D Hirotani and K Morikawa ldquoInventorycontrol in a two-echelon dual-channel supply chain with setupof production and deliveryrdquo International Journal of ProductionEconomics vol 133 no 1 pp 403ndash415 2011

[8] D W Carlton and J A Chevalier ldquoFree riding and salesstrategies for the Internetrdquo Journal of Industrial Economics vol49 no 4 pp 441ndash461 2001

[9] K D Antia M Bergen and S Dutta ldquoCompeting with graymarketsrdquoMIT SloanManagement Review vol 46 no 1 pp 63ndash69 2004

[10] J Shin ldquoHow does free riding on customer service affectcompetitionrdquo Marketing Science vol 26 no 4 pp 488ndash5032007

[11] G Iyer and J M Villas-Boas ldquoA bargaining theory of distribu-tion channelsrdquo Journal of Marketing Research vol 40 no 1 pp80ndash100 2003

[12] A Dukes and Y Liu ldquoIn-store media and distribution channelcoordinationrdquoMarketing Science vol 29 no 1 pp 94ndash107 2010

[13] H Ahn I Duenyas and R Zhang ldquoPrice competition betweenretailers and manufacturer-owned storesrdquoWorking Paper Uni-versity of California at Berkeley 2002

[14] K Cattani W Gilland H S Heese and J SwaminathanldquoBoiling frogs pricing strategies for a manufacturer addinga direct channel that competes with the traditional channelrdquoProduction and Operations Management vol 15 no 1 pp 40ndash56 2006

[15] K-Y Chen M Kaya and O Ozer ldquoDual sales channel man-agement with service competitionrdquo Manufacturing and ServiceOperations Management vol 10 no 4 pp 654ndash675 2008

[16] G Hua S Wang and T C E Cheng ldquoPrice and lead timedecisions in dual-channel supply chainsrdquo European Journal ofOperational Research vol 205 no 1 pp 113ndash126 2010

[17] W S Yoo andE Lee ldquoInternet channel entry a strategic analysisof mixed channel structuresrdquo Marketing Science vol 30 no 1pp 29ndash41 2011

[18] Y Xiong W Yan K Fernandes Z-K Xiong and N GuoldquoldquoBricks vs clicksrdquo the impact of manufacturer encroachmentwith a dealer leasing and selling of durable goodsrdquo EuropeanJournal of Operational Research vol 217 no 1 pp 75ndash83 2012

[19] Q Lu and N Liu ldquoPricing games of mixed conventional ande-commerce distribution channelsrdquo Computers and IndustrialEngineering vol 64 no 1 pp 122ndash132 2013

[20] Q Xu Z Liu and B Shen ldquoThe impact of price comparisonservice on pricing strategy in a dual-channel supply chainrdquoMathematical Problems in Engineering vol 2013 Article ID613528 13 pages 2013

[21] C A Ingene and M E Parry ldquoChannel coordination whenretailers competerdquoMarketing Science vol 14 no 4 pp 360ndash3771995

[22] 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

[23] J Raju and Z J Zhang ldquoChannel coordination in the presenceof a dominant retailerrdquoMarketing Science vol 24 no 2 pp 254ndash262 2005

[24] K L Webb and C J Lambe ldquoInternal multi-channel conflictan exploratory investigation and conceptual frameworkrdquo Indus-trial Marketing Management vol 36 no 1 pp 29ndash43 2007

[25] S K Mukhopadhyay D-Q Yao and X Yue ldquoInformationsharing of value-adding retailer in a mixed channel hi-techsupply chainrdquo Journal of Business Research vol 61 no 9 pp950ndash958 2008

[26] R Yan ldquoManaging channel coordination in a multi-channelmanufacturer-retailer supply chainrdquo Industrial Marketing Man-agement vol 40 no 4 pp 636ndash642 2011

[27] E Cao YMa CWan andM Lai ldquoContracting with asymmet-ric cost information in a dual-channel supply chainrdquoOperationsResearch Letters vol 41 no 4 pp 410ndash414 2013

[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] Y Liu S Gupta and Z J Zhang ldquoNote on self-restraint as anonline entry-deterrence strategyrdquoManagement Science vol 52no 11 pp 1799ndash1809 2006

[30] Z Cheng and B R Nault ldquoInternet channel entry retailcoverage and entry cost advantagerdquo Information Technology andManagement vol 8 no 2 pp 111ndash132 2007

[31] X Zhang ldquoRetailersrsquo multichannel and price advertising strate-giesrdquoMarketing Science vol 28 no 6 pp 1080ndash1094 2009

[32] W Huang and J M Swaminathan ldquoIntroduction of a secondchannel implications for pricing and profitsrdquo European Journalof Operational Research vol 194 no 1 pp 258ndash279 2009

[33] H Hotelling ldquoStability in competitionrdquo The Economic Journalvol 39 no 153 pp 41ndash57 1929

[34] J Zhang ldquoThe perils of behavior-based personalizationrdquo Mar-keting Science vol 30 no 1 pp 170ndash186 2011

[35] T Kabiraj and C Lee ldquoLicensing contracts in hotelling struc-turerdquoTheoretical Economics Letters vol 1 no 3 pp 57ndash62 2011

[36] HWang andTNariu ldquoDistribution channelmanagement in aninternet age equilibrium and social welfarerdquo Journal of IndustryCompetition and Trade vol 12 no 3 pp 285ndash298 2012

[37] M Lijesen ldquoHotellingrsquos webshoprdquo Journal of Economics vol 109no 2 pp 193ndash200 2013

[38] R Gulati and J Garino ldquoGet the right mix of bricks amp clicksrdquoHarvard Business Review vol 78 no 3 pp 107ndash214 2000

[39] K-J Chung S-D Lin and H M Srivastava ldquoThe completesolution procedures for the mathematical analysis of somefamilies of optimal inventorymodels with order-size dependenttrade credit and deterministic and constant demandrdquo AppliedMathematics and Computation vol 219 no 1 pp 142ndash157 2012

[40] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels under conditional trade credit in a supply chain systemrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 24 pp10036ndash10052 2013

[41] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels for deteriorating items in the discounted cash-flowsapproach under conditional trade credit and cash discount ina supply chain systemrdquo Applied Mathematics and InformationSciences vol 8 no 5 pp 2103ndash2111 2014

[42] J Luo and Q Zhang ldquoTrade credit a new mechanism tocoordinate supply chainrdquo Operations Research Letters vol 40no 5 pp 378ndash384 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

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Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

consumersrsquo disutility of purchasing a product fromInternet store Otherwise her strategic motive would beweakened

Proposition 16 Suppose that the manufacturer has operatedan Internet store the best choice for dominant retailer is not toopen an Internet store

Proposition 16 implies that under the condition of themanufacturer has operated an Internet store regardless ofconsumersrsquo disutility of purchasing a product from Internetstore is small or larger it is best for the dominant retailer notto open an Internet store Otherwise his profit will decreasedue to costly setup cost or the manufacturerrsquos low pricestrategy that attract more consumers to buy the product fromher Internet store

Proposition 17 Suppose that the manufacturer has notopened an Internet store if consumersrsquo disutility of purchasinga product from Internet store is low enough (ie 120575 lt 1199053) andthe setup cost of opening an Internet store for the manufactureris intermediate 119865

119898isin [(119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 (119905 minus

120575)120573 minus (119905 minus 120575)120575119905] the dominant retailer opening an Internetstore can lead to the well-known contagion-like effect

Proposition 17 implies that under the condition of themanufacturer has not opened an Internet store when con-sumersrsquo disutility of purchasing a product from Internet storeis relatively small and the set-up cost of opening an Internetstore for the manufacturer is intermediate the dominantretailerrsquos Internet store entry may induce the manufacturerto open her own Internet store competing with him

FromProposition 17 we observe that the upper and lowerbounds of 119865

119898are related to 120575 for a given 120573 so we have the

following corollary

Corollary 18 When consumersrsquo disutility of purchasing aproduct from Internet store is low enough (ie 120575 lt 1199053) ifthe dominant retailerrsquos bargaining power is relatively small (ie120573 lt 4119905(7119905minus120575)) the contagion-like effect would be expanded byincreasing consumersrsquo disutility of purchasing a product fromInternet store However if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 gt 4119905(7119905 minus 120575)) the contagion-like effect would be diminished

Based on aforementioned propositions we now showwhen do the manufacturer and dominant retailer open theirown Internet stores to a traditional supply chain and how dothey set prices after opening Internet stores in Table 3

5 Analytical Results onBoth Playersrsquo Pricing Policies

From Lemmas 6 and 7 we know that the T-channel andRD-channel are monopoly settings So the dominant retailercharges the optimal monopoly price and sells the productto all consumers However under the MD-channel and M-channel the manufacturer and dominant retailer engage in

price competition To investigate the impacts of the dom-inant retailerrsquos bargaining power and consumersrsquo disutilityof purchasing a product from Internet store on the manu-facturer and dominant retailerrsquos pricing strategies we obtainthe following propositions and the proofs are provided inAppendix C

Proposition 19 Suppose that only the manufacturer can openan Internet store then

(1) 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0(2) 120597119901MD

119903120597120575 = 12120573 gt 0 and 120597119901MD

119898120597120575 = (2 minus 3120573)4120573

and if 120573 isin (0 23) then 120597119901MD119898

120597120575 gt 0 if 120573 isin (23 1)then 120597119901MD

119898120597120575 lt 0

(3) if 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

if 120575 = 1199053 then 119901MD119898

=

119901MD119903

and if 120575 gt 1199053 then 119901MD119898

lt 119901MD119903

Proposition 19 indicates that when the manufacturer canopen an Internet store

(1) she should also lower the price to induce consumersto purchase the product from her Internet store asthe increasing dominant retailerrsquos bargaining powerotherwise the dominant retailer will also provideprice incentives for consumers to buy the productfrom his physical store

(2) if the dominant retailerrsquos bargaining power is rela-tively small (ie 120573 lt 23) she should raise the pricein her Internet store with increasing consumersrsquo disu-tility However if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 gt 23) she should cutdown the price in her Internet store with increasingconsumersrsquo disutility

(3) if consumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) shemust provide strong price incentives for consumersto purchase the product from her Internet storeotherwise her profits will cut down owing to someconsumers buying the product from the dominantretailerrsquos physical store on the contrary the domi-nant retailer will provide strong price incentives forconsumers to purchase the product from his physicalstore when consumersrsquo disutility of purchasing aproduct from Internet store is low enough (ie 120575 lt

1199053) then the manufacturerrsquos retail price is higherthan the dominant retailerrsquos If and only if consumersrsquodisutility of purchasing a product from Internet storesatisfies 120575 = 1199053 the manufacturer can set her retailprice to be equal to the dominant retailerrsquos

Proposition 20 Suppose that both the manufacturer anddominant retailer can open their Internet stores simultaneouslythen

(1) If 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0120597119901

M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0

(2) If 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 120597119901M119898120597120575 = (2 minus 3120573)4120573 120597119901M

119903120597120575 = 12120573 gt 0 and

Mathematical Problems in Engineering 7

Table 3 Strategic conditions for opening Internet stores to T-channel and pricing policies

Strategic conditions M and Rrsquos activities Pricing policiesM has not opened an Internet store and119865119903lt 120573(119905 minus 120575)

R can open an Internet store Monopoly pricing

R has not opened an Internet store and119865119898lt (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905)

M can open an Internet store

When 120575 lt 1199053then 119901MD

119898gt 119901

MD119903

When 120575 = 1199053then 119901MD

119898= 119901

MD119903

When 120575 gt 1199053then 119901MD

119898lt 119901

MD119903

When 120575 lt 1199053 119865119903lt (119905 minus 120575)120575119905 minus 120573(119881 minus 119905) and

119865119898lt (119905 minus 120575)120573 minus (119905 minus 120575)120575119905 minus (1 minus 120573)(119881 minus 119905)

Both M and R can open their Internet stores simultaneously119901M119898= 119901

M119903

When 120575 gt 1199053 119865119903lt (119905 + 120575)

2

8119905 minus 120573(119881 minus 119905) and119865119898lt (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905)

119901M119898lt 119901

M119903

when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0 but when 120573 isin

(23 1) then 120597119901M119898120597120575 lt 0

(3) If 120575 le 3119905 then 119901M119898= 119901

M119903 if 120575 gt 1199053 then 119901M

119898lt 119901

M119903

Proposition 20 indicates when both the manufacturerand dominant retailer can open their Internet stores simul-taneously

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) bothof them can set same price and lower prices as theincreasing consumersrsquo disutility On the contrary ifconsumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) themanufacturer must provide lower price incentivesthan the dominant retailer which may induce con-sumers to purchase the product from her Internetstore It should be pointed out that when the dom-inant retailerrsquos bargaining power is relatively small(ie 120573 lt 23) the manufacturerrsquos price increaseswith increasing consumersrsquo disutility but when thedominant retailerrsquos bargaining power is relativelylarger (ie 120573 gt 23) the manufacturerrsquos retail pricedecreases with increasing consumersrsquo disutility

(2) When consumersrsquo disutility of purchasing a prod-uct from Internet store is low enough (ie 120575 lt

1199053) the dominant retailerrsquos price decreases reducewith increasing consumersrsquo disutility but when con-sumersrsquo disutility of purchasing a product from Inter-net store is relatively larger (ie 120575 gt 1199053) thedominant retailerrsquos price decreases with increasingconsumersrsquo disutility Speaking frankly that is thedominant retailerrsquos smart pricing strategiesThe dom-inant retailer will raise the retail price when mostof consumers with a large disutility of purchasing aproduct from Internet store buy the product from hisphysical store and lower the retail price when mostof consumers with a small disutility of purchasing aproduct from Internet store buy the product from themanufacturerrsquos Internet store

Proposition 21 Given that the dominant retailerrsquos bargainingpower we obtain the following results about the manufacturerrsquoswholesale price under RD-channel MD-channel and M-channel

(1) 120597119908RD120597120575 = minus(1 minus 120573) lt 0

(2) 120597119908MD120597120575 = (1 minus 120573)2120573 gt 0

(3) if 120575 lt 1199053 then 120597119908M120597120575 = minus(1 minus 120573)120573 lt 0 if 120575 gt 1199053

then 120597119908M120597120575 = (1 minus 120573)2120573 gt 0

Proposition 21 indicates that the manufacturer should setthe wholesale prices differentially across the RD-channelMD-channel andM-channel and raise or lower thewholesaleprices in the light of consumersrsquo disutility of buying theproduct from Internet store More specifically the man-ufacturer can lower the wholesale price with increasingconsumersrsquo disutility of buying the product from Internetstore in the RD-channel but in theMD-channel she can raisethe wholesale price with increasing consumersrsquo disutility ofbuying from Internet store However in theM-channel whenthe consumersrsquo disutility of buying from Internet store is lowenough (ie 120575 lt 1199053) she can lower the wholesale pricewith increasing consumersrsquo disutility but when consumersrsquodisutility of buying from Internet store is relatively larger (ie120575 gt 1199053) she should raise the wholesale price with increasingconsumersrsquo disutility

Proposition 22 Given that the dominant retailerrsquos bargainingpower we obtain the following results about the manufacturerrsquosretail price at her Internet store under MD-channel and M-channel

(1) If 120575 lt 1199053 when 120573 isin (0 23) then 120597119901MD119898

120597120575 =

(2 minus 3120573)4120573 gt 0 120597119901M119898120597120575 = minus1120573 lt 0 but when 120573 isin

(23 1) then 120597119901MD119898

120597120575 = (2 minus 3120573)4120573 lt 0 120597119901M119898120597120575 =

minus1120573 lt 0(2) If 120575 gt 1199053 when 120573 isin (0 23) then 120597119901

MD119898

120597120575 =

120597119901M119898120597120575 gt 0 but when 120573 isin (23 1) then 120597119901MD

119898120597120575 =

120597119901M119898120597120575 lt 0

Proposition 22 indicates that themanufacturer should setthe retail prices at her Internet store differentially across the

8 Mathematical Problems in Engineering

MD-channel and M-channel and raise or lower the prices inthe light of consumersrsquo disutility of buying the product fromInternet store More specifically if the consumersrsquo disutilityof buying from Internet store is low enough (ie 120575 lt 1199053)the manufacturer can raise the retail price at her Internetstore with increasing consumersrsquo disutility of buying fromInternet store when the dominant retailerrsquos bargaining poweris relatively small (ie 120573 lt 23) and the dominant retailerdoes not open Internet store However if the dominantretailer also opens an Internet store the manufacturer shouldlower the retail price at her Internet store so as to attractconsumers to buy the product from her Internet store On thecontrary if the consumersrsquo disutility of buying from Internetstore is relatively larger (ie 120575 gt 1199053) and the dominantretailer also opens an Internet store then the manufacturershould set the same price with the dominant retailerrsquos andadjust the price following the dominant retailer

Proposition 23 Given that the dominant retailerrsquos bargainingpower we obtain the following results about dominant retailerrsquosretail price under RD-channel MD-channel and M-channel

(1) If 120575 lt 1199053 then 120597119901RD119903120597120575 = minus1 lt 0 120597119901MD

119903120597120575 = 12120573 gt

0 and 120597119901M119903120597120575 = minus1120573 lt 0

(2) If 120575 gt 1199053 then 120597119901RD119903120597120575 = minus1 lt 0 120597119901

MD119903

120597120575 =

12120573 gt 0 and 120597119901M119903120597120575 = 12120573 gt 0

Proposition 23 indicates that no matter when the con-sumersrsquo disutility of buying from Internet store is small orlarger the dominant retailer should lower the retail price withincreasing consumersrsquo disutility buying from Internet store inthe RD-channel but in the MD-channel he always raises theretail price with increasing consumersrsquo disutility Howeverin the M-channel when consumersrsquo disutility buying fromInternet store is low enough (ie 120575 lt 1199053) he should lowerthe price with increasing consumersrsquo disutility but whenconsumersrsquo disutility is relatively larger (ie 120575 gt 1199053) he canset the price same as the price in the MD-channel and raisethe price with increasing consumersrsquo disutility

6 Numerical Examples

In this section we present numerical examples to illustratethe theoretical results about impacts of consumersrsquo disutilityof buying from Internet store on the manufacturer anddominant retailerrsquos pricing policies with different bargainingpower for the dominant retailerrsquos among RD-channel MD-channel and M-channel which are summarized in Figures2ndash11 where 119881 = 14 119905 = 6 120575 isin (0 6) and 120573 = 02 120573 = 08The parametersrsquo values satisfy the assumptions in Section 3 inorder to make the models feasible and meaningful

Comparing Figure 2 with Figure 3 we can observe thatwhen the dominant retailerrsquos bargaining power is relativelysmall (ie 120573 = 02) both of them can increase prices asincreasing consumersrsquo disutility of purchasing from Internetstore in MD-channel However when the dominant retailerrsquosbargaining power is relatively larger (ie 120573 = 08) themanufacturer has no choice but to lower the retail price soas to attract consumers to buy the product from her Internet

0 1 2 3 4 5 612

14

16

18

20

22

24

26

28

30

wMD

pMDm

pMDr

120575

Figure 2 Impacts of 120575 on prices in the MD-channel when 120573 = 02

0 1 2 3 4 5 60

1

2

3

4

5

6

7

8

wMD

pMDm

pMDr

120575

Figure 3 Impacts of 120575 on prices in the MD-channel when 120573 = 08

store In addition Figures 2 and 3 show that when consumersrsquodisutility buying from Internet store is low enough (ie 120575 lt

2) the manufacturer can set her retail price to be larger thanthe dominant retailerrsquos However when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2)the manufacturer can set her retail price to be lower than thedominant retailerrsquos

Figures 4 and 5 show that when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)both the manufacturer and dominant retailer should lowerprices to increase consumersrsquo disutility buying from Internet

Mathematical Problems in Engineering 9

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

wM

pMm

pMr

Figure 4 Impacts of 120575 on prices in the M-channel when 120573 = 02

0 1 2 3 4 5 61

2

3

4

5

6

7

8

120575

wM

pMm

pMr

Figure 5 Impacts of 120575 on prices in the M-channel when 120573 = 08

store It is noted that the rate of change of manufacturerrsquosretail price with respect to consumersrsquo disutility buying fromInternet store is equal to that of dominant retailerrsquos retailprice However when consumersrsquo disutility buying fromInternet store is relatively larger (ie 120575 gt 2) if the dominantretailerrsquos bargaining power is relatively small (ie 120573 =

02) the manufacturer can raise retail price following thedominant retailer as increasing consumersrsquo disutility buyingfrom Internet store if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 = 08) the manufacturershould cut down the retail price in her Internet store withincreasing consumersrsquo disutility

0 1 2 3 4 5 66

8

10

12

14

16

18

20

22

24

wMD

wRD

wM

120575

Figure 6 The wholesale prices in different channels when 120573 = 02

0 1 2 3 4 5 605

1

15

2

25

3

120575

wMD

wRD

wM

Figure 7 The wholesale prices in different channels when 120573 = 08

Figures 6 and 7 show that no matter whether thedominant retailerrsquos bargaining power is small or large themanufacturer can raise the wholesale price with increasingconsumersrsquo disutility buying from Internet store in the MD-channel but in the RD-channel the manufacturer shouldlower the wholesale price with increasing consumersrsquo disutil-ity However in the M-channel when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower the wholesale price withincreasing consumersrsquo disutility when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2) themanufacturer can raise the wholesale price with increasing

10 Mathematical Problems in Engineering

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

pMDm

pMm

Figure 8 Manufacturerrsquos retail prices in different channels when120573 = 02

0 1 2 3 4 5 645

5

55

6

65

7

75

120575

pMDm

pMm

Figure 9 Manufacturerrsquos retail prices in different channels when120573 = 08

consumersrsquo disutility and set the wholesale price the same asin the MD-channel

Figures 8 and 9 show that when the dominant retailerrsquosbargaining power is relatively small (ie 120573 = 02) inthe MD-channel the manufacturer can raise retail pricewith increasing consumersrsquo disutility buying from Internetstore but when the dominant retailerrsquos bargaining power isrelatively larger (ie 120573 = 08) the manufacturer should lowerretail price with increasing consumersrsquo disutility Howeverin the M-channel no matter whether the dominant retailerrsquosbargaining power is small or large when consumersrsquo disutility

0 1 2 3 4 5 65

10

15

20

25

30

120575

pRDr

pMDr

pMr

Figure 10 Dominant retailerrsquos prices in different channels when120573 =02

buying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower retail price with increasingconsumersrsquo disutility but when consumersrsquo disutility buyingfrom Internet store is relatively larger (ie 120575 gt 2) if thedominant retailerrsquos bargaining power is relatively small (ie120573 = 02) the manufacturer can raise retail price withincreasing consumersrsquo disutility buying from Internet storeif the dominant retailerrsquos bargaining power is relatively larger(ie 120573 = 08) themanufacturer should lower retail price withincreasing consumersrsquo disutility

Figures 10 and 11 show that no matter whether thedominant retailerrsquos bargaining power is small or larger healways lowers the retail price with increasing consumersrsquodisutility buying from Internet store in the RD-channel butin the MD-channel he always raises the retail price withincreasing consumersrsquo disutility However in the M-channelwhen consumersrsquo disutility buying from Internet store islow enough (ie 120575 lt 2) the dominant retailer shouldlower retail price with increasing consumersrsquo disutility butwhen consumersrsquo disutility is relatively larger (ie 120575 gt 2)the dominant retailer can raise retail price with increasingconsumersrsquo disutility buying from Internet store

7 Conclusions and Future Research

To investigate when the manufacturer and dominant retaileropen their own Internet stores with different setup costsand how set prices to ensure opening Internet stores areprofitable in a supply chain we first present the equilibriumoutcomes under four possible supply chain structures andthen discuss the strategic conditions for the manufacturerand dominant retailer when it is optimal to open an Internetstore In addition we analyze both playersrsquo pricing policies

Mathematical Problems in Engineering 11

0 1 2 3 4 5 62

4

6

8

10

12

14

120575

pMDr

pRDr

pMr

Figure 11 Dominant retailerrsquos prices in different channels when 120573 =08

after they open their Internet stores and discuss the impactsof the dominant retailerrsquos bargaining power and consumersrsquodisutility of purchasing a product from Internet store onthe manufacturer and dominant retailerrsquos pricing strategiesFinally we conduct numerical examples to illustrate thetheoretical results

We obtain some new results differing from those inthe literature We find that the optimal choices for themanufacturer and dominant retailer to open an Internetstore are largely determined by their respective setup costswhich are closely related to the dominant retailerrsquos bargainingpower and consumersrsquo disutility of buying from Internetstore It is worth mentioning that multichannel retailing forthe dominant retailer is not necessarily the best strategyIn other words if the dominant retailer opens an Internetstore the marketing plan for him to attract more consumersby charging a lower price is impossible to achieve and hecan induce the manufacturer to open an Internet store tocompetewith himOnlywhen the setup cost for the dominantretailer to open an Internet store is sufficiently low then he isprofitable

What is more we also find that the manufacturerrsquosoptimal price at her Internet store is not always being lowerthan the dominant retailerrsquos For example if the consumersrsquodisutility of buying from Internet store is sufficiently highthe manufacturer must provide strong price incentives forconsumers to purchase the product from the Internet store

Although this research provides new insights for themanufacturer and dominant retailer to open an Internetstore and set prices in a supply chain there are severaldirections that could be extended First this study assumedthat all information is known to the manufacturer anddominant retailer in our model However information couldbe asymmetric in the supply chain since both players haveprivate information about their own internal variable costs

for example the setup cost of opening an Internet storecustomersrsquo purchase patterns and search costsTherefore wecan explore the competitive equilibrium under asymmetricinformation settings Second we assume that consumersrsquodisutility of buy from Internet store is independent of theunit transportation cost which can be relaxed in the futureresearch Third trade credit is widely used in practice andhas important impact on supply chain management [39ndash41] In recent years trade credit has become one of themajor transactions between suppliers and retailers in a valuechain For example Wal-Mart Carrefour and GOME (alarge Chinese home appliance chain retailer) even delayedpayments to their suppliers for as long as one year [42]Hence it is worthy to understand how the trade creditaffects supply channel configuration together with pricingstrategies in the E-commerce market A final issue worthyof investigation is how different types of customers affectthe manufacturer and dominant retailerrsquos channel selectionstrategies We leave these questions for future research

Appendices

A Equilibrium Outcome ofthe Four Channel Structures

Proof of Lemma 6 (1) In the T-channel both the manufac-turer and dominant retailer do not open their Internet storesThere is only the dominant retailerrsquos physical store in themarket So the dominant retailer acts as a monopolist andoptimally charges a price 119881 minus 119905 such that the market isjust covered For the manufacturer given that the dominantretailerrsquos optimal retail price the optimal wholesale price is119908

T= (1 minus 120573)(119881 minus 119905) Since the manufacturer produces

the product at a constant unit (marginal) cost which isnormalized to zero and the market is just covered that is thesize of the market is one the profit for the manufacturer isprod

T119898= (1minus120573)(119881minus119905) Accordingly the profit for the dominant

retailer isprodT119903= 120573(119881 minus 119905)

(2) In RD-channel only the dominant retailer opens anInternet store (RIS) If a consumer locates at a distance fromphysical store (PS) he will get a net utility of by purchasingthe product from PS and a net utility of by purchasing theproduct from RIS To ensure the full market coverage thedominant retailer charges the monopoly price 119881 minus 120575 acrosshis two stores and sells the product to all consumers Forthe manufacturer given the dominant retailerrsquos optimal retailprice the optimal wholesale price is 119908RD

= (1 minus 120573)(119881 minus 120575)Since the manufacturer produces the product at a constantunit (marginal) cost which is normalized to zero and 119905 thesize of the market is one the profits for the manufacturer anddominant retailer are prodRD

119898= (1 minus 120573)(119881 minus 120575) and prod

RD119903

=

120573(119881 minus 120575) respectively(3) In MD-channel the manufacturer opens an Internet

store but dominant retailer does not So consumers canhave convenient access to the product through the dominantretailerrsquos physical store (PS) at price 119901

119903or the manufacturerrsquos

Internet store (MIS) at price 119901119898 their decision about which

store to buy revolves around the comparison of their net

12 Mathematical Problems in Engineering

utility derived fromPS119880PS = 119881minus119901119903minus119905119909 and119880MIS = 119881minus119901119898minus120575by buying the product from MIS Therefore the marginalconsumers are located at 119909 = (119901

119898minus 119901119903+ 120575)119905 So the profit

functions for the manufacturer and dominant retailer can bewritten as

prod

119898

= 119908[

(119901119898minus 119901119903+ 120575)

119905

] + 119901119898[

(119901119903minus 119901119898+ 119905 minus 120575)

119905

] minus 119865119898

(A1)

prod

119903

= (119901119903minus 119908) [

(119901119898minus 119901119903+ 120575)

119905

] (A2)

Under the assumption proposed in Section 3 the dom-inant retailer is the price leader and the manufacturer isthe follower As before the game is solved backwards Inthis market we firstly need to calculate the manufacturerrsquosoptimal price given any dominant retailerrsquos price

Themanufacturerrsquos reaction function can be derived fromthe first-order condition

120597prod119898

120597119901119898

=

[(2 minus 120573) 119901119903minus 2119901119898+ 119905 minus 120575]

119905

= 0

that is 119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A3)

Substituting (A3) into (A2) we get

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

(A4)

Taking the first-order derivative of (A4) with respect to119901119903and letting the derivative be zero we have

119901MD119903

=

(119905 + 120575)

2120573

(A5)

Given the wholesale price bargaining process we canobtain the manufacturerrsquos optimal wholesale price 119908MD

=

(1 minus 120573)(119905 + 120575)2120573 and substituting (A5) into (A3) we getthe manufacturerrsquos optimal retail price

119901MD119898

=

(2 + 120573) 119905 + (2 minus 3120573) 120575

4120573

(A6)

Substituting (A5) and (A6) into (A1) and (A2) wecan obtain the equilibrium profits for the manufacturers anddominant retailer respectively

MDprod

119898

=

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus 119865119898

MDprod

119903

=

(119905 + 120575)2

8119905

(A7)

Proof of Lemma 7 In the M-channel both the manufacturerand dominant retailer simultaneously open their own Inter-net stores then customers are able to purchase a product

either from the dominant retailerrsquos physical store (PS) or fromthe alternative Internet stores (MISRIS) They can get a netutility of 119880PS = 119881 minus 119901

119903minus 119905119909 by buying the product from PS

and a net utility of 119880MIS = 119881 minus 119901119898minus 120575 by buying the product

fromMIS and a net utility of119880RIS = 119881minus 119901119903minus 120575 by buying the

product from RISAccording to the basicmodel we know that the dominant

retailer firstmakes pricing decision as the price leader and themanufacturer is the follower If the dominant retailer chargesa price higher than the manufacturerrsquos price (119901

119903gt 119901119898) then

no consumer will buy the product from his Internet storeUnder this condition the dominant retailer makes no sale inhis Internet store and makes a profit of minus119865

119903 Therefore the

demand functions for the manufacturerrsquos Internet store anddominant retailerrsquos physical store are given respectively asfollows

119863MIS =(119901119903minus 119901119898+ 119905 minus 120575)

119905

(A8)

119863PS =(119901119898minus 119901119903+ 120575)

119905

(A9)

Hence the manufacturerrsquos profit function can be written as

prod

119898

=

[119908 (119901119898minus 119901119903+ 120575) + 119901

119898(119901119903minus 119901119898+ 119905 minus 120575)]

119905

minus 119865119898

(A10)

From the first-order condition we have

119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A11)

Given the condition of 119901119903gt 119901119898 this implies that 119901

119903gt (119905 minus

120575)120573 However when 119901119903le (119905 minus 120575)120573 and 119901

119903gt 119901119898 we always

have 120597prodM119898120597119901119898= [(2 minus 120573)119901

119903minus 2119901119898+ 119905 minus 120575]119905 gt 0

Therefore the manufacturer optimally sets its price at119901119898= 119901119903 and her optimal pricing schedule is as follows

119901119898=

119901119903 119901

119903le

119905 minus 120575

120572

(2 minus 120573) 119901119903+ 119905 minus 120575

2

119901119903gt

119905 minus 120575

120572

(A12)

Given the manufacturerrsquos pricing schedule the dominantretailerrsquos profit is given as follows

prod

119903

=

(119901119903minus 119908)

120575

119905

minus 119865119903 119901

119903le

119905 minus 120575

120573

(119901119903minus 119908)

119905 + 120575 minus 120573119901119903

2119905

minus 119865119903 119901119903gt

119905 minus 120575

120573

(A13)

Under the condition of 119901119903gt (119905 minus 120575)120573 the dominant

retailerrsquos profit is

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

minus 119865119903 (A14)

Taking the first-order derivative of (A14) with respect to 119901119903

and letting the derivative be zero we have 119901M119903= (119905 + 120575)2120573

Mathematical Problems in Engineering 13

Submitting it into (A11) we get the manufacturerrsquos optimalprice in her Internet store 119901M

119898= [(2 + 120573)119905 + (2 minus 3120573)120575]4120573

Hence the manufacturer and dominant retailerrsquos optimalprofits are prodM

119898= (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus 119865119898

andprodM119903= (119905 + 120575)

2

8119905 minus 119865119903 respectively

According to the previous assumption 119901119903gt (119905 minus 120575)120573

which implies that (119905 + 120575)2120573 gt (119905 minus 120575)120573 120575must satisfy 120575 gt1199053 However when 120575 lt 1199053 we always have

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](minus)

gt 0

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](+)

lt 0 (A15)

So the dominant retailerrsquos optimal retail price in the M-channel is 119901M

119903= (119905 minus 120575)120573 Therefore the manufacturer and

dominant retailerrsquos optimal profits areprodM119898= (119905 minus 120575)120573 minus [(119905 minus

120575)120575]119905 minus 119865119898andprodM

119903= [(119905 minus 120575)120575]119905 minus 119865

119903 respectively

B Strategic Conditions forOpening an Internet Store

Proofs of Proposition 8 and Corollary 9 From Lemma 6 weanalyse the equilibrium profits for the dominant retailerbetween the T-channel and RD-channel and note that onlywhen 119865

119903lt 120573(119905 minus 120575) then prodRD

119903gt prod

T119903 This implies that as

long as the setup cost of opening an Internet store satisfies119865119903

lt 120573(119905 minus 120575) ≜ 1198611 it is always optimal to open an

Internet store for the dominant retailer In addition we notethat 120597119861

1120597120575 = minus120573 lt 0 So the dominant retailerrsquos strategic

motive for opening an Internet store would be weakened byincreasing consumersrsquo disutility of purchasing a product fromInternet store

Proofs of Proposition 10 and Corollary 11 From Lemma 6 weanalyse the equilibrium profits for the manufacturer betweenthe T-channel and MD-channel and note that only when thesetup cost of opening an Internet store satisfies 119865

119898lt (119905 +

120575)2120573+[(119905minus120575)2

minus12119905120575]16119905minus(1minus120573)(119881minus119905) ≜ 1198612 thenprodMD

119898gt

prodT119898 In addition we note that 120597119861

2120597120575 = [4119905 minus 120573(7119905 minus 120575)]8120573119905

and find when 0 lt 120573 lt 4119905(7119905 minus 120575) then 1205971198612120597120575 gt 0 and

when 4119905(7119905 minus 120575) lt 120573 lt 1 then 1205971198612120597120575 lt 0

Proofs of Proposition 12 and Corollary 13 FromLemmas 6 and7 we analyse the equilibriumprofits for themanufacturer anddominant retailer between the T-channel andM-channel wenote that under the condition of 120575 lt 1199053 only when the setupcosts of opening an Internet store for the manufacturer anddominant retailer simultaneously satisfy

119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198613

119865119903lt

[(119905 minus 120575) 120575]

119905

minus 120573 (119881 minus 119905) ≜ 1198614

(B1)

thenMprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B2)

Similarly under the condition of 120575 gt 1199053 only when thesetup costs of opening an Internet store for the manufacturerand dominant retailer simultaneously satisfy

119865119898lt

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198615

119865119903lt

(119905 + 120575)2

8119905

minus 120573 (119881 minus 119905) ≜ 1198616

(B3)

then

Mprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B4)

In addition we note that both 1205971198613120597120575 = minus[119905 + 120573(119905 minus

2120575)]120573119905 lt 0 and 1205971198614120597120575 = (119905 minus 2120575)119905 gt 0 are held under

the condition of 120575 lt 1199053 Furthermore under the conditionof 120575 gt 1199053 we also find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198615120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

5120597120575 lt 0

1205971198616120597120575 = 2(119905 + 120575)8119905 gt 0

Proofs of Proposition 14 and Corollary 15 From Lemmas 6and 7 we analyse the manufacturerrsquos equilibrium profits inthe RD-channel and M-channel we note that under thecondition of 120575 lt 1199053 only when the setup cost of opening anInternet store for her satisfies 119865

119898lt (119905 minus 120575)120573 minus [(119905 minus 120575)120575]119905 minus

(1 minus 120573)(119881 minus 120575) ≜ 1198617 thenprodM

119898gt prod

RD119898 In addition we find

1205971198617120597120575 = minus[(1 + 120573

2

)119905 minus 2120573120575]120573119905 lt 0But under the condition of 120575 gt 1199053 only when the setup

cost of opening an Internet store for her satisfies 119865119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 120575) ≜ 1198618 then

prodM119898gt prod

RD119898 In addition 120597119861

8120597120575 = [120573(119905+120575)+4119905(1minus2120573

2

)]8120573119905

we find that when 0 lt 120573 lt [(119905 + 120575) + radic(119905 + 120575)2

+ 1281199052]16119905

then 1205971198618120597120575 gt 0 andwhen [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905 lt

120573 lt 1 then 1205971198618120597120575 lt 0

Proofs of Proposition 16 From Lemmas 6 and 7 we analysethe dominant retailerrsquos equilibriumprofits in theMD-channeland M-channel and note that when 120575 lt 1199053 then prod

M119903minus

prodMD119903

= minus(119905 minus 3120575)2

8119905 minus 119865119903lt 0 and when 120575 gt 1199053

then prodM119903minus prod

MD119903

= minus119865119903lt 0 These imply that when the

manufacturer has operated an Internet store the best choicefor dominant retailer is not to open an Internet store

Proofs of Proposition 17 and Corollary 18 From Lemmas 6and 7 we analyse the dominant retailerrsquos equilibrium profitsin the MD-channel and M-channel and note that under thecondition of 120575 lt 1199053 thenprodM

119898minus prod

MD119898

= [8119905(119905 minus 3120575) minus 120573[(119905 +

120575)2

minus 161205752

]8119905]16120573119905 This implies that the manufacturer willopen her Internet store when the dominant retailer opens an

14 Mathematical Problems in Engineering

Internet store and the setup costs of opening an Internet storefor her satisfies

1198619≜

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

lt 119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

≜ 11986110

(B5)

In addition we find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198619120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

9120597120575 lt 0

and 12059711986110120597120575 = minus[119905 + 120573(119905 minus 2120575)]120573119905 lt 0

C The ManufacturerDominantRetailers Pricing Policies

Proof of Proposition 19 In the MD-channel we respectivelydifferentiate between119901MD

119898and119901MD

119903with respect to 120573 and find

that 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0 For any given120573 differentiating between 119901MD

119898and 119901MD

119903with respect to 120575 we

have 120597119901MD119903

120597120575 = 12120573 gt 0 and 120597119901MD119898

120597120575 = (2 minus 3120573)4120573and if 120573 isin (0 23) then 120597119901MD

119898120597120575 gt 0 if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 In addition we find that 119901MD119898

minus 119901MD119903

= (119905 minus

3120575)4 it is obvious that when 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

when 120575 = 1199053 then 119901MD

119898= 119901

MD119903

and when 120575 gt 1199053 then119901MD119898

lt 119901MD119903

Proof of Proposition 20 In the M-channel we respectivelydifferentiate between 119901M

119898and 119901M

119903with respect to 120573 and find

that when 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0

and when 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 For any given 120573 we respectively differentiate between 119901M119898

and 119901M119903with respect to 120575 and find that when 120575 lt 1199053 then

120597119901M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0 when 120575 gt 1199053 then

120597119901M119898120597120575 = (2 minus 3120573)4120573 and 120597119901M

119903120597120575 = 12120573 gt 0

It is easy to note that when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0

but when 120573 isin (23 1) then 120597119901M119898120597120575 lt 0

Proof of Proposition 21 From Lemmas 6 and 7 we note that120597119908

RD120597120575 = minus(1 minus 120573) lt 0 and 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0In addition if 120575 lt 1199053 then 120597119908M

120597120575 = minus(1 minus 120573)120573 lt 0 if120575 gt 1199053 then 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0

Proof of Proposition 22 From the proofs of Propositions 19and 20 we note that when 120575 lt 1199053 if 120573 isin (0 23) then120597119901

MD119898

120597120575 gt 0 120597119901M119898120597120575 lt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 120597119901M119898120597120575 lt 0 when 120575 gt 1199053 if 120573 isin (0 23)

then 120597119901MD119898

120597120575 = 120597119901M119898120597120575 gt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 = 120597119901M119898120597120575 lt 0

Proof of Proposition 23 From Lemmas 6 and 7 we note that120597119901

RD119903120597120575 = minus1 lt 0 and 120597119901MD

119903120597120575 = 12120572 gt 0 In addition if

120575 lt 1199053 then 120597119901M119903120597120575 = minus1120572 lt 0 if 120575 gt 1199053 then 120597119901M

119903120597120575 =

12120572 gt 0

Abbreviations

UK The consumerrsquos utility of purchasing theproduct from K storeK isin PSRISMIS

119881 The value of consumers willing to payfor the product

120575 The consumersrsquo disutility of purchasingthe product from Internet store(MISRIS)

119905 The per unit transportation cost ofpurchasing the product from physicalstore (PS)

120573 The dominant retailerrsquos bargainingpower in the distribution channel

119908j The manufacturerrsquos wholesale price in

the j-channel j isin TRDMDM

119901j119903 The dominant retailerrsquos price in the

j-channel j isin TRDMDM

119901j119898 The manufacturerrsquos price in the

j-channel j isin MDM

119865119898119865119903 The setup cost of opening an Internetstore by the manufacturerdominantretailer

Πj119898Πj119903 The manufacturerdominant retailerrsquosprofit in the j-channelj isin TRDMDM

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been supported by theNational Natural Sci-ence Foundation of China (71271225) Chongqingrsquos NaturalScience Foundation (cstc2012jjA1404) and the Open Fund ofChongqing Key Laboratory of Logistics (CQKLL12001)

References

[1] L Hsiao and Y-J Chen ldquoStrategic motive for introducinginternet channels in a supply chainrdquo Production and OperationsManagement vol 23 no 1 pp 36ndash47 2014

[2] I Geyskens K Gielens and M G Dekimpe ldquoThe marketvaluation of Internet channel additionsrdquo Journal of Marketingvol 66 no 2 pp 102ndash119 2002

[3] 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

[4] S-H Chun and J-C Kim ldquoPricing strategies in B2C electroniccommerce analytical and empirical approachesrdquo Decision Sup-port Systems vol 40 no 2 pp 375ndash388 2005

[5] S K Mukhopadhyay X Zhu and X Yue ldquoOptimal contractdesign for mixed channels under information asymmetryrdquoProduction and Operations Management vol 17 no 6 pp 641ndash650 2008

Mathematical Problems in Engineering 15

[6] G S Cai ldquoChannel selection and coordination in dual-channelsupply chainsrdquo Journal of Retailing vol 86 no 1 pp 22ndash36 2010

[7] K Takahashi T Aoi D Hirotani and K Morikawa ldquoInventorycontrol in a two-echelon dual-channel supply chain with setupof production and deliveryrdquo International Journal of ProductionEconomics vol 133 no 1 pp 403ndash415 2011

[8] D W Carlton and J A Chevalier ldquoFree riding and salesstrategies for the Internetrdquo Journal of Industrial Economics vol49 no 4 pp 441ndash461 2001

[9] K D Antia M Bergen and S Dutta ldquoCompeting with graymarketsrdquoMIT SloanManagement Review vol 46 no 1 pp 63ndash69 2004

[10] J Shin ldquoHow does free riding on customer service affectcompetitionrdquo Marketing Science vol 26 no 4 pp 488ndash5032007

[11] G Iyer and J M Villas-Boas ldquoA bargaining theory of distribu-tion channelsrdquo Journal of Marketing Research vol 40 no 1 pp80ndash100 2003

[12] A Dukes and Y Liu ldquoIn-store media and distribution channelcoordinationrdquoMarketing Science vol 29 no 1 pp 94ndash107 2010

[13] H Ahn I Duenyas and R Zhang ldquoPrice competition betweenretailers and manufacturer-owned storesrdquoWorking Paper Uni-versity of California at Berkeley 2002

[14] K Cattani W Gilland H S Heese and J SwaminathanldquoBoiling frogs pricing strategies for a manufacturer addinga direct channel that competes with the traditional channelrdquoProduction and Operations Management vol 15 no 1 pp 40ndash56 2006

[15] K-Y Chen M Kaya and O Ozer ldquoDual sales channel man-agement with service competitionrdquo Manufacturing and ServiceOperations Management vol 10 no 4 pp 654ndash675 2008

[16] G Hua S Wang and T C E Cheng ldquoPrice and lead timedecisions in dual-channel supply chainsrdquo European Journal ofOperational Research vol 205 no 1 pp 113ndash126 2010

[17] W S Yoo andE Lee ldquoInternet channel entry a strategic analysisof mixed channel structuresrdquo Marketing Science vol 30 no 1pp 29ndash41 2011

[18] Y Xiong W Yan K Fernandes Z-K Xiong and N GuoldquoldquoBricks vs clicksrdquo the impact of manufacturer encroachmentwith a dealer leasing and selling of durable goodsrdquo EuropeanJournal of Operational Research vol 217 no 1 pp 75ndash83 2012

[19] Q Lu and N Liu ldquoPricing games of mixed conventional ande-commerce distribution channelsrdquo Computers and IndustrialEngineering vol 64 no 1 pp 122ndash132 2013

[20] Q Xu Z Liu and B Shen ldquoThe impact of price comparisonservice on pricing strategy in a dual-channel supply chainrdquoMathematical Problems in Engineering vol 2013 Article ID613528 13 pages 2013

[21] C A Ingene and M E Parry ldquoChannel coordination whenretailers competerdquoMarketing Science vol 14 no 4 pp 360ndash3771995

[22] 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

[23] J Raju and Z J Zhang ldquoChannel coordination in the presenceof a dominant retailerrdquoMarketing Science vol 24 no 2 pp 254ndash262 2005

[24] K L Webb and C J Lambe ldquoInternal multi-channel conflictan exploratory investigation and conceptual frameworkrdquo Indus-trial Marketing Management vol 36 no 1 pp 29ndash43 2007

[25] S K Mukhopadhyay D-Q Yao and X Yue ldquoInformationsharing of value-adding retailer in a mixed channel hi-techsupply chainrdquo Journal of Business Research vol 61 no 9 pp950ndash958 2008

[26] R Yan ldquoManaging channel coordination in a multi-channelmanufacturer-retailer supply chainrdquo Industrial Marketing Man-agement vol 40 no 4 pp 636ndash642 2011

[27] E Cao YMa CWan andM Lai ldquoContracting with asymmet-ric cost information in a dual-channel supply chainrdquoOperationsResearch Letters vol 41 no 4 pp 410ndash414 2013

[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] Y Liu S Gupta and Z J Zhang ldquoNote on self-restraint as anonline entry-deterrence strategyrdquoManagement Science vol 52no 11 pp 1799ndash1809 2006

[30] Z Cheng and B R Nault ldquoInternet channel entry retailcoverage and entry cost advantagerdquo Information Technology andManagement vol 8 no 2 pp 111ndash132 2007

[31] X Zhang ldquoRetailersrsquo multichannel and price advertising strate-giesrdquoMarketing Science vol 28 no 6 pp 1080ndash1094 2009

[32] W Huang and J M Swaminathan ldquoIntroduction of a secondchannel implications for pricing and profitsrdquo European Journalof Operational Research vol 194 no 1 pp 258ndash279 2009

[33] H Hotelling ldquoStability in competitionrdquo The Economic Journalvol 39 no 153 pp 41ndash57 1929

[34] J Zhang ldquoThe perils of behavior-based personalizationrdquo Mar-keting Science vol 30 no 1 pp 170ndash186 2011

[35] T Kabiraj and C Lee ldquoLicensing contracts in hotelling struc-turerdquoTheoretical Economics Letters vol 1 no 3 pp 57ndash62 2011

[36] HWang andTNariu ldquoDistribution channelmanagement in aninternet age equilibrium and social welfarerdquo Journal of IndustryCompetition and Trade vol 12 no 3 pp 285ndash298 2012

[37] M Lijesen ldquoHotellingrsquos webshoprdquo Journal of Economics vol 109no 2 pp 193ndash200 2013

[38] R Gulati and J Garino ldquoGet the right mix of bricks amp clicksrdquoHarvard Business Review vol 78 no 3 pp 107ndash214 2000

[39] K-J Chung S-D Lin and H M Srivastava ldquoThe completesolution procedures for the mathematical analysis of somefamilies of optimal inventorymodels with order-size dependenttrade credit and deterministic and constant demandrdquo AppliedMathematics and Computation vol 219 no 1 pp 142ndash157 2012

[40] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels under conditional trade credit in a supply chain systemrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 24 pp10036ndash10052 2013

[41] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels for deteriorating items in the discounted cash-flowsapproach under conditional trade credit and cash discount ina supply chain systemrdquo Applied Mathematics and InformationSciences vol 8 no 5 pp 2103ndash2111 2014

[42] J Luo and Q Zhang ldquoTrade credit a new mechanism tocoordinate supply chainrdquo Operations Research Letters vol 40no 5 pp 378ndash384 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

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Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

Table 3 Strategic conditions for opening Internet stores to T-channel and pricing policies

Strategic conditions M and Rrsquos activities Pricing policiesM has not opened an Internet store and119865119903lt 120573(119905 minus 120575)

R can open an Internet store Monopoly pricing

R has not opened an Internet store and119865119898lt (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905)

M can open an Internet store

When 120575 lt 1199053then 119901MD

119898gt 119901

MD119903

When 120575 = 1199053then 119901MD

119898= 119901

MD119903

When 120575 gt 1199053then 119901MD

119898lt 119901

MD119903

When 120575 lt 1199053 119865119903lt (119905 minus 120575)120575119905 minus 120573(119881 minus 119905) and

119865119898lt (119905 minus 120575)120573 minus (119905 minus 120575)120575119905 minus (1 minus 120573)(119881 minus 119905)

Both M and R can open their Internet stores simultaneously119901M119898= 119901

M119903

When 120575 gt 1199053 119865119903lt (119905 + 120575)

2

8119905 minus 120573(119881 minus 119905) and119865119898lt (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 119905)

119901M119898lt 119901

M119903

when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0 but when 120573 isin

(23 1) then 120597119901M119898120597120575 lt 0

(3) If 120575 le 3119905 then 119901M119898= 119901

M119903 if 120575 gt 1199053 then 119901M

119898lt 119901

M119903

Proposition 20 indicates when both the manufacturerand dominant retailer can open their Internet stores simul-taneously

(1) If consumersrsquo disutility of purchasing a product fromInternet store is low enough (ie 120575 lt 1199053) bothof them can set same price and lower prices as theincreasing consumersrsquo disutility On the contrary ifconsumersrsquo disutility of purchasing a product fromInternet store is relatively larger (ie 120575 gt 1199053) themanufacturer must provide lower price incentivesthan the dominant retailer which may induce con-sumers to purchase the product from her Internetstore It should be pointed out that when the dom-inant retailerrsquos bargaining power is relatively small(ie 120573 lt 23) the manufacturerrsquos price increaseswith increasing consumersrsquo disutility but when thedominant retailerrsquos bargaining power is relativelylarger (ie 120573 gt 23) the manufacturerrsquos retail pricedecreases with increasing consumersrsquo disutility

(2) When consumersrsquo disutility of purchasing a prod-uct from Internet store is low enough (ie 120575 lt

1199053) the dominant retailerrsquos price decreases reducewith increasing consumersrsquo disutility but when con-sumersrsquo disutility of purchasing a product from Inter-net store is relatively larger (ie 120575 gt 1199053) thedominant retailerrsquos price decreases with increasingconsumersrsquo disutility Speaking frankly that is thedominant retailerrsquos smart pricing strategiesThe dom-inant retailer will raise the retail price when mostof consumers with a large disutility of purchasing aproduct from Internet store buy the product from hisphysical store and lower the retail price when mostof consumers with a small disutility of purchasing aproduct from Internet store buy the product from themanufacturerrsquos Internet store

Proposition 21 Given that the dominant retailerrsquos bargainingpower we obtain the following results about the manufacturerrsquoswholesale price under RD-channel MD-channel and M-channel

(1) 120597119908RD120597120575 = minus(1 minus 120573) lt 0

(2) 120597119908MD120597120575 = (1 minus 120573)2120573 gt 0

(3) if 120575 lt 1199053 then 120597119908M120597120575 = minus(1 minus 120573)120573 lt 0 if 120575 gt 1199053

then 120597119908M120597120575 = (1 minus 120573)2120573 gt 0

Proposition 21 indicates that the manufacturer should setthe wholesale prices differentially across the RD-channelMD-channel andM-channel and raise or lower thewholesaleprices in the light of consumersrsquo disutility of buying theproduct from Internet store More specifically the man-ufacturer can lower the wholesale price with increasingconsumersrsquo disutility of buying the product from Internetstore in the RD-channel but in theMD-channel she can raisethe wholesale price with increasing consumersrsquo disutility ofbuying from Internet store However in theM-channel whenthe consumersrsquo disutility of buying from Internet store is lowenough (ie 120575 lt 1199053) she can lower the wholesale pricewith increasing consumersrsquo disutility but when consumersrsquodisutility of buying from Internet store is relatively larger (ie120575 gt 1199053) she should raise the wholesale price with increasingconsumersrsquo disutility

Proposition 22 Given that the dominant retailerrsquos bargainingpower we obtain the following results about the manufacturerrsquosretail price at her Internet store under MD-channel and M-channel

(1) If 120575 lt 1199053 when 120573 isin (0 23) then 120597119901MD119898

120597120575 =

(2 minus 3120573)4120573 gt 0 120597119901M119898120597120575 = minus1120573 lt 0 but when 120573 isin

(23 1) then 120597119901MD119898

120597120575 = (2 minus 3120573)4120573 lt 0 120597119901M119898120597120575 =

minus1120573 lt 0(2) If 120575 gt 1199053 when 120573 isin (0 23) then 120597119901

MD119898

120597120575 =

120597119901M119898120597120575 gt 0 but when 120573 isin (23 1) then 120597119901MD

119898120597120575 =

120597119901M119898120597120575 lt 0

Proposition 22 indicates that themanufacturer should setthe retail prices at her Internet store differentially across the

8 Mathematical Problems in Engineering

MD-channel and M-channel and raise or lower the prices inthe light of consumersrsquo disutility of buying the product fromInternet store More specifically if the consumersrsquo disutilityof buying from Internet store is low enough (ie 120575 lt 1199053)the manufacturer can raise the retail price at her Internetstore with increasing consumersrsquo disutility of buying fromInternet store when the dominant retailerrsquos bargaining poweris relatively small (ie 120573 lt 23) and the dominant retailerdoes not open Internet store However if the dominantretailer also opens an Internet store the manufacturer shouldlower the retail price at her Internet store so as to attractconsumers to buy the product from her Internet store On thecontrary if the consumersrsquo disutility of buying from Internetstore is relatively larger (ie 120575 gt 1199053) and the dominantretailer also opens an Internet store then the manufacturershould set the same price with the dominant retailerrsquos andadjust the price following the dominant retailer

Proposition 23 Given that the dominant retailerrsquos bargainingpower we obtain the following results about dominant retailerrsquosretail price under RD-channel MD-channel and M-channel

(1) If 120575 lt 1199053 then 120597119901RD119903120597120575 = minus1 lt 0 120597119901MD

119903120597120575 = 12120573 gt

0 and 120597119901M119903120597120575 = minus1120573 lt 0

(2) If 120575 gt 1199053 then 120597119901RD119903120597120575 = minus1 lt 0 120597119901

MD119903

120597120575 =

12120573 gt 0 and 120597119901M119903120597120575 = 12120573 gt 0

Proposition 23 indicates that no matter when the con-sumersrsquo disutility of buying from Internet store is small orlarger the dominant retailer should lower the retail price withincreasing consumersrsquo disutility buying from Internet store inthe RD-channel but in the MD-channel he always raises theretail price with increasing consumersrsquo disutility Howeverin the M-channel when consumersrsquo disutility buying fromInternet store is low enough (ie 120575 lt 1199053) he should lowerthe price with increasing consumersrsquo disutility but whenconsumersrsquo disutility is relatively larger (ie 120575 gt 1199053) he canset the price same as the price in the MD-channel and raisethe price with increasing consumersrsquo disutility

6 Numerical Examples

In this section we present numerical examples to illustratethe theoretical results about impacts of consumersrsquo disutilityof buying from Internet store on the manufacturer anddominant retailerrsquos pricing policies with different bargainingpower for the dominant retailerrsquos among RD-channel MD-channel and M-channel which are summarized in Figures2ndash11 where 119881 = 14 119905 = 6 120575 isin (0 6) and 120573 = 02 120573 = 08The parametersrsquo values satisfy the assumptions in Section 3 inorder to make the models feasible and meaningful

Comparing Figure 2 with Figure 3 we can observe thatwhen the dominant retailerrsquos bargaining power is relativelysmall (ie 120573 = 02) both of them can increase prices asincreasing consumersrsquo disutility of purchasing from Internetstore in MD-channel However when the dominant retailerrsquosbargaining power is relatively larger (ie 120573 = 08) themanufacturer has no choice but to lower the retail price soas to attract consumers to buy the product from her Internet

0 1 2 3 4 5 612

14

16

18

20

22

24

26

28

30

wMD

pMDm

pMDr

120575

Figure 2 Impacts of 120575 on prices in the MD-channel when 120573 = 02

0 1 2 3 4 5 60

1

2

3

4

5

6

7

8

wMD

pMDm

pMDr

120575

Figure 3 Impacts of 120575 on prices in the MD-channel when 120573 = 08

store In addition Figures 2 and 3 show that when consumersrsquodisutility buying from Internet store is low enough (ie 120575 lt

2) the manufacturer can set her retail price to be larger thanthe dominant retailerrsquos However when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2)the manufacturer can set her retail price to be lower than thedominant retailerrsquos

Figures 4 and 5 show that when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)both the manufacturer and dominant retailer should lowerprices to increase consumersrsquo disutility buying from Internet

Mathematical Problems in Engineering 9

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

wM

pMm

pMr

Figure 4 Impacts of 120575 on prices in the M-channel when 120573 = 02

0 1 2 3 4 5 61

2

3

4

5

6

7

8

120575

wM

pMm

pMr

Figure 5 Impacts of 120575 on prices in the M-channel when 120573 = 08

store It is noted that the rate of change of manufacturerrsquosretail price with respect to consumersrsquo disutility buying fromInternet store is equal to that of dominant retailerrsquos retailprice However when consumersrsquo disutility buying fromInternet store is relatively larger (ie 120575 gt 2) if the dominantretailerrsquos bargaining power is relatively small (ie 120573 =

02) the manufacturer can raise retail price following thedominant retailer as increasing consumersrsquo disutility buyingfrom Internet store if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 = 08) the manufacturershould cut down the retail price in her Internet store withincreasing consumersrsquo disutility

0 1 2 3 4 5 66

8

10

12

14

16

18

20

22

24

wMD

wRD

wM

120575

Figure 6 The wholesale prices in different channels when 120573 = 02

0 1 2 3 4 5 605

1

15

2

25

3

120575

wMD

wRD

wM

Figure 7 The wholesale prices in different channels when 120573 = 08

Figures 6 and 7 show that no matter whether thedominant retailerrsquos bargaining power is small or large themanufacturer can raise the wholesale price with increasingconsumersrsquo disutility buying from Internet store in the MD-channel but in the RD-channel the manufacturer shouldlower the wholesale price with increasing consumersrsquo disutil-ity However in the M-channel when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower the wholesale price withincreasing consumersrsquo disutility when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2) themanufacturer can raise the wholesale price with increasing

10 Mathematical Problems in Engineering

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

pMDm

pMm

Figure 8 Manufacturerrsquos retail prices in different channels when120573 = 02

0 1 2 3 4 5 645

5

55

6

65

7

75

120575

pMDm

pMm

Figure 9 Manufacturerrsquos retail prices in different channels when120573 = 08

consumersrsquo disutility and set the wholesale price the same asin the MD-channel

Figures 8 and 9 show that when the dominant retailerrsquosbargaining power is relatively small (ie 120573 = 02) inthe MD-channel the manufacturer can raise retail pricewith increasing consumersrsquo disutility buying from Internetstore but when the dominant retailerrsquos bargaining power isrelatively larger (ie 120573 = 08) the manufacturer should lowerretail price with increasing consumersrsquo disutility Howeverin the M-channel no matter whether the dominant retailerrsquosbargaining power is small or large when consumersrsquo disutility

0 1 2 3 4 5 65

10

15

20

25

30

120575

pRDr

pMDr

pMr

Figure 10 Dominant retailerrsquos prices in different channels when120573 =02

buying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower retail price with increasingconsumersrsquo disutility but when consumersrsquo disutility buyingfrom Internet store is relatively larger (ie 120575 gt 2) if thedominant retailerrsquos bargaining power is relatively small (ie120573 = 02) the manufacturer can raise retail price withincreasing consumersrsquo disutility buying from Internet storeif the dominant retailerrsquos bargaining power is relatively larger(ie 120573 = 08) themanufacturer should lower retail price withincreasing consumersrsquo disutility

Figures 10 and 11 show that no matter whether thedominant retailerrsquos bargaining power is small or larger healways lowers the retail price with increasing consumersrsquodisutility buying from Internet store in the RD-channel butin the MD-channel he always raises the retail price withincreasing consumersrsquo disutility However in the M-channelwhen consumersrsquo disutility buying from Internet store islow enough (ie 120575 lt 2) the dominant retailer shouldlower retail price with increasing consumersrsquo disutility butwhen consumersrsquo disutility is relatively larger (ie 120575 gt 2)the dominant retailer can raise retail price with increasingconsumersrsquo disutility buying from Internet store

7 Conclusions and Future Research

To investigate when the manufacturer and dominant retaileropen their own Internet stores with different setup costsand how set prices to ensure opening Internet stores areprofitable in a supply chain we first present the equilibriumoutcomes under four possible supply chain structures andthen discuss the strategic conditions for the manufacturerand dominant retailer when it is optimal to open an Internetstore In addition we analyze both playersrsquo pricing policies

Mathematical Problems in Engineering 11

0 1 2 3 4 5 62

4

6

8

10

12

14

120575

pMDr

pRDr

pMr

Figure 11 Dominant retailerrsquos prices in different channels when 120573 =08

after they open their Internet stores and discuss the impactsof the dominant retailerrsquos bargaining power and consumersrsquodisutility of purchasing a product from Internet store onthe manufacturer and dominant retailerrsquos pricing strategiesFinally we conduct numerical examples to illustrate thetheoretical results

We obtain some new results differing from those inthe literature We find that the optimal choices for themanufacturer and dominant retailer to open an Internetstore are largely determined by their respective setup costswhich are closely related to the dominant retailerrsquos bargainingpower and consumersrsquo disutility of buying from Internetstore It is worth mentioning that multichannel retailing forthe dominant retailer is not necessarily the best strategyIn other words if the dominant retailer opens an Internetstore the marketing plan for him to attract more consumersby charging a lower price is impossible to achieve and hecan induce the manufacturer to open an Internet store tocompetewith himOnlywhen the setup cost for the dominantretailer to open an Internet store is sufficiently low then he isprofitable

What is more we also find that the manufacturerrsquosoptimal price at her Internet store is not always being lowerthan the dominant retailerrsquos For example if the consumersrsquodisutility of buying from Internet store is sufficiently highthe manufacturer must provide strong price incentives forconsumers to purchase the product from the Internet store

Although this research provides new insights for themanufacturer and dominant retailer to open an Internetstore and set prices in a supply chain there are severaldirections that could be extended First this study assumedthat all information is known to the manufacturer anddominant retailer in our model However information couldbe asymmetric in the supply chain since both players haveprivate information about their own internal variable costs

for example the setup cost of opening an Internet storecustomersrsquo purchase patterns and search costsTherefore wecan explore the competitive equilibrium under asymmetricinformation settings Second we assume that consumersrsquodisutility of buy from Internet store is independent of theunit transportation cost which can be relaxed in the futureresearch Third trade credit is widely used in practice andhas important impact on supply chain management [39ndash41] In recent years trade credit has become one of themajor transactions between suppliers and retailers in a valuechain For example Wal-Mart Carrefour and GOME (alarge Chinese home appliance chain retailer) even delayedpayments to their suppliers for as long as one year [42]Hence it is worthy to understand how the trade creditaffects supply channel configuration together with pricingstrategies in the E-commerce market A final issue worthyof investigation is how different types of customers affectthe manufacturer and dominant retailerrsquos channel selectionstrategies We leave these questions for future research

Appendices

A Equilibrium Outcome ofthe Four Channel Structures

Proof of Lemma 6 (1) In the T-channel both the manufac-turer and dominant retailer do not open their Internet storesThere is only the dominant retailerrsquos physical store in themarket So the dominant retailer acts as a monopolist andoptimally charges a price 119881 minus 119905 such that the market isjust covered For the manufacturer given that the dominantretailerrsquos optimal retail price the optimal wholesale price is119908

T= (1 minus 120573)(119881 minus 119905) Since the manufacturer produces

the product at a constant unit (marginal) cost which isnormalized to zero and the market is just covered that is thesize of the market is one the profit for the manufacturer isprod

T119898= (1minus120573)(119881minus119905) Accordingly the profit for the dominant

retailer isprodT119903= 120573(119881 minus 119905)

(2) In RD-channel only the dominant retailer opens anInternet store (RIS) If a consumer locates at a distance fromphysical store (PS) he will get a net utility of by purchasingthe product from PS and a net utility of by purchasing theproduct from RIS To ensure the full market coverage thedominant retailer charges the monopoly price 119881 minus 120575 acrosshis two stores and sells the product to all consumers Forthe manufacturer given the dominant retailerrsquos optimal retailprice the optimal wholesale price is 119908RD

= (1 minus 120573)(119881 minus 120575)Since the manufacturer produces the product at a constantunit (marginal) cost which is normalized to zero and 119905 thesize of the market is one the profits for the manufacturer anddominant retailer are prodRD

119898= (1 minus 120573)(119881 minus 120575) and prod

RD119903

=

120573(119881 minus 120575) respectively(3) In MD-channel the manufacturer opens an Internet

store but dominant retailer does not So consumers canhave convenient access to the product through the dominantretailerrsquos physical store (PS) at price 119901

119903or the manufacturerrsquos

Internet store (MIS) at price 119901119898 their decision about which

store to buy revolves around the comparison of their net

12 Mathematical Problems in Engineering

utility derived fromPS119880PS = 119881minus119901119903minus119905119909 and119880MIS = 119881minus119901119898minus120575by buying the product from MIS Therefore the marginalconsumers are located at 119909 = (119901

119898minus 119901119903+ 120575)119905 So the profit

functions for the manufacturer and dominant retailer can bewritten as

prod

119898

= 119908[

(119901119898minus 119901119903+ 120575)

119905

] + 119901119898[

(119901119903minus 119901119898+ 119905 minus 120575)

119905

] minus 119865119898

(A1)

prod

119903

= (119901119903minus 119908) [

(119901119898minus 119901119903+ 120575)

119905

] (A2)

Under the assumption proposed in Section 3 the dom-inant retailer is the price leader and the manufacturer isthe follower As before the game is solved backwards Inthis market we firstly need to calculate the manufacturerrsquosoptimal price given any dominant retailerrsquos price

Themanufacturerrsquos reaction function can be derived fromthe first-order condition

120597prod119898

120597119901119898

=

[(2 minus 120573) 119901119903minus 2119901119898+ 119905 minus 120575]

119905

= 0

that is 119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A3)

Substituting (A3) into (A2) we get

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

(A4)

Taking the first-order derivative of (A4) with respect to119901119903and letting the derivative be zero we have

119901MD119903

=

(119905 + 120575)

2120573

(A5)

Given the wholesale price bargaining process we canobtain the manufacturerrsquos optimal wholesale price 119908MD

=

(1 minus 120573)(119905 + 120575)2120573 and substituting (A5) into (A3) we getthe manufacturerrsquos optimal retail price

119901MD119898

=

(2 + 120573) 119905 + (2 minus 3120573) 120575

4120573

(A6)

Substituting (A5) and (A6) into (A1) and (A2) wecan obtain the equilibrium profits for the manufacturers anddominant retailer respectively

MDprod

119898

=

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus 119865119898

MDprod

119903

=

(119905 + 120575)2

8119905

(A7)

Proof of Lemma 7 In the M-channel both the manufacturerand dominant retailer simultaneously open their own Inter-net stores then customers are able to purchase a product

either from the dominant retailerrsquos physical store (PS) or fromthe alternative Internet stores (MISRIS) They can get a netutility of 119880PS = 119881 minus 119901

119903minus 119905119909 by buying the product from PS

and a net utility of 119880MIS = 119881 minus 119901119898minus 120575 by buying the product

fromMIS and a net utility of119880RIS = 119881minus 119901119903minus 120575 by buying the

product from RISAccording to the basicmodel we know that the dominant

retailer firstmakes pricing decision as the price leader and themanufacturer is the follower If the dominant retailer chargesa price higher than the manufacturerrsquos price (119901

119903gt 119901119898) then

no consumer will buy the product from his Internet storeUnder this condition the dominant retailer makes no sale inhis Internet store and makes a profit of minus119865

119903 Therefore the

demand functions for the manufacturerrsquos Internet store anddominant retailerrsquos physical store are given respectively asfollows

119863MIS =(119901119903minus 119901119898+ 119905 minus 120575)

119905

(A8)

119863PS =(119901119898minus 119901119903+ 120575)

119905

(A9)

Hence the manufacturerrsquos profit function can be written as

prod

119898

=

[119908 (119901119898minus 119901119903+ 120575) + 119901

119898(119901119903minus 119901119898+ 119905 minus 120575)]

119905

minus 119865119898

(A10)

From the first-order condition we have

119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A11)

Given the condition of 119901119903gt 119901119898 this implies that 119901

119903gt (119905 minus

120575)120573 However when 119901119903le (119905 minus 120575)120573 and 119901

119903gt 119901119898 we always

have 120597prodM119898120597119901119898= [(2 minus 120573)119901

119903minus 2119901119898+ 119905 minus 120575]119905 gt 0

Therefore the manufacturer optimally sets its price at119901119898= 119901119903 and her optimal pricing schedule is as follows

119901119898=

119901119903 119901

119903le

119905 minus 120575

120572

(2 minus 120573) 119901119903+ 119905 minus 120575

2

119901119903gt

119905 minus 120575

120572

(A12)

Given the manufacturerrsquos pricing schedule the dominantretailerrsquos profit is given as follows

prod

119903

=

(119901119903minus 119908)

120575

119905

minus 119865119903 119901

119903le

119905 minus 120575

120573

(119901119903minus 119908)

119905 + 120575 minus 120573119901119903

2119905

minus 119865119903 119901119903gt

119905 minus 120575

120573

(A13)

Under the condition of 119901119903gt (119905 minus 120575)120573 the dominant

retailerrsquos profit is

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

minus 119865119903 (A14)

Taking the first-order derivative of (A14) with respect to 119901119903

and letting the derivative be zero we have 119901M119903= (119905 + 120575)2120573

Mathematical Problems in Engineering 13

Submitting it into (A11) we get the manufacturerrsquos optimalprice in her Internet store 119901M

119898= [(2 + 120573)119905 + (2 minus 3120573)120575]4120573

Hence the manufacturer and dominant retailerrsquos optimalprofits are prodM

119898= (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus 119865119898

andprodM119903= (119905 + 120575)

2

8119905 minus 119865119903 respectively

According to the previous assumption 119901119903gt (119905 minus 120575)120573

which implies that (119905 + 120575)2120573 gt (119905 minus 120575)120573 120575must satisfy 120575 gt1199053 However when 120575 lt 1199053 we always have

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](minus)

gt 0

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](+)

lt 0 (A15)

So the dominant retailerrsquos optimal retail price in the M-channel is 119901M

119903= (119905 minus 120575)120573 Therefore the manufacturer and

dominant retailerrsquos optimal profits areprodM119898= (119905 minus 120575)120573 minus [(119905 minus

120575)120575]119905 minus 119865119898andprodM

119903= [(119905 minus 120575)120575]119905 minus 119865

119903 respectively

B Strategic Conditions forOpening an Internet Store

Proofs of Proposition 8 and Corollary 9 From Lemma 6 weanalyse the equilibrium profits for the dominant retailerbetween the T-channel and RD-channel and note that onlywhen 119865

119903lt 120573(119905 minus 120575) then prodRD

119903gt prod

T119903 This implies that as

long as the setup cost of opening an Internet store satisfies119865119903

lt 120573(119905 minus 120575) ≜ 1198611 it is always optimal to open an

Internet store for the dominant retailer In addition we notethat 120597119861

1120597120575 = minus120573 lt 0 So the dominant retailerrsquos strategic

motive for opening an Internet store would be weakened byincreasing consumersrsquo disutility of purchasing a product fromInternet store

Proofs of Proposition 10 and Corollary 11 From Lemma 6 weanalyse the equilibrium profits for the manufacturer betweenthe T-channel and MD-channel and note that only when thesetup cost of opening an Internet store satisfies 119865

119898lt (119905 +

120575)2120573+[(119905minus120575)2

minus12119905120575]16119905minus(1minus120573)(119881minus119905) ≜ 1198612 thenprodMD

119898gt

prodT119898 In addition we note that 120597119861

2120597120575 = [4119905 minus 120573(7119905 minus 120575)]8120573119905

and find when 0 lt 120573 lt 4119905(7119905 minus 120575) then 1205971198612120597120575 gt 0 and

when 4119905(7119905 minus 120575) lt 120573 lt 1 then 1205971198612120597120575 lt 0

Proofs of Proposition 12 and Corollary 13 FromLemmas 6 and7 we analyse the equilibriumprofits for themanufacturer anddominant retailer between the T-channel andM-channel wenote that under the condition of 120575 lt 1199053 only when the setupcosts of opening an Internet store for the manufacturer anddominant retailer simultaneously satisfy

119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198613

119865119903lt

[(119905 minus 120575) 120575]

119905

minus 120573 (119881 minus 119905) ≜ 1198614

(B1)

thenMprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B2)

Similarly under the condition of 120575 gt 1199053 only when thesetup costs of opening an Internet store for the manufacturerand dominant retailer simultaneously satisfy

119865119898lt

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198615

119865119903lt

(119905 + 120575)2

8119905

minus 120573 (119881 minus 119905) ≜ 1198616

(B3)

then

Mprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B4)

In addition we note that both 1205971198613120597120575 = minus[119905 + 120573(119905 minus

2120575)]120573119905 lt 0 and 1205971198614120597120575 = (119905 minus 2120575)119905 gt 0 are held under

the condition of 120575 lt 1199053 Furthermore under the conditionof 120575 gt 1199053 we also find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198615120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

5120597120575 lt 0

1205971198616120597120575 = 2(119905 + 120575)8119905 gt 0

Proofs of Proposition 14 and Corollary 15 From Lemmas 6and 7 we analyse the manufacturerrsquos equilibrium profits inthe RD-channel and M-channel we note that under thecondition of 120575 lt 1199053 only when the setup cost of opening anInternet store for her satisfies 119865

119898lt (119905 minus 120575)120573 minus [(119905 minus 120575)120575]119905 minus

(1 minus 120573)(119881 minus 120575) ≜ 1198617 thenprodM

119898gt prod

RD119898 In addition we find

1205971198617120597120575 = minus[(1 + 120573

2

)119905 minus 2120573120575]120573119905 lt 0But under the condition of 120575 gt 1199053 only when the setup

cost of opening an Internet store for her satisfies 119865119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 120575) ≜ 1198618 then

prodM119898gt prod

RD119898 In addition 120597119861

8120597120575 = [120573(119905+120575)+4119905(1minus2120573

2

)]8120573119905

we find that when 0 lt 120573 lt [(119905 + 120575) + radic(119905 + 120575)2

+ 1281199052]16119905

then 1205971198618120597120575 gt 0 andwhen [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905 lt

120573 lt 1 then 1205971198618120597120575 lt 0

Proofs of Proposition 16 From Lemmas 6 and 7 we analysethe dominant retailerrsquos equilibriumprofits in theMD-channeland M-channel and note that when 120575 lt 1199053 then prod

M119903minus

prodMD119903

= minus(119905 minus 3120575)2

8119905 minus 119865119903lt 0 and when 120575 gt 1199053

then prodM119903minus prod

MD119903

= minus119865119903lt 0 These imply that when the

manufacturer has operated an Internet store the best choicefor dominant retailer is not to open an Internet store

Proofs of Proposition 17 and Corollary 18 From Lemmas 6and 7 we analyse the dominant retailerrsquos equilibrium profitsin the MD-channel and M-channel and note that under thecondition of 120575 lt 1199053 thenprodM

119898minus prod

MD119898

= [8119905(119905 minus 3120575) minus 120573[(119905 +

120575)2

minus 161205752

]8119905]16120573119905 This implies that the manufacturer willopen her Internet store when the dominant retailer opens an

14 Mathematical Problems in Engineering

Internet store and the setup costs of opening an Internet storefor her satisfies

1198619≜

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

lt 119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

≜ 11986110

(B5)

In addition we find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198619120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

9120597120575 lt 0

and 12059711986110120597120575 = minus[119905 + 120573(119905 minus 2120575)]120573119905 lt 0

C The ManufacturerDominantRetailers Pricing Policies

Proof of Proposition 19 In the MD-channel we respectivelydifferentiate between119901MD

119898and119901MD

119903with respect to 120573 and find

that 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0 For any given120573 differentiating between 119901MD

119898and 119901MD

119903with respect to 120575 we

have 120597119901MD119903

120597120575 = 12120573 gt 0 and 120597119901MD119898

120597120575 = (2 minus 3120573)4120573and if 120573 isin (0 23) then 120597119901MD

119898120597120575 gt 0 if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 In addition we find that 119901MD119898

minus 119901MD119903

= (119905 minus

3120575)4 it is obvious that when 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

when 120575 = 1199053 then 119901MD

119898= 119901

MD119903

and when 120575 gt 1199053 then119901MD119898

lt 119901MD119903

Proof of Proposition 20 In the M-channel we respectivelydifferentiate between 119901M

119898and 119901M

119903with respect to 120573 and find

that when 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0

and when 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 For any given 120573 we respectively differentiate between 119901M119898

and 119901M119903with respect to 120575 and find that when 120575 lt 1199053 then

120597119901M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0 when 120575 gt 1199053 then

120597119901M119898120597120575 = (2 minus 3120573)4120573 and 120597119901M

119903120597120575 = 12120573 gt 0

It is easy to note that when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0

but when 120573 isin (23 1) then 120597119901M119898120597120575 lt 0

Proof of Proposition 21 From Lemmas 6 and 7 we note that120597119908

RD120597120575 = minus(1 minus 120573) lt 0 and 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0In addition if 120575 lt 1199053 then 120597119908M

120597120575 = minus(1 minus 120573)120573 lt 0 if120575 gt 1199053 then 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0

Proof of Proposition 22 From the proofs of Propositions 19and 20 we note that when 120575 lt 1199053 if 120573 isin (0 23) then120597119901

MD119898

120597120575 gt 0 120597119901M119898120597120575 lt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 120597119901M119898120597120575 lt 0 when 120575 gt 1199053 if 120573 isin (0 23)

then 120597119901MD119898

120597120575 = 120597119901M119898120597120575 gt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 = 120597119901M119898120597120575 lt 0

Proof of Proposition 23 From Lemmas 6 and 7 we note that120597119901

RD119903120597120575 = minus1 lt 0 and 120597119901MD

119903120597120575 = 12120572 gt 0 In addition if

120575 lt 1199053 then 120597119901M119903120597120575 = minus1120572 lt 0 if 120575 gt 1199053 then 120597119901M

119903120597120575 =

12120572 gt 0

Abbreviations

UK The consumerrsquos utility of purchasing theproduct from K storeK isin PSRISMIS

119881 The value of consumers willing to payfor the product

120575 The consumersrsquo disutility of purchasingthe product from Internet store(MISRIS)

119905 The per unit transportation cost ofpurchasing the product from physicalstore (PS)

120573 The dominant retailerrsquos bargainingpower in the distribution channel

119908j The manufacturerrsquos wholesale price in

the j-channel j isin TRDMDM

119901j119903 The dominant retailerrsquos price in the

j-channel j isin TRDMDM

119901j119898 The manufacturerrsquos price in the

j-channel j isin MDM

119865119898119865119903 The setup cost of opening an Internetstore by the manufacturerdominantretailer

Πj119898Πj119903 The manufacturerdominant retailerrsquosprofit in the j-channelj isin TRDMDM

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been supported by theNational Natural Sci-ence Foundation of China (71271225) Chongqingrsquos NaturalScience Foundation (cstc2012jjA1404) and the Open Fund ofChongqing Key Laboratory of Logistics (CQKLL12001)

References

[1] L Hsiao and Y-J Chen ldquoStrategic motive for introducinginternet channels in a supply chainrdquo Production and OperationsManagement vol 23 no 1 pp 36ndash47 2014

[2] I Geyskens K Gielens and M G Dekimpe ldquoThe marketvaluation of Internet channel additionsrdquo Journal of Marketingvol 66 no 2 pp 102ndash119 2002

[3] 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

[4] S-H Chun and J-C Kim ldquoPricing strategies in B2C electroniccommerce analytical and empirical approachesrdquo Decision Sup-port Systems vol 40 no 2 pp 375ndash388 2005

[5] S K Mukhopadhyay X Zhu and X Yue ldquoOptimal contractdesign for mixed channels under information asymmetryrdquoProduction and Operations Management vol 17 no 6 pp 641ndash650 2008

Mathematical Problems in Engineering 15

[6] G S Cai ldquoChannel selection and coordination in dual-channelsupply chainsrdquo Journal of Retailing vol 86 no 1 pp 22ndash36 2010

[7] K Takahashi T Aoi D Hirotani and K Morikawa ldquoInventorycontrol in a two-echelon dual-channel supply chain with setupof production and deliveryrdquo International Journal of ProductionEconomics vol 133 no 1 pp 403ndash415 2011

[8] D W Carlton and J A Chevalier ldquoFree riding and salesstrategies for the Internetrdquo Journal of Industrial Economics vol49 no 4 pp 441ndash461 2001

[9] K D Antia M Bergen and S Dutta ldquoCompeting with graymarketsrdquoMIT SloanManagement Review vol 46 no 1 pp 63ndash69 2004

[10] J Shin ldquoHow does free riding on customer service affectcompetitionrdquo Marketing Science vol 26 no 4 pp 488ndash5032007

[11] G Iyer and J M Villas-Boas ldquoA bargaining theory of distribu-tion channelsrdquo Journal of Marketing Research vol 40 no 1 pp80ndash100 2003

[12] A Dukes and Y Liu ldquoIn-store media and distribution channelcoordinationrdquoMarketing Science vol 29 no 1 pp 94ndash107 2010

[13] H Ahn I Duenyas and R Zhang ldquoPrice competition betweenretailers and manufacturer-owned storesrdquoWorking Paper Uni-versity of California at Berkeley 2002

[14] K Cattani W Gilland H S Heese and J SwaminathanldquoBoiling frogs pricing strategies for a manufacturer addinga direct channel that competes with the traditional channelrdquoProduction and Operations Management vol 15 no 1 pp 40ndash56 2006

[15] K-Y Chen M Kaya and O Ozer ldquoDual sales channel man-agement with service competitionrdquo Manufacturing and ServiceOperations Management vol 10 no 4 pp 654ndash675 2008

[16] G Hua S Wang and T C E Cheng ldquoPrice and lead timedecisions in dual-channel supply chainsrdquo European Journal ofOperational Research vol 205 no 1 pp 113ndash126 2010

[17] W S Yoo andE Lee ldquoInternet channel entry a strategic analysisof mixed channel structuresrdquo Marketing Science vol 30 no 1pp 29ndash41 2011

[18] Y Xiong W Yan K Fernandes Z-K Xiong and N GuoldquoldquoBricks vs clicksrdquo the impact of manufacturer encroachmentwith a dealer leasing and selling of durable goodsrdquo EuropeanJournal of Operational Research vol 217 no 1 pp 75ndash83 2012

[19] Q Lu and N Liu ldquoPricing games of mixed conventional ande-commerce distribution channelsrdquo Computers and IndustrialEngineering vol 64 no 1 pp 122ndash132 2013

[20] Q Xu Z Liu and B Shen ldquoThe impact of price comparisonservice on pricing strategy in a dual-channel supply chainrdquoMathematical Problems in Engineering vol 2013 Article ID613528 13 pages 2013

[21] C A Ingene and M E Parry ldquoChannel coordination whenretailers competerdquoMarketing Science vol 14 no 4 pp 360ndash3771995

[22] 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

[23] J Raju and Z J Zhang ldquoChannel coordination in the presenceof a dominant retailerrdquoMarketing Science vol 24 no 2 pp 254ndash262 2005

[24] K L Webb and C J Lambe ldquoInternal multi-channel conflictan exploratory investigation and conceptual frameworkrdquo Indus-trial Marketing Management vol 36 no 1 pp 29ndash43 2007

[25] S K Mukhopadhyay D-Q Yao and X Yue ldquoInformationsharing of value-adding retailer in a mixed channel hi-techsupply chainrdquo Journal of Business Research vol 61 no 9 pp950ndash958 2008

[26] R Yan ldquoManaging channel coordination in a multi-channelmanufacturer-retailer supply chainrdquo Industrial Marketing Man-agement vol 40 no 4 pp 636ndash642 2011

[27] E Cao YMa CWan andM Lai ldquoContracting with asymmet-ric cost information in a dual-channel supply chainrdquoOperationsResearch Letters vol 41 no 4 pp 410ndash414 2013

[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] Y Liu S Gupta and Z J Zhang ldquoNote on self-restraint as anonline entry-deterrence strategyrdquoManagement Science vol 52no 11 pp 1799ndash1809 2006

[30] Z Cheng and B R Nault ldquoInternet channel entry retailcoverage and entry cost advantagerdquo Information Technology andManagement vol 8 no 2 pp 111ndash132 2007

[31] X Zhang ldquoRetailersrsquo multichannel and price advertising strate-giesrdquoMarketing Science vol 28 no 6 pp 1080ndash1094 2009

[32] W Huang and J M Swaminathan ldquoIntroduction of a secondchannel implications for pricing and profitsrdquo European Journalof Operational Research vol 194 no 1 pp 258ndash279 2009

[33] H Hotelling ldquoStability in competitionrdquo The Economic Journalvol 39 no 153 pp 41ndash57 1929

[34] J Zhang ldquoThe perils of behavior-based personalizationrdquo Mar-keting Science vol 30 no 1 pp 170ndash186 2011

[35] T Kabiraj and C Lee ldquoLicensing contracts in hotelling struc-turerdquoTheoretical Economics Letters vol 1 no 3 pp 57ndash62 2011

[36] HWang andTNariu ldquoDistribution channelmanagement in aninternet age equilibrium and social welfarerdquo Journal of IndustryCompetition and Trade vol 12 no 3 pp 285ndash298 2012

[37] M Lijesen ldquoHotellingrsquos webshoprdquo Journal of Economics vol 109no 2 pp 193ndash200 2013

[38] R Gulati and J Garino ldquoGet the right mix of bricks amp clicksrdquoHarvard Business Review vol 78 no 3 pp 107ndash214 2000

[39] K-J Chung S-D Lin and H M Srivastava ldquoThe completesolution procedures for the mathematical analysis of somefamilies of optimal inventorymodels with order-size dependenttrade credit and deterministic and constant demandrdquo AppliedMathematics and Computation vol 219 no 1 pp 142ndash157 2012

[40] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels under conditional trade credit in a supply chain systemrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 24 pp10036ndash10052 2013

[41] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels for deteriorating items in the discounted cash-flowsapproach under conditional trade credit and cash discount ina supply chain systemrdquo Applied Mathematics and InformationSciences vol 8 no 5 pp 2103ndash2111 2014

[42] J Luo and Q Zhang ldquoTrade credit a new mechanism tocoordinate supply chainrdquo Operations Research Letters vol 40no 5 pp 378ndash384 2012

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

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Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

MD-channel and M-channel and raise or lower the prices inthe light of consumersrsquo disutility of buying the product fromInternet store More specifically if the consumersrsquo disutilityof buying from Internet store is low enough (ie 120575 lt 1199053)the manufacturer can raise the retail price at her Internetstore with increasing consumersrsquo disutility of buying fromInternet store when the dominant retailerrsquos bargaining poweris relatively small (ie 120573 lt 23) and the dominant retailerdoes not open Internet store However if the dominantretailer also opens an Internet store the manufacturer shouldlower the retail price at her Internet store so as to attractconsumers to buy the product from her Internet store On thecontrary if the consumersrsquo disutility of buying from Internetstore is relatively larger (ie 120575 gt 1199053) and the dominantretailer also opens an Internet store then the manufacturershould set the same price with the dominant retailerrsquos andadjust the price following the dominant retailer

Proposition 23 Given that the dominant retailerrsquos bargainingpower we obtain the following results about dominant retailerrsquosretail price under RD-channel MD-channel and M-channel

(1) If 120575 lt 1199053 then 120597119901RD119903120597120575 = minus1 lt 0 120597119901MD

119903120597120575 = 12120573 gt

0 and 120597119901M119903120597120575 = minus1120573 lt 0

(2) If 120575 gt 1199053 then 120597119901RD119903120597120575 = minus1 lt 0 120597119901

MD119903

120597120575 =

12120573 gt 0 and 120597119901M119903120597120575 = 12120573 gt 0

Proposition 23 indicates that no matter when the con-sumersrsquo disutility of buying from Internet store is small orlarger the dominant retailer should lower the retail price withincreasing consumersrsquo disutility buying from Internet store inthe RD-channel but in the MD-channel he always raises theretail price with increasing consumersrsquo disutility Howeverin the M-channel when consumersrsquo disutility buying fromInternet store is low enough (ie 120575 lt 1199053) he should lowerthe price with increasing consumersrsquo disutility but whenconsumersrsquo disutility is relatively larger (ie 120575 gt 1199053) he canset the price same as the price in the MD-channel and raisethe price with increasing consumersrsquo disutility

6 Numerical Examples

In this section we present numerical examples to illustratethe theoretical results about impacts of consumersrsquo disutilityof buying from Internet store on the manufacturer anddominant retailerrsquos pricing policies with different bargainingpower for the dominant retailerrsquos among RD-channel MD-channel and M-channel which are summarized in Figures2ndash11 where 119881 = 14 119905 = 6 120575 isin (0 6) and 120573 = 02 120573 = 08The parametersrsquo values satisfy the assumptions in Section 3 inorder to make the models feasible and meaningful

Comparing Figure 2 with Figure 3 we can observe thatwhen the dominant retailerrsquos bargaining power is relativelysmall (ie 120573 = 02) both of them can increase prices asincreasing consumersrsquo disutility of purchasing from Internetstore in MD-channel However when the dominant retailerrsquosbargaining power is relatively larger (ie 120573 = 08) themanufacturer has no choice but to lower the retail price soas to attract consumers to buy the product from her Internet

0 1 2 3 4 5 612

14

16

18

20

22

24

26

28

30

wMD

pMDm

pMDr

120575

Figure 2 Impacts of 120575 on prices in the MD-channel when 120573 = 02

0 1 2 3 4 5 60

1

2

3

4

5

6

7

8

wMD

pMDm

pMDr

120575

Figure 3 Impacts of 120575 on prices in the MD-channel when 120573 = 08

store In addition Figures 2 and 3 show that when consumersrsquodisutility buying from Internet store is low enough (ie 120575 lt

2) the manufacturer can set her retail price to be larger thanthe dominant retailerrsquos However when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2)the manufacturer can set her retail price to be lower than thedominant retailerrsquos

Figures 4 and 5 show that when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)both the manufacturer and dominant retailer should lowerprices to increase consumersrsquo disutility buying from Internet

Mathematical Problems in Engineering 9

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

wM

pMm

pMr

Figure 4 Impacts of 120575 on prices in the M-channel when 120573 = 02

0 1 2 3 4 5 61

2

3

4

5

6

7

8

120575

wM

pMm

pMr

Figure 5 Impacts of 120575 on prices in the M-channel when 120573 = 08

store It is noted that the rate of change of manufacturerrsquosretail price with respect to consumersrsquo disutility buying fromInternet store is equal to that of dominant retailerrsquos retailprice However when consumersrsquo disutility buying fromInternet store is relatively larger (ie 120575 gt 2) if the dominantretailerrsquos bargaining power is relatively small (ie 120573 =

02) the manufacturer can raise retail price following thedominant retailer as increasing consumersrsquo disutility buyingfrom Internet store if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 = 08) the manufacturershould cut down the retail price in her Internet store withincreasing consumersrsquo disutility

0 1 2 3 4 5 66

8

10

12

14

16

18

20

22

24

wMD

wRD

wM

120575

Figure 6 The wholesale prices in different channels when 120573 = 02

0 1 2 3 4 5 605

1

15

2

25

3

120575

wMD

wRD

wM

Figure 7 The wholesale prices in different channels when 120573 = 08

Figures 6 and 7 show that no matter whether thedominant retailerrsquos bargaining power is small or large themanufacturer can raise the wholesale price with increasingconsumersrsquo disutility buying from Internet store in the MD-channel but in the RD-channel the manufacturer shouldlower the wholesale price with increasing consumersrsquo disutil-ity However in the M-channel when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower the wholesale price withincreasing consumersrsquo disutility when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2) themanufacturer can raise the wholesale price with increasing

10 Mathematical Problems in Engineering

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

pMDm

pMm

Figure 8 Manufacturerrsquos retail prices in different channels when120573 = 02

0 1 2 3 4 5 645

5

55

6

65

7

75

120575

pMDm

pMm

Figure 9 Manufacturerrsquos retail prices in different channels when120573 = 08

consumersrsquo disutility and set the wholesale price the same asin the MD-channel

Figures 8 and 9 show that when the dominant retailerrsquosbargaining power is relatively small (ie 120573 = 02) inthe MD-channel the manufacturer can raise retail pricewith increasing consumersrsquo disutility buying from Internetstore but when the dominant retailerrsquos bargaining power isrelatively larger (ie 120573 = 08) the manufacturer should lowerretail price with increasing consumersrsquo disutility Howeverin the M-channel no matter whether the dominant retailerrsquosbargaining power is small or large when consumersrsquo disutility

0 1 2 3 4 5 65

10

15

20

25

30

120575

pRDr

pMDr

pMr

Figure 10 Dominant retailerrsquos prices in different channels when120573 =02

buying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower retail price with increasingconsumersrsquo disutility but when consumersrsquo disutility buyingfrom Internet store is relatively larger (ie 120575 gt 2) if thedominant retailerrsquos bargaining power is relatively small (ie120573 = 02) the manufacturer can raise retail price withincreasing consumersrsquo disutility buying from Internet storeif the dominant retailerrsquos bargaining power is relatively larger(ie 120573 = 08) themanufacturer should lower retail price withincreasing consumersrsquo disutility

Figures 10 and 11 show that no matter whether thedominant retailerrsquos bargaining power is small or larger healways lowers the retail price with increasing consumersrsquodisutility buying from Internet store in the RD-channel butin the MD-channel he always raises the retail price withincreasing consumersrsquo disutility However in the M-channelwhen consumersrsquo disutility buying from Internet store islow enough (ie 120575 lt 2) the dominant retailer shouldlower retail price with increasing consumersrsquo disutility butwhen consumersrsquo disutility is relatively larger (ie 120575 gt 2)the dominant retailer can raise retail price with increasingconsumersrsquo disutility buying from Internet store

7 Conclusions and Future Research

To investigate when the manufacturer and dominant retaileropen their own Internet stores with different setup costsand how set prices to ensure opening Internet stores areprofitable in a supply chain we first present the equilibriumoutcomes under four possible supply chain structures andthen discuss the strategic conditions for the manufacturerand dominant retailer when it is optimal to open an Internetstore In addition we analyze both playersrsquo pricing policies

Mathematical Problems in Engineering 11

0 1 2 3 4 5 62

4

6

8

10

12

14

120575

pMDr

pRDr

pMr

Figure 11 Dominant retailerrsquos prices in different channels when 120573 =08

after they open their Internet stores and discuss the impactsof the dominant retailerrsquos bargaining power and consumersrsquodisutility of purchasing a product from Internet store onthe manufacturer and dominant retailerrsquos pricing strategiesFinally we conduct numerical examples to illustrate thetheoretical results

We obtain some new results differing from those inthe literature We find that the optimal choices for themanufacturer and dominant retailer to open an Internetstore are largely determined by their respective setup costswhich are closely related to the dominant retailerrsquos bargainingpower and consumersrsquo disutility of buying from Internetstore It is worth mentioning that multichannel retailing forthe dominant retailer is not necessarily the best strategyIn other words if the dominant retailer opens an Internetstore the marketing plan for him to attract more consumersby charging a lower price is impossible to achieve and hecan induce the manufacturer to open an Internet store tocompetewith himOnlywhen the setup cost for the dominantretailer to open an Internet store is sufficiently low then he isprofitable

What is more we also find that the manufacturerrsquosoptimal price at her Internet store is not always being lowerthan the dominant retailerrsquos For example if the consumersrsquodisutility of buying from Internet store is sufficiently highthe manufacturer must provide strong price incentives forconsumers to purchase the product from the Internet store

Although this research provides new insights for themanufacturer and dominant retailer to open an Internetstore and set prices in a supply chain there are severaldirections that could be extended First this study assumedthat all information is known to the manufacturer anddominant retailer in our model However information couldbe asymmetric in the supply chain since both players haveprivate information about their own internal variable costs

for example the setup cost of opening an Internet storecustomersrsquo purchase patterns and search costsTherefore wecan explore the competitive equilibrium under asymmetricinformation settings Second we assume that consumersrsquodisutility of buy from Internet store is independent of theunit transportation cost which can be relaxed in the futureresearch Third trade credit is widely used in practice andhas important impact on supply chain management [39ndash41] In recent years trade credit has become one of themajor transactions between suppliers and retailers in a valuechain For example Wal-Mart Carrefour and GOME (alarge Chinese home appliance chain retailer) even delayedpayments to their suppliers for as long as one year [42]Hence it is worthy to understand how the trade creditaffects supply channel configuration together with pricingstrategies in the E-commerce market A final issue worthyof investigation is how different types of customers affectthe manufacturer and dominant retailerrsquos channel selectionstrategies We leave these questions for future research

Appendices

A Equilibrium Outcome ofthe Four Channel Structures

Proof of Lemma 6 (1) In the T-channel both the manufac-turer and dominant retailer do not open their Internet storesThere is only the dominant retailerrsquos physical store in themarket So the dominant retailer acts as a monopolist andoptimally charges a price 119881 minus 119905 such that the market isjust covered For the manufacturer given that the dominantretailerrsquos optimal retail price the optimal wholesale price is119908

T= (1 minus 120573)(119881 minus 119905) Since the manufacturer produces

the product at a constant unit (marginal) cost which isnormalized to zero and the market is just covered that is thesize of the market is one the profit for the manufacturer isprod

T119898= (1minus120573)(119881minus119905) Accordingly the profit for the dominant

retailer isprodT119903= 120573(119881 minus 119905)

(2) In RD-channel only the dominant retailer opens anInternet store (RIS) If a consumer locates at a distance fromphysical store (PS) he will get a net utility of by purchasingthe product from PS and a net utility of by purchasing theproduct from RIS To ensure the full market coverage thedominant retailer charges the monopoly price 119881 minus 120575 acrosshis two stores and sells the product to all consumers Forthe manufacturer given the dominant retailerrsquos optimal retailprice the optimal wholesale price is 119908RD

= (1 minus 120573)(119881 minus 120575)Since the manufacturer produces the product at a constantunit (marginal) cost which is normalized to zero and 119905 thesize of the market is one the profits for the manufacturer anddominant retailer are prodRD

119898= (1 minus 120573)(119881 minus 120575) and prod

RD119903

=

120573(119881 minus 120575) respectively(3) In MD-channel the manufacturer opens an Internet

store but dominant retailer does not So consumers canhave convenient access to the product through the dominantretailerrsquos physical store (PS) at price 119901

119903or the manufacturerrsquos

Internet store (MIS) at price 119901119898 their decision about which

store to buy revolves around the comparison of their net

12 Mathematical Problems in Engineering

utility derived fromPS119880PS = 119881minus119901119903minus119905119909 and119880MIS = 119881minus119901119898minus120575by buying the product from MIS Therefore the marginalconsumers are located at 119909 = (119901

119898minus 119901119903+ 120575)119905 So the profit

functions for the manufacturer and dominant retailer can bewritten as

prod

119898

= 119908[

(119901119898minus 119901119903+ 120575)

119905

] + 119901119898[

(119901119903minus 119901119898+ 119905 minus 120575)

119905

] minus 119865119898

(A1)

prod

119903

= (119901119903minus 119908) [

(119901119898minus 119901119903+ 120575)

119905

] (A2)

Under the assumption proposed in Section 3 the dom-inant retailer is the price leader and the manufacturer isthe follower As before the game is solved backwards Inthis market we firstly need to calculate the manufacturerrsquosoptimal price given any dominant retailerrsquos price

Themanufacturerrsquos reaction function can be derived fromthe first-order condition

120597prod119898

120597119901119898

=

[(2 minus 120573) 119901119903minus 2119901119898+ 119905 minus 120575]

119905

= 0

that is 119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A3)

Substituting (A3) into (A2) we get

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

(A4)

Taking the first-order derivative of (A4) with respect to119901119903and letting the derivative be zero we have

119901MD119903

=

(119905 + 120575)

2120573

(A5)

Given the wholesale price bargaining process we canobtain the manufacturerrsquos optimal wholesale price 119908MD

=

(1 minus 120573)(119905 + 120575)2120573 and substituting (A5) into (A3) we getthe manufacturerrsquos optimal retail price

119901MD119898

=

(2 + 120573) 119905 + (2 minus 3120573) 120575

4120573

(A6)

Substituting (A5) and (A6) into (A1) and (A2) wecan obtain the equilibrium profits for the manufacturers anddominant retailer respectively

MDprod

119898

=

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus 119865119898

MDprod

119903

=

(119905 + 120575)2

8119905

(A7)

Proof of Lemma 7 In the M-channel both the manufacturerand dominant retailer simultaneously open their own Inter-net stores then customers are able to purchase a product

either from the dominant retailerrsquos physical store (PS) or fromthe alternative Internet stores (MISRIS) They can get a netutility of 119880PS = 119881 minus 119901

119903minus 119905119909 by buying the product from PS

and a net utility of 119880MIS = 119881 minus 119901119898minus 120575 by buying the product

fromMIS and a net utility of119880RIS = 119881minus 119901119903minus 120575 by buying the

product from RISAccording to the basicmodel we know that the dominant

retailer firstmakes pricing decision as the price leader and themanufacturer is the follower If the dominant retailer chargesa price higher than the manufacturerrsquos price (119901

119903gt 119901119898) then

no consumer will buy the product from his Internet storeUnder this condition the dominant retailer makes no sale inhis Internet store and makes a profit of minus119865

119903 Therefore the

demand functions for the manufacturerrsquos Internet store anddominant retailerrsquos physical store are given respectively asfollows

119863MIS =(119901119903minus 119901119898+ 119905 minus 120575)

119905

(A8)

119863PS =(119901119898minus 119901119903+ 120575)

119905

(A9)

Hence the manufacturerrsquos profit function can be written as

prod

119898

=

[119908 (119901119898minus 119901119903+ 120575) + 119901

119898(119901119903minus 119901119898+ 119905 minus 120575)]

119905

minus 119865119898

(A10)

From the first-order condition we have

119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A11)

Given the condition of 119901119903gt 119901119898 this implies that 119901

119903gt (119905 minus

120575)120573 However when 119901119903le (119905 minus 120575)120573 and 119901

119903gt 119901119898 we always

have 120597prodM119898120597119901119898= [(2 minus 120573)119901

119903minus 2119901119898+ 119905 minus 120575]119905 gt 0

Therefore the manufacturer optimally sets its price at119901119898= 119901119903 and her optimal pricing schedule is as follows

119901119898=

119901119903 119901

119903le

119905 minus 120575

120572

(2 minus 120573) 119901119903+ 119905 minus 120575

2

119901119903gt

119905 minus 120575

120572

(A12)

Given the manufacturerrsquos pricing schedule the dominantretailerrsquos profit is given as follows

prod

119903

=

(119901119903minus 119908)

120575

119905

minus 119865119903 119901

119903le

119905 minus 120575

120573

(119901119903minus 119908)

119905 + 120575 minus 120573119901119903

2119905

minus 119865119903 119901119903gt

119905 minus 120575

120573

(A13)

Under the condition of 119901119903gt (119905 minus 120575)120573 the dominant

retailerrsquos profit is

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

minus 119865119903 (A14)

Taking the first-order derivative of (A14) with respect to 119901119903

and letting the derivative be zero we have 119901M119903= (119905 + 120575)2120573

Mathematical Problems in Engineering 13

Submitting it into (A11) we get the manufacturerrsquos optimalprice in her Internet store 119901M

119898= [(2 + 120573)119905 + (2 minus 3120573)120575]4120573

Hence the manufacturer and dominant retailerrsquos optimalprofits are prodM

119898= (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus 119865119898

andprodM119903= (119905 + 120575)

2

8119905 minus 119865119903 respectively

According to the previous assumption 119901119903gt (119905 minus 120575)120573

which implies that (119905 + 120575)2120573 gt (119905 minus 120575)120573 120575must satisfy 120575 gt1199053 However when 120575 lt 1199053 we always have

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](minus)

gt 0

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](+)

lt 0 (A15)

So the dominant retailerrsquos optimal retail price in the M-channel is 119901M

119903= (119905 minus 120575)120573 Therefore the manufacturer and

dominant retailerrsquos optimal profits areprodM119898= (119905 minus 120575)120573 minus [(119905 minus

120575)120575]119905 minus 119865119898andprodM

119903= [(119905 minus 120575)120575]119905 minus 119865

119903 respectively

B Strategic Conditions forOpening an Internet Store

Proofs of Proposition 8 and Corollary 9 From Lemma 6 weanalyse the equilibrium profits for the dominant retailerbetween the T-channel and RD-channel and note that onlywhen 119865

119903lt 120573(119905 minus 120575) then prodRD

119903gt prod

T119903 This implies that as

long as the setup cost of opening an Internet store satisfies119865119903

lt 120573(119905 minus 120575) ≜ 1198611 it is always optimal to open an

Internet store for the dominant retailer In addition we notethat 120597119861

1120597120575 = minus120573 lt 0 So the dominant retailerrsquos strategic

motive for opening an Internet store would be weakened byincreasing consumersrsquo disutility of purchasing a product fromInternet store

Proofs of Proposition 10 and Corollary 11 From Lemma 6 weanalyse the equilibrium profits for the manufacturer betweenthe T-channel and MD-channel and note that only when thesetup cost of opening an Internet store satisfies 119865

119898lt (119905 +

120575)2120573+[(119905minus120575)2

minus12119905120575]16119905minus(1minus120573)(119881minus119905) ≜ 1198612 thenprodMD

119898gt

prodT119898 In addition we note that 120597119861

2120597120575 = [4119905 minus 120573(7119905 minus 120575)]8120573119905

and find when 0 lt 120573 lt 4119905(7119905 minus 120575) then 1205971198612120597120575 gt 0 and

when 4119905(7119905 minus 120575) lt 120573 lt 1 then 1205971198612120597120575 lt 0

Proofs of Proposition 12 and Corollary 13 FromLemmas 6 and7 we analyse the equilibriumprofits for themanufacturer anddominant retailer between the T-channel andM-channel wenote that under the condition of 120575 lt 1199053 only when the setupcosts of opening an Internet store for the manufacturer anddominant retailer simultaneously satisfy

119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198613

119865119903lt

[(119905 minus 120575) 120575]

119905

minus 120573 (119881 minus 119905) ≜ 1198614

(B1)

thenMprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B2)

Similarly under the condition of 120575 gt 1199053 only when thesetup costs of opening an Internet store for the manufacturerand dominant retailer simultaneously satisfy

119865119898lt

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198615

119865119903lt

(119905 + 120575)2

8119905

minus 120573 (119881 minus 119905) ≜ 1198616

(B3)

then

Mprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B4)

In addition we note that both 1205971198613120597120575 = minus[119905 + 120573(119905 minus

2120575)]120573119905 lt 0 and 1205971198614120597120575 = (119905 minus 2120575)119905 gt 0 are held under

the condition of 120575 lt 1199053 Furthermore under the conditionof 120575 gt 1199053 we also find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198615120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

5120597120575 lt 0

1205971198616120597120575 = 2(119905 + 120575)8119905 gt 0

Proofs of Proposition 14 and Corollary 15 From Lemmas 6and 7 we analyse the manufacturerrsquos equilibrium profits inthe RD-channel and M-channel we note that under thecondition of 120575 lt 1199053 only when the setup cost of opening anInternet store for her satisfies 119865

119898lt (119905 minus 120575)120573 minus [(119905 minus 120575)120575]119905 minus

(1 minus 120573)(119881 minus 120575) ≜ 1198617 thenprodM

119898gt prod

RD119898 In addition we find

1205971198617120597120575 = minus[(1 + 120573

2

)119905 minus 2120573120575]120573119905 lt 0But under the condition of 120575 gt 1199053 only when the setup

cost of opening an Internet store for her satisfies 119865119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 120575) ≜ 1198618 then

prodM119898gt prod

RD119898 In addition 120597119861

8120597120575 = [120573(119905+120575)+4119905(1minus2120573

2

)]8120573119905

we find that when 0 lt 120573 lt [(119905 + 120575) + radic(119905 + 120575)2

+ 1281199052]16119905

then 1205971198618120597120575 gt 0 andwhen [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905 lt

120573 lt 1 then 1205971198618120597120575 lt 0

Proofs of Proposition 16 From Lemmas 6 and 7 we analysethe dominant retailerrsquos equilibriumprofits in theMD-channeland M-channel and note that when 120575 lt 1199053 then prod

M119903minus

prodMD119903

= minus(119905 minus 3120575)2

8119905 minus 119865119903lt 0 and when 120575 gt 1199053

then prodM119903minus prod

MD119903

= minus119865119903lt 0 These imply that when the

manufacturer has operated an Internet store the best choicefor dominant retailer is not to open an Internet store

Proofs of Proposition 17 and Corollary 18 From Lemmas 6and 7 we analyse the dominant retailerrsquos equilibrium profitsin the MD-channel and M-channel and note that under thecondition of 120575 lt 1199053 thenprodM

119898minus prod

MD119898

= [8119905(119905 minus 3120575) minus 120573[(119905 +

120575)2

minus 161205752

]8119905]16120573119905 This implies that the manufacturer willopen her Internet store when the dominant retailer opens an

14 Mathematical Problems in Engineering

Internet store and the setup costs of opening an Internet storefor her satisfies

1198619≜

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

lt 119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

≜ 11986110

(B5)

In addition we find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198619120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

9120597120575 lt 0

and 12059711986110120597120575 = minus[119905 + 120573(119905 minus 2120575)]120573119905 lt 0

C The ManufacturerDominantRetailers Pricing Policies

Proof of Proposition 19 In the MD-channel we respectivelydifferentiate between119901MD

119898and119901MD

119903with respect to 120573 and find

that 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0 For any given120573 differentiating between 119901MD

119898and 119901MD

119903with respect to 120575 we

have 120597119901MD119903

120597120575 = 12120573 gt 0 and 120597119901MD119898

120597120575 = (2 minus 3120573)4120573and if 120573 isin (0 23) then 120597119901MD

119898120597120575 gt 0 if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 In addition we find that 119901MD119898

minus 119901MD119903

= (119905 minus

3120575)4 it is obvious that when 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

when 120575 = 1199053 then 119901MD

119898= 119901

MD119903

and when 120575 gt 1199053 then119901MD119898

lt 119901MD119903

Proof of Proposition 20 In the M-channel we respectivelydifferentiate between 119901M

119898and 119901M

119903with respect to 120573 and find

that when 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0

and when 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 For any given 120573 we respectively differentiate between 119901M119898

and 119901M119903with respect to 120575 and find that when 120575 lt 1199053 then

120597119901M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0 when 120575 gt 1199053 then

120597119901M119898120597120575 = (2 minus 3120573)4120573 and 120597119901M

119903120597120575 = 12120573 gt 0

It is easy to note that when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0

but when 120573 isin (23 1) then 120597119901M119898120597120575 lt 0

Proof of Proposition 21 From Lemmas 6 and 7 we note that120597119908

RD120597120575 = minus(1 minus 120573) lt 0 and 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0In addition if 120575 lt 1199053 then 120597119908M

120597120575 = minus(1 minus 120573)120573 lt 0 if120575 gt 1199053 then 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0

Proof of Proposition 22 From the proofs of Propositions 19and 20 we note that when 120575 lt 1199053 if 120573 isin (0 23) then120597119901

MD119898

120597120575 gt 0 120597119901M119898120597120575 lt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 120597119901M119898120597120575 lt 0 when 120575 gt 1199053 if 120573 isin (0 23)

then 120597119901MD119898

120597120575 = 120597119901M119898120597120575 gt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 = 120597119901M119898120597120575 lt 0

Proof of Proposition 23 From Lemmas 6 and 7 we note that120597119901

RD119903120597120575 = minus1 lt 0 and 120597119901MD

119903120597120575 = 12120572 gt 0 In addition if

120575 lt 1199053 then 120597119901M119903120597120575 = minus1120572 lt 0 if 120575 gt 1199053 then 120597119901M

119903120597120575 =

12120572 gt 0

Abbreviations

UK The consumerrsquos utility of purchasing theproduct from K storeK isin PSRISMIS

119881 The value of consumers willing to payfor the product

120575 The consumersrsquo disutility of purchasingthe product from Internet store(MISRIS)

119905 The per unit transportation cost ofpurchasing the product from physicalstore (PS)

120573 The dominant retailerrsquos bargainingpower in the distribution channel

119908j The manufacturerrsquos wholesale price in

the j-channel j isin TRDMDM

119901j119903 The dominant retailerrsquos price in the

j-channel j isin TRDMDM

119901j119898 The manufacturerrsquos price in the

j-channel j isin MDM

119865119898119865119903 The setup cost of opening an Internetstore by the manufacturerdominantretailer

Πj119898Πj119903 The manufacturerdominant retailerrsquosprofit in the j-channelj isin TRDMDM

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been supported by theNational Natural Sci-ence Foundation of China (71271225) Chongqingrsquos NaturalScience Foundation (cstc2012jjA1404) and the Open Fund ofChongqing Key Laboratory of Logistics (CQKLL12001)

References

[1] L Hsiao and Y-J Chen ldquoStrategic motive for introducinginternet channels in a supply chainrdquo Production and OperationsManagement vol 23 no 1 pp 36ndash47 2014

[2] I Geyskens K Gielens and M G Dekimpe ldquoThe marketvaluation of Internet channel additionsrdquo Journal of Marketingvol 66 no 2 pp 102ndash119 2002

[3] 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

[4] S-H Chun and J-C Kim ldquoPricing strategies in B2C electroniccommerce analytical and empirical approachesrdquo Decision Sup-port Systems vol 40 no 2 pp 375ndash388 2005

[5] S K Mukhopadhyay X Zhu and X Yue ldquoOptimal contractdesign for mixed channels under information asymmetryrdquoProduction and Operations Management vol 17 no 6 pp 641ndash650 2008

Mathematical Problems in Engineering 15

[6] G S Cai ldquoChannel selection and coordination in dual-channelsupply chainsrdquo Journal of Retailing vol 86 no 1 pp 22ndash36 2010

[7] K Takahashi T Aoi D Hirotani and K Morikawa ldquoInventorycontrol in a two-echelon dual-channel supply chain with setupof production and deliveryrdquo International Journal of ProductionEconomics vol 133 no 1 pp 403ndash415 2011

[8] D W Carlton and J A Chevalier ldquoFree riding and salesstrategies for the Internetrdquo Journal of Industrial Economics vol49 no 4 pp 441ndash461 2001

[9] K D Antia M Bergen and S Dutta ldquoCompeting with graymarketsrdquoMIT SloanManagement Review vol 46 no 1 pp 63ndash69 2004

[10] J Shin ldquoHow does free riding on customer service affectcompetitionrdquo Marketing Science vol 26 no 4 pp 488ndash5032007

[11] G Iyer and J M Villas-Boas ldquoA bargaining theory of distribu-tion channelsrdquo Journal of Marketing Research vol 40 no 1 pp80ndash100 2003

[12] A Dukes and Y Liu ldquoIn-store media and distribution channelcoordinationrdquoMarketing Science vol 29 no 1 pp 94ndash107 2010

[13] H Ahn I Duenyas and R Zhang ldquoPrice competition betweenretailers and manufacturer-owned storesrdquoWorking Paper Uni-versity of California at Berkeley 2002

[14] K Cattani W Gilland H S Heese and J SwaminathanldquoBoiling frogs pricing strategies for a manufacturer addinga direct channel that competes with the traditional channelrdquoProduction and Operations Management vol 15 no 1 pp 40ndash56 2006

[15] K-Y Chen M Kaya and O Ozer ldquoDual sales channel man-agement with service competitionrdquo Manufacturing and ServiceOperations Management vol 10 no 4 pp 654ndash675 2008

[16] G Hua S Wang and T C E Cheng ldquoPrice and lead timedecisions in dual-channel supply chainsrdquo European Journal ofOperational Research vol 205 no 1 pp 113ndash126 2010

[17] W S Yoo andE Lee ldquoInternet channel entry a strategic analysisof mixed channel structuresrdquo Marketing Science vol 30 no 1pp 29ndash41 2011

[18] Y Xiong W Yan K Fernandes Z-K Xiong and N GuoldquoldquoBricks vs clicksrdquo the impact of manufacturer encroachmentwith a dealer leasing and selling of durable goodsrdquo EuropeanJournal of Operational Research vol 217 no 1 pp 75ndash83 2012

[19] Q Lu and N Liu ldquoPricing games of mixed conventional ande-commerce distribution channelsrdquo Computers and IndustrialEngineering vol 64 no 1 pp 122ndash132 2013

[20] Q Xu Z Liu and B Shen ldquoThe impact of price comparisonservice on pricing strategy in a dual-channel supply chainrdquoMathematical Problems in Engineering vol 2013 Article ID613528 13 pages 2013

[21] C A Ingene and M E Parry ldquoChannel coordination whenretailers competerdquoMarketing Science vol 14 no 4 pp 360ndash3771995

[22] 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

[23] J Raju and Z J Zhang ldquoChannel coordination in the presenceof a dominant retailerrdquoMarketing Science vol 24 no 2 pp 254ndash262 2005

[24] K L Webb and C J Lambe ldquoInternal multi-channel conflictan exploratory investigation and conceptual frameworkrdquo Indus-trial Marketing Management vol 36 no 1 pp 29ndash43 2007

[25] S K Mukhopadhyay D-Q Yao and X Yue ldquoInformationsharing of value-adding retailer in a mixed channel hi-techsupply chainrdquo Journal of Business Research vol 61 no 9 pp950ndash958 2008

[26] R Yan ldquoManaging channel coordination in a multi-channelmanufacturer-retailer supply chainrdquo Industrial Marketing Man-agement vol 40 no 4 pp 636ndash642 2011

[27] E Cao YMa CWan andM Lai ldquoContracting with asymmet-ric cost information in a dual-channel supply chainrdquoOperationsResearch Letters vol 41 no 4 pp 410ndash414 2013

[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] Y Liu S Gupta and Z J Zhang ldquoNote on self-restraint as anonline entry-deterrence strategyrdquoManagement Science vol 52no 11 pp 1799ndash1809 2006

[30] Z Cheng and B R Nault ldquoInternet channel entry retailcoverage and entry cost advantagerdquo Information Technology andManagement vol 8 no 2 pp 111ndash132 2007

[31] X Zhang ldquoRetailersrsquo multichannel and price advertising strate-giesrdquoMarketing Science vol 28 no 6 pp 1080ndash1094 2009

[32] W Huang and J M Swaminathan ldquoIntroduction of a secondchannel implications for pricing and profitsrdquo European Journalof Operational Research vol 194 no 1 pp 258ndash279 2009

[33] H Hotelling ldquoStability in competitionrdquo The Economic Journalvol 39 no 153 pp 41ndash57 1929

[34] J Zhang ldquoThe perils of behavior-based personalizationrdquo Mar-keting Science vol 30 no 1 pp 170ndash186 2011

[35] T Kabiraj and C Lee ldquoLicensing contracts in hotelling struc-turerdquoTheoretical Economics Letters vol 1 no 3 pp 57ndash62 2011

[36] HWang andTNariu ldquoDistribution channelmanagement in aninternet age equilibrium and social welfarerdquo Journal of IndustryCompetition and Trade vol 12 no 3 pp 285ndash298 2012

[37] M Lijesen ldquoHotellingrsquos webshoprdquo Journal of Economics vol 109no 2 pp 193ndash200 2013

[38] R Gulati and J Garino ldquoGet the right mix of bricks amp clicksrdquoHarvard Business Review vol 78 no 3 pp 107ndash214 2000

[39] K-J Chung S-D Lin and H M Srivastava ldquoThe completesolution procedures for the mathematical analysis of somefamilies of optimal inventorymodels with order-size dependenttrade credit and deterministic and constant demandrdquo AppliedMathematics and Computation vol 219 no 1 pp 142ndash157 2012

[40] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels under conditional trade credit in a supply chain systemrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 24 pp10036ndash10052 2013

[41] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels for deteriorating items in the discounted cash-flowsapproach under conditional trade credit and cash discount ina supply chain systemrdquo Applied Mathematics and InformationSciences vol 8 no 5 pp 2103ndash2111 2014

[42] J Luo and Q Zhang ldquoTrade credit a new mechanism tocoordinate supply chainrdquo Operations Research Letters vol 40no 5 pp 378ndash384 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

Mathematical Problems in Engineering 9

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

wM

pMm

pMr

Figure 4 Impacts of 120575 on prices in the M-channel when 120573 = 02

0 1 2 3 4 5 61

2

3

4

5

6

7

8

120575

wM

pMm

pMr

Figure 5 Impacts of 120575 on prices in the M-channel when 120573 = 08

store It is noted that the rate of change of manufacturerrsquosretail price with respect to consumersrsquo disutility buying fromInternet store is equal to that of dominant retailerrsquos retailprice However when consumersrsquo disutility buying fromInternet store is relatively larger (ie 120575 gt 2) if the dominantretailerrsquos bargaining power is relatively small (ie 120573 =

02) the manufacturer can raise retail price following thedominant retailer as increasing consumersrsquo disutility buyingfrom Internet store if the dominant retailerrsquos bargainingpower is relatively larger (ie 120573 = 08) the manufacturershould cut down the retail price in her Internet store withincreasing consumersrsquo disutility

0 1 2 3 4 5 66

8

10

12

14

16

18

20

22

24

wMD

wRD

wM

120575

Figure 6 The wholesale prices in different channels when 120573 = 02

0 1 2 3 4 5 605

1

15

2

25

3

120575

wMD

wRD

wM

Figure 7 The wholesale prices in different channels when 120573 = 08

Figures 6 and 7 show that no matter whether thedominant retailerrsquos bargaining power is small or large themanufacturer can raise the wholesale price with increasingconsumersrsquo disutility buying from Internet store in the MD-channel but in the RD-channel the manufacturer shouldlower the wholesale price with increasing consumersrsquo disutil-ity However in the M-channel when consumersrsquo disutilitybuying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower the wholesale price withincreasing consumersrsquo disutility when consumersrsquo disutilitybuying from Internet store is relatively larger (ie 120575 gt 2) themanufacturer can raise the wholesale price with increasing

10 Mathematical Problems in Engineering

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

pMDm

pMm

Figure 8 Manufacturerrsquos retail prices in different channels when120573 = 02

0 1 2 3 4 5 645

5

55

6

65

7

75

120575

pMDm

pMm

Figure 9 Manufacturerrsquos retail prices in different channels when120573 = 08

consumersrsquo disutility and set the wholesale price the same asin the MD-channel

Figures 8 and 9 show that when the dominant retailerrsquosbargaining power is relatively small (ie 120573 = 02) inthe MD-channel the manufacturer can raise retail pricewith increasing consumersrsquo disutility buying from Internetstore but when the dominant retailerrsquos bargaining power isrelatively larger (ie 120573 = 08) the manufacturer should lowerretail price with increasing consumersrsquo disutility Howeverin the M-channel no matter whether the dominant retailerrsquosbargaining power is small or large when consumersrsquo disutility

0 1 2 3 4 5 65

10

15

20

25

30

120575

pRDr

pMDr

pMr

Figure 10 Dominant retailerrsquos prices in different channels when120573 =02

buying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower retail price with increasingconsumersrsquo disutility but when consumersrsquo disutility buyingfrom Internet store is relatively larger (ie 120575 gt 2) if thedominant retailerrsquos bargaining power is relatively small (ie120573 = 02) the manufacturer can raise retail price withincreasing consumersrsquo disutility buying from Internet storeif the dominant retailerrsquos bargaining power is relatively larger(ie 120573 = 08) themanufacturer should lower retail price withincreasing consumersrsquo disutility

Figures 10 and 11 show that no matter whether thedominant retailerrsquos bargaining power is small or larger healways lowers the retail price with increasing consumersrsquodisutility buying from Internet store in the RD-channel butin the MD-channel he always raises the retail price withincreasing consumersrsquo disutility However in the M-channelwhen consumersrsquo disutility buying from Internet store islow enough (ie 120575 lt 2) the dominant retailer shouldlower retail price with increasing consumersrsquo disutility butwhen consumersrsquo disutility is relatively larger (ie 120575 gt 2)the dominant retailer can raise retail price with increasingconsumersrsquo disutility buying from Internet store

7 Conclusions and Future Research

To investigate when the manufacturer and dominant retaileropen their own Internet stores with different setup costsand how set prices to ensure opening Internet stores areprofitable in a supply chain we first present the equilibriumoutcomes under four possible supply chain structures andthen discuss the strategic conditions for the manufacturerand dominant retailer when it is optimal to open an Internetstore In addition we analyze both playersrsquo pricing policies

Mathematical Problems in Engineering 11

0 1 2 3 4 5 62

4

6

8

10

12

14

120575

pMDr

pRDr

pMr

Figure 11 Dominant retailerrsquos prices in different channels when 120573 =08

after they open their Internet stores and discuss the impactsof the dominant retailerrsquos bargaining power and consumersrsquodisutility of purchasing a product from Internet store onthe manufacturer and dominant retailerrsquos pricing strategiesFinally we conduct numerical examples to illustrate thetheoretical results

We obtain some new results differing from those inthe literature We find that the optimal choices for themanufacturer and dominant retailer to open an Internetstore are largely determined by their respective setup costswhich are closely related to the dominant retailerrsquos bargainingpower and consumersrsquo disutility of buying from Internetstore It is worth mentioning that multichannel retailing forthe dominant retailer is not necessarily the best strategyIn other words if the dominant retailer opens an Internetstore the marketing plan for him to attract more consumersby charging a lower price is impossible to achieve and hecan induce the manufacturer to open an Internet store tocompetewith himOnlywhen the setup cost for the dominantretailer to open an Internet store is sufficiently low then he isprofitable

What is more we also find that the manufacturerrsquosoptimal price at her Internet store is not always being lowerthan the dominant retailerrsquos For example if the consumersrsquodisutility of buying from Internet store is sufficiently highthe manufacturer must provide strong price incentives forconsumers to purchase the product from the Internet store

Although this research provides new insights for themanufacturer and dominant retailer to open an Internetstore and set prices in a supply chain there are severaldirections that could be extended First this study assumedthat all information is known to the manufacturer anddominant retailer in our model However information couldbe asymmetric in the supply chain since both players haveprivate information about their own internal variable costs

for example the setup cost of opening an Internet storecustomersrsquo purchase patterns and search costsTherefore wecan explore the competitive equilibrium under asymmetricinformation settings Second we assume that consumersrsquodisutility of buy from Internet store is independent of theunit transportation cost which can be relaxed in the futureresearch Third trade credit is widely used in practice andhas important impact on supply chain management [39ndash41] In recent years trade credit has become one of themajor transactions between suppliers and retailers in a valuechain For example Wal-Mart Carrefour and GOME (alarge Chinese home appliance chain retailer) even delayedpayments to their suppliers for as long as one year [42]Hence it is worthy to understand how the trade creditaffects supply channel configuration together with pricingstrategies in the E-commerce market A final issue worthyof investigation is how different types of customers affectthe manufacturer and dominant retailerrsquos channel selectionstrategies We leave these questions for future research

Appendices

A Equilibrium Outcome ofthe Four Channel Structures

Proof of Lemma 6 (1) In the T-channel both the manufac-turer and dominant retailer do not open their Internet storesThere is only the dominant retailerrsquos physical store in themarket So the dominant retailer acts as a monopolist andoptimally charges a price 119881 minus 119905 such that the market isjust covered For the manufacturer given that the dominantretailerrsquos optimal retail price the optimal wholesale price is119908

T= (1 minus 120573)(119881 minus 119905) Since the manufacturer produces

the product at a constant unit (marginal) cost which isnormalized to zero and the market is just covered that is thesize of the market is one the profit for the manufacturer isprod

T119898= (1minus120573)(119881minus119905) Accordingly the profit for the dominant

retailer isprodT119903= 120573(119881 minus 119905)

(2) In RD-channel only the dominant retailer opens anInternet store (RIS) If a consumer locates at a distance fromphysical store (PS) he will get a net utility of by purchasingthe product from PS and a net utility of by purchasing theproduct from RIS To ensure the full market coverage thedominant retailer charges the monopoly price 119881 minus 120575 acrosshis two stores and sells the product to all consumers Forthe manufacturer given the dominant retailerrsquos optimal retailprice the optimal wholesale price is 119908RD

= (1 minus 120573)(119881 minus 120575)Since the manufacturer produces the product at a constantunit (marginal) cost which is normalized to zero and 119905 thesize of the market is one the profits for the manufacturer anddominant retailer are prodRD

119898= (1 minus 120573)(119881 minus 120575) and prod

RD119903

=

120573(119881 minus 120575) respectively(3) In MD-channel the manufacturer opens an Internet

store but dominant retailer does not So consumers canhave convenient access to the product through the dominantretailerrsquos physical store (PS) at price 119901

119903or the manufacturerrsquos

Internet store (MIS) at price 119901119898 their decision about which

store to buy revolves around the comparison of their net

12 Mathematical Problems in Engineering

utility derived fromPS119880PS = 119881minus119901119903minus119905119909 and119880MIS = 119881minus119901119898minus120575by buying the product from MIS Therefore the marginalconsumers are located at 119909 = (119901

119898minus 119901119903+ 120575)119905 So the profit

functions for the manufacturer and dominant retailer can bewritten as

prod

119898

= 119908[

(119901119898minus 119901119903+ 120575)

119905

] + 119901119898[

(119901119903minus 119901119898+ 119905 minus 120575)

119905

] minus 119865119898

(A1)

prod

119903

= (119901119903minus 119908) [

(119901119898minus 119901119903+ 120575)

119905

] (A2)

Under the assumption proposed in Section 3 the dom-inant retailer is the price leader and the manufacturer isthe follower As before the game is solved backwards Inthis market we firstly need to calculate the manufacturerrsquosoptimal price given any dominant retailerrsquos price

Themanufacturerrsquos reaction function can be derived fromthe first-order condition

120597prod119898

120597119901119898

=

[(2 minus 120573) 119901119903minus 2119901119898+ 119905 minus 120575]

119905

= 0

that is 119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A3)

Substituting (A3) into (A2) we get

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

(A4)

Taking the first-order derivative of (A4) with respect to119901119903and letting the derivative be zero we have

119901MD119903

=

(119905 + 120575)

2120573

(A5)

Given the wholesale price bargaining process we canobtain the manufacturerrsquos optimal wholesale price 119908MD

=

(1 minus 120573)(119905 + 120575)2120573 and substituting (A5) into (A3) we getthe manufacturerrsquos optimal retail price

119901MD119898

=

(2 + 120573) 119905 + (2 minus 3120573) 120575

4120573

(A6)

Substituting (A5) and (A6) into (A1) and (A2) wecan obtain the equilibrium profits for the manufacturers anddominant retailer respectively

MDprod

119898

=

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus 119865119898

MDprod

119903

=

(119905 + 120575)2

8119905

(A7)

Proof of Lemma 7 In the M-channel both the manufacturerand dominant retailer simultaneously open their own Inter-net stores then customers are able to purchase a product

either from the dominant retailerrsquos physical store (PS) or fromthe alternative Internet stores (MISRIS) They can get a netutility of 119880PS = 119881 minus 119901

119903minus 119905119909 by buying the product from PS

and a net utility of 119880MIS = 119881 minus 119901119898minus 120575 by buying the product

fromMIS and a net utility of119880RIS = 119881minus 119901119903minus 120575 by buying the

product from RISAccording to the basicmodel we know that the dominant

retailer firstmakes pricing decision as the price leader and themanufacturer is the follower If the dominant retailer chargesa price higher than the manufacturerrsquos price (119901

119903gt 119901119898) then

no consumer will buy the product from his Internet storeUnder this condition the dominant retailer makes no sale inhis Internet store and makes a profit of minus119865

119903 Therefore the

demand functions for the manufacturerrsquos Internet store anddominant retailerrsquos physical store are given respectively asfollows

119863MIS =(119901119903minus 119901119898+ 119905 minus 120575)

119905

(A8)

119863PS =(119901119898minus 119901119903+ 120575)

119905

(A9)

Hence the manufacturerrsquos profit function can be written as

prod

119898

=

[119908 (119901119898minus 119901119903+ 120575) + 119901

119898(119901119903minus 119901119898+ 119905 minus 120575)]

119905

minus 119865119898

(A10)

From the first-order condition we have

119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A11)

Given the condition of 119901119903gt 119901119898 this implies that 119901

119903gt (119905 minus

120575)120573 However when 119901119903le (119905 minus 120575)120573 and 119901

119903gt 119901119898 we always

have 120597prodM119898120597119901119898= [(2 minus 120573)119901

119903minus 2119901119898+ 119905 minus 120575]119905 gt 0

Therefore the manufacturer optimally sets its price at119901119898= 119901119903 and her optimal pricing schedule is as follows

119901119898=

119901119903 119901

119903le

119905 minus 120575

120572

(2 minus 120573) 119901119903+ 119905 minus 120575

2

119901119903gt

119905 minus 120575

120572

(A12)

Given the manufacturerrsquos pricing schedule the dominantretailerrsquos profit is given as follows

prod

119903

=

(119901119903minus 119908)

120575

119905

minus 119865119903 119901

119903le

119905 minus 120575

120573

(119901119903minus 119908)

119905 + 120575 minus 120573119901119903

2119905

minus 119865119903 119901119903gt

119905 minus 120575

120573

(A13)

Under the condition of 119901119903gt (119905 minus 120575)120573 the dominant

retailerrsquos profit is

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

minus 119865119903 (A14)

Taking the first-order derivative of (A14) with respect to 119901119903

and letting the derivative be zero we have 119901M119903= (119905 + 120575)2120573

Mathematical Problems in Engineering 13

Submitting it into (A11) we get the manufacturerrsquos optimalprice in her Internet store 119901M

119898= [(2 + 120573)119905 + (2 minus 3120573)120575]4120573

Hence the manufacturer and dominant retailerrsquos optimalprofits are prodM

119898= (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus 119865119898

andprodM119903= (119905 + 120575)

2

8119905 minus 119865119903 respectively

According to the previous assumption 119901119903gt (119905 minus 120575)120573

which implies that (119905 + 120575)2120573 gt (119905 minus 120575)120573 120575must satisfy 120575 gt1199053 However when 120575 lt 1199053 we always have

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](minus)

gt 0

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](+)

lt 0 (A15)

So the dominant retailerrsquos optimal retail price in the M-channel is 119901M

119903= (119905 minus 120575)120573 Therefore the manufacturer and

dominant retailerrsquos optimal profits areprodM119898= (119905 minus 120575)120573 minus [(119905 minus

120575)120575]119905 minus 119865119898andprodM

119903= [(119905 minus 120575)120575]119905 minus 119865

119903 respectively

B Strategic Conditions forOpening an Internet Store

Proofs of Proposition 8 and Corollary 9 From Lemma 6 weanalyse the equilibrium profits for the dominant retailerbetween the T-channel and RD-channel and note that onlywhen 119865

119903lt 120573(119905 minus 120575) then prodRD

119903gt prod

T119903 This implies that as

long as the setup cost of opening an Internet store satisfies119865119903

lt 120573(119905 minus 120575) ≜ 1198611 it is always optimal to open an

Internet store for the dominant retailer In addition we notethat 120597119861

1120597120575 = minus120573 lt 0 So the dominant retailerrsquos strategic

motive for opening an Internet store would be weakened byincreasing consumersrsquo disutility of purchasing a product fromInternet store

Proofs of Proposition 10 and Corollary 11 From Lemma 6 weanalyse the equilibrium profits for the manufacturer betweenthe T-channel and MD-channel and note that only when thesetup cost of opening an Internet store satisfies 119865

119898lt (119905 +

120575)2120573+[(119905minus120575)2

minus12119905120575]16119905minus(1minus120573)(119881minus119905) ≜ 1198612 thenprodMD

119898gt

prodT119898 In addition we note that 120597119861

2120597120575 = [4119905 minus 120573(7119905 minus 120575)]8120573119905

and find when 0 lt 120573 lt 4119905(7119905 minus 120575) then 1205971198612120597120575 gt 0 and

when 4119905(7119905 minus 120575) lt 120573 lt 1 then 1205971198612120597120575 lt 0

Proofs of Proposition 12 and Corollary 13 FromLemmas 6 and7 we analyse the equilibriumprofits for themanufacturer anddominant retailer between the T-channel andM-channel wenote that under the condition of 120575 lt 1199053 only when the setupcosts of opening an Internet store for the manufacturer anddominant retailer simultaneously satisfy

119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198613

119865119903lt

[(119905 minus 120575) 120575]

119905

minus 120573 (119881 minus 119905) ≜ 1198614

(B1)

thenMprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B2)

Similarly under the condition of 120575 gt 1199053 only when thesetup costs of opening an Internet store for the manufacturerand dominant retailer simultaneously satisfy

119865119898lt

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198615

119865119903lt

(119905 + 120575)2

8119905

minus 120573 (119881 minus 119905) ≜ 1198616

(B3)

then

Mprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B4)

In addition we note that both 1205971198613120597120575 = minus[119905 + 120573(119905 minus

2120575)]120573119905 lt 0 and 1205971198614120597120575 = (119905 minus 2120575)119905 gt 0 are held under

the condition of 120575 lt 1199053 Furthermore under the conditionof 120575 gt 1199053 we also find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198615120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

5120597120575 lt 0

1205971198616120597120575 = 2(119905 + 120575)8119905 gt 0

Proofs of Proposition 14 and Corollary 15 From Lemmas 6and 7 we analyse the manufacturerrsquos equilibrium profits inthe RD-channel and M-channel we note that under thecondition of 120575 lt 1199053 only when the setup cost of opening anInternet store for her satisfies 119865

119898lt (119905 minus 120575)120573 minus [(119905 minus 120575)120575]119905 minus

(1 minus 120573)(119881 minus 120575) ≜ 1198617 thenprodM

119898gt prod

RD119898 In addition we find

1205971198617120597120575 = minus[(1 + 120573

2

)119905 minus 2120573120575]120573119905 lt 0But under the condition of 120575 gt 1199053 only when the setup

cost of opening an Internet store for her satisfies 119865119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 120575) ≜ 1198618 then

prodM119898gt prod

RD119898 In addition 120597119861

8120597120575 = [120573(119905+120575)+4119905(1minus2120573

2

)]8120573119905

we find that when 0 lt 120573 lt [(119905 + 120575) + radic(119905 + 120575)2

+ 1281199052]16119905

then 1205971198618120597120575 gt 0 andwhen [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905 lt

120573 lt 1 then 1205971198618120597120575 lt 0

Proofs of Proposition 16 From Lemmas 6 and 7 we analysethe dominant retailerrsquos equilibriumprofits in theMD-channeland M-channel and note that when 120575 lt 1199053 then prod

M119903minus

prodMD119903

= minus(119905 minus 3120575)2

8119905 minus 119865119903lt 0 and when 120575 gt 1199053

then prodM119903minus prod

MD119903

= minus119865119903lt 0 These imply that when the

manufacturer has operated an Internet store the best choicefor dominant retailer is not to open an Internet store

Proofs of Proposition 17 and Corollary 18 From Lemmas 6and 7 we analyse the dominant retailerrsquos equilibrium profitsin the MD-channel and M-channel and note that under thecondition of 120575 lt 1199053 thenprodM

119898minus prod

MD119898

= [8119905(119905 minus 3120575) minus 120573[(119905 +

120575)2

minus 161205752

]8119905]16120573119905 This implies that the manufacturer willopen her Internet store when the dominant retailer opens an

14 Mathematical Problems in Engineering

Internet store and the setup costs of opening an Internet storefor her satisfies

1198619≜

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

lt 119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

≜ 11986110

(B5)

In addition we find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198619120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

9120597120575 lt 0

and 12059711986110120597120575 = minus[119905 + 120573(119905 minus 2120575)]120573119905 lt 0

C The ManufacturerDominantRetailers Pricing Policies

Proof of Proposition 19 In the MD-channel we respectivelydifferentiate between119901MD

119898and119901MD

119903with respect to 120573 and find

that 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0 For any given120573 differentiating between 119901MD

119898and 119901MD

119903with respect to 120575 we

have 120597119901MD119903

120597120575 = 12120573 gt 0 and 120597119901MD119898

120597120575 = (2 minus 3120573)4120573and if 120573 isin (0 23) then 120597119901MD

119898120597120575 gt 0 if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 In addition we find that 119901MD119898

minus 119901MD119903

= (119905 minus

3120575)4 it is obvious that when 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

when 120575 = 1199053 then 119901MD

119898= 119901

MD119903

and when 120575 gt 1199053 then119901MD119898

lt 119901MD119903

Proof of Proposition 20 In the M-channel we respectivelydifferentiate between 119901M

119898and 119901M

119903with respect to 120573 and find

that when 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0

and when 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 For any given 120573 we respectively differentiate between 119901M119898

and 119901M119903with respect to 120575 and find that when 120575 lt 1199053 then

120597119901M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0 when 120575 gt 1199053 then

120597119901M119898120597120575 = (2 minus 3120573)4120573 and 120597119901M

119903120597120575 = 12120573 gt 0

It is easy to note that when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0

but when 120573 isin (23 1) then 120597119901M119898120597120575 lt 0

Proof of Proposition 21 From Lemmas 6 and 7 we note that120597119908

RD120597120575 = minus(1 minus 120573) lt 0 and 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0In addition if 120575 lt 1199053 then 120597119908M

120597120575 = minus(1 minus 120573)120573 lt 0 if120575 gt 1199053 then 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0

Proof of Proposition 22 From the proofs of Propositions 19and 20 we note that when 120575 lt 1199053 if 120573 isin (0 23) then120597119901

MD119898

120597120575 gt 0 120597119901M119898120597120575 lt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 120597119901M119898120597120575 lt 0 when 120575 gt 1199053 if 120573 isin (0 23)

then 120597119901MD119898

120597120575 = 120597119901M119898120597120575 gt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 = 120597119901M119898120597120575 lt 0

Proof of Proposition 23 From Lemmas 6 and 7 we note that120597119901

RD119903120597120575 = minus1 lt 0 and 120597119901MD

119903120597120575 = 12120572 gt 0 In addition if

120575 lt 1199053 then 120597119901M119903120597120575 = minus1120572 lt 0 if 120575 gt 1199053 then 120597119901M

119903120597120575 =

12120572 gt 0

Abbreviations

UK The consumerrsquos utility of purchasing theproduct from K storeK isin PSRISMIS

119881 The value of consumers willing to payfor the product

120575 The consumersrsquo disutility of purchasingthe product from Internet store(MISRIS)

119905 The per unit transportation cost ofpurchasing the product from physicalstore (PS)

120573 The dominant retailerrsquos bargainingpower in the distribution channel

119908j The manufacturerrsquos wholesale price in

the j-channel j isin TRDMDM

119901j119903 The dominant retailerrsquos price in the

j-channel j isin TRDMDM

119901j119898 The manufacturerrsquos price in the

j-channel j isin MDM

119865119898119865119903 The setup cost of opening an Internetstore by the manufacturerdominantretailer

Πj119898Πj119903 The manufacturerdominant retailerrsquosprofit in the j-channelj isin TRDMDM

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been supported by theNational Natural Sci-ence Foundation of China (71271225) Chongqingrsquos NaturalScience Foundation (cstc2012jjA1404) and the Open Fund ofChongqing Key Laboratory of Logistics (CQKLL12001)

References

[1] L Hsiao and Y-J Chen ldquoStrategic motive for introducinginternet channels in a supply chainrdquo Production and OperationsManagement vol 23 no 1 pp 36ndash47 2014

[2] I Geyskens K Gielens and M G Dekimpe ldquoThe marketvaluation of Internet channel additionsrdquo Journal of Marketingvol 66 no 2 pp 102ndash119 2002

[3] 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

[4] S-H Chun and J-C Kim ldquoPricing strategies in B2C electroniccommerce analytical and empirical approachesrdquo Decision Sup-port Systems vol 40 no 2 pp 375ndash388 2005

[5] S K Mukhopadhyay X Zhu and X Yue ldquoOptimal contractdesign for mixed channels under information asymmetryrdquoProduction and Operations Management vol 17 no 6 pp 641ndash650 2008

Mathematical Problems in Engineering 15

[6] G S Cai ldquoChannel selection and coordination in dual-channelsupply chainsrdquo Journal of Retailing vol 86 no 1 pp 22ndash36 2010

[7] K Takahashi T Aoi D Hirotani and K Morikawa ldquoInventorycontrol in a two-echelon dual-channel supply chain with setupof production and deliveryrdquo International Journal of ProductionEconomics vol 133 no 1 pp 403ndash415 2011

[8] D W Carlton and J A Chevalier ldquoFree riding and salesstrategies for the Internetrdquo Journal of Industrial Economics vol49 no 4 pp 441ndash461 2001

[9] K D Antia M Bergen and S Dutta ldquoCompeting with graymarketsrdquoMIT SloanManagement Review vol 46 no 1 pp 63ndash69 2004

[10] J Shin ldquoHow does free riding on customer service affectcompetitionrdquo Marketing Science vol 26 no 4 pp 488ndash5032007

[11] G Iyer and J M Villas-Boas ldquoA bargaining theory of distribu-tion channelsrdquo Journal of Marketing Research vol 40 no 1 pp80ndash100 2003

[12] A Dukes and Y Liu ldquoIn-store media and distribution channelcoordinationrdquoMarketing Science vol 29 no 1 pp 94ndash107 2010

[13] H Ahn I Duenyas and R Zhang ldquoPrice competition betweenretailers and manufacturer-owned storesrdquoWorking Paper Uni-versity of California at Berkeley 2002

[14] K Cattani W Gilland H S Heese and J SwaminathanldquoBoiling frogs pricing strategies for a manufacturer addinga direct channel that competes with the traditional channelrdquoProduction and Operations Management vol 15 no 1 pp 40ndash56 2006

[15] K-Y Chen M Kaya and O Ozer ldquoDual sales channel man-agement with service competitionrdquo Manufacturing and ServiceOperations Management vol 10 no 4 pp 654ndash675 2008

[16] G Hua S Wang and T C E Cheng ldquoPrice and lead timedecisions in dual-channel supply chainsrdquo European Journal ofOperational Research vol 205 no 1 pp 113ndash126 2010

[17] W S Yoo andE Lee ldquoInternet channel entry a strategic analysisof mixed channel structuresrdquo Marketing Science vol 30 no 1pp 29ndash41 2011

[18] Y Xiong W Yan K Fernandes Z-K Xiong and N GuoldquoldquoBricks vs clicksrdquo the impact of manufacturer encroachmentwith a dealer leasing and selling of durable goodsrdquo EuropeanJournal of Operational Research vol 217 no 1 pp 75ndash83 2012

[19] Q Lu and N Liu ldquoPricing games of mixed conventional ande-commerce distribution channelsrdquo Computers and IndustrialEngineering vol 64 no 1 pp 122ndash132 2013

[20] Q Xu Z Liu and B Shen ldquoThe impact of price comparisonservice on pricing strategy in a dual-channel supply chainrdquoMathematical Problems in Engineering vol 2013 Article ID613528 13 pages 2013

[21] C A Ingene and M E Parry ldquoChannel coordination whenretailers competerdquoMarketing Science vol 14 no 4 pp 360ndash3771995

[22] 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

[23] J Raju and Z J Zhang ldquoChannel coordination in the presenceof a dominant retailerrdquoMarketing Science vol 24 no 2 pp 254ndash262 2005

[24] K L Webb and C J Lambe ldquoInternal multi-channel conflictan exploratory investigation and conceptual frameworkrdquo Indus-trial Marketing Management vol 36 no 1 pp 29ndash43 2007

[25] S K Mukhopadhyay D-Q Yao and X Yue ldquoInformationsharing of value-adding retailer in a mixed channel hi-techsupply chainrdquo Journal of Business Research vol 61 no 9 pp950ndash958 2008

[26] R Yan ldquoManaging channel coordination in a multi-channelmanufacturer-retailer supply chainrdquo Industrial Marketing Man-agement vol 40 no 4 pp 636ndash642 2011

[27] E Cao YMa CWan andM Lai ldquoContracting with asymmet-ric cost information in a dual-channel supply chainrdquoOperationsResearch Letters vol 41 no 4 pp 410ndash414 2013

[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] Y Liu S Gupta and Z J Zhang ldquoNote on self-restraint as anonline entry-deterrence strategyrdquoManagement Science vol 52no 11 pp 1799ndash1809 2006

[30] Z Cheng and B R Nault ldquoInternet channel entry retailcoverage and entry cost advantagerdquo Information Technology andManagement vol 8 no 2 pp 111ndash132 2007

[31] X Zhang ldquoRetailersrsquo multichannel and price advertising strate-giesrdquoMarketing Science vol 28 no 6 pp 1080ndash1094 2009

[32] W Huang and J M Swaminathan ldquoIntroduction of a secondchannel implications for pricing and profitsrdquo European Journalof Operational Research vol 194 no 1 pp 258ndash279 2009

[33] H Hotelling ldquoStability in competitionrdquo The Economic Journalvol 39 no 153 pp 41ndash57 1929

[34] J Zhang ldquoThe perils of behavior-based personalizationrdquo Mar-keting Science vol 30 no 1 pp 170ndash186 2011

[35] T Kabiraj and C Lee ldquoLicensing contracts in hotelling struc-turerdquoTheoretical Economics Letters vol 1 no 3 pp 57ndash62 2011

[36] HWang andTNariu ldquoDistribution channelmanagement in aninternet age equilibrium and social welfarerdquo Journal of IndustryCompetition and Trade vol 12 no 3 pp 285ndash298 2012

[37] M Lijesen ldquoHotellingrsquos webshoprdquo Journal of Economics vol 109no 2 pp 193ndash200 2013

[38] R Gulati and J Garino ldquoGet the right mix of bricks amp clicksrdquoHarvard Business Review vol 78 no 3 pp 107ndash214 2000

[39] K-J Chung S-D Lin and H M Srivastava ldquoThe completesolution procedures for the mathematical analysis of somefamilies of optimal inventorymodels with order-size dependenttrade credit and deterministic and constant demandrdquo AppliedMathematics and Computation vol 219 no 1 pp 142ndash157 2012

[40] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels under conditional trade credit in a supply chain systemrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 24 pp10036ndash10052 2013

[41] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels for deteriorating items in the discounted cash-flowsapproach under conditional trade credit and cash discount ina supply chain systemrdquo Applied Mathematics and InformationSciences vol 8 no 5 pp 2103ndash2111 2014

[42] J Luo and Q Zhang ldquoTrade credit a new mechanism tocoordinate supply chainrdquo Operations Research Letters vol 40no 5 pp 378ndash384 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

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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

10 Mathematical Problems in Engineering

0 1 2 3 4 5 616

18

20

22

24

26

28

30

120575

pMDm

pMm

Figure 8 Manufacturerrsquos retail prices in different channels when120573 = 02

0 1 2 3 4 5 645

5

55

6

65

7

75

120575

pMDm

pMm

Figure 9 Manufacturerrsquos retail prices in different channels when120573 = 08

consumersrsquo disutility and set the wholesale price the same asin the MD-channel

Figures 8 and 9 show that when the dominant retailerrsquosbargaining power is relatively small (ie 120573 = 02) inthe MD-channel the manufacturer can raise retail pricewith increasing consumersrsquo disutility buying from Internetstore but when the dominant retailerrsquos bargaining power isrelatively larger (ie 120573 = 08) the manufacturer should lowerretail price with increasing consumersrsquo disutility Howeverin the M-channel no matter whether the dominant retailerrsquosbargaining power is small or large when consumersrsquo disutility

0 1 2 3 4 5 65

10

15

20

25

30

120575

pRDr

pMDr

pMr

Figure 10 Dominant retailerrsquos prices in different channels when120573 =02

buying from Internet store is low enough (ie 120575 lt 2)the manufacturer should lower retail price with increasingconsumersrsquo disutility but when consumersrsquo disutility buyingfrom Internet store is relatively larger (ie 120575 gt 2) if thedominant retailerrsquos bargaining power is relatively small (ie120573 = 02) the manufacturer can raise retail price withincreasing consumersrsquo disutility buying from Internet storeif the dominant retailerrsquos bargaining power is relatively larger(ie 120573 = 08) themanufacturer should lower retail price withincreasing consumersrsquo disutility

Figures 10 and 11 show that no matter whether thedominant retailerrsquos bargaining power is small or larger healways lowers the retail price with increasing consumersrsquodisutility buying from Internet store in the RD-channel butin the MD-channel he always raises the retail price withincreasing consumersrsquo disutility However in the M-channelwhen consumersrsquo disutility buying from Internet store islow enough (ie 120575 lt 2) the dominant retailer shouldlower retail price with increasing consumersrsquo disutility butwhen consumersrsquo disutility is relatively larger (ie 120575 gt 2)the dominant retailer can raise retail price with increasingconsumersrsquo disutility buying from Internet store

7 Conclusions and Future Research

To investigate when the manufacturer and dominant retaileropen their own Internet stores with different setup costsand how set prices to ensure opening Internet stores areprofitable in a supply chain we first present the equilibriumoutcomes under four possible supply chain structures andthen discuss the strategic conditions for the manufacturerand dominant retailer when it is optimal to open an Internetstore In addition we analyze both playersrsquo pricing policies

Mathematical Problems in Engineering 11

0 1 2 3 4 5 62

4

6

8

10

12

14

120575

pMDr

pRDr

pMr

Figure 11 Dominant retailerrsquos prices in different channels when 120573 =08

after they open their Internet stores and discuss the impactsof the dominant retailerrsquos bargaining power and consumersrsquodisutility of purchasing a product from Internet store onthe manufacturer and dominant retailerrsquos pricing strategiesFinally we conduct numerical examples to illustrate thetheoretical results

We obtain some new results differing from those inthe literature We find that the optimal choices for themanufacturer and dominant retailer to open an Internetstore are largely determined by their respective setup costswhich are closely related to the dominant retailerrsquos bargainingpower and consumersrsquo disutility of buying from Internetstore It is worth mentioning that multichannel retailing forthe dominant retailer is not necessarily the best strategyIn other words if the dominant retailer opens an Internetstore the marketing plan for him to attract more consumersby charging a lower price is impossible to achieve and hecan induce the manufacturer to open an Internet store tocompetewith himOnlywhen the setup cost for the dominantretailer to open an Internet store is sufficiently low then he isprofitable

What is more we also find that the manufacturerrsquosoptimal price at her Internet store is not always being lowerthan the dominant retailerrsquos For example if the consumersrsquodisutility of buying from Internet store is sufficiently highthe manufacturer must provide strong price incentives forconsumers to purchase the product from the Internet store

Although this research provides new insights for themanufacturer and dominant retailer to open an Internetstore and set prices in a supply chain there are severaldirections that could be extended First this study assumedthat all information is known to the manufacturer anddominant retailer in our model However information couldbe asymmetric in the supply chain since both players haveprivate information about their own internal variable costs

for example the setup cost of opening an Internet storecustomersrsquo purchase patterns and search costsTherefore wecan explore the competitive equilibrium under asymmetricinformation settings Second we assume that consumersrsquodisutility of buy from Internet store is independent of theunit transportation cost which can be relaxed in the futureresearch Third trade credit is widely used in practice andhas important impact on supply chain management [39ndash41] In recent years trade credit has become one of themajor transactions between suppliers and retailers in a valuechain For example Wal-Mart Carrefour and GOME (alarge Chinese home appliance chain retailer) even delayedpayments to their suppliers for as long as one year [42]Hence it is worthy to understand how the trade creditaffects supply channel configuration together with pricingstrategies in the E-commerce market A final issue worthyof investigation is how different types of customers affectthe manufacturer and dominant retailerrsquos channel selectionstrategies We leave these questions for future research

Appendices

A Equilibrium Outcome ofthe Four Channel Structures

Proof of Lemma 6 (1) In the T-channel both the manufac-turer and dominant retailer do not open their Internet storesThere is only the dominant retailerrsquos physical store in themarket So the dominant retailer acts as a monopolist andoptimally charges a price 119881 minus 119905 such that the market isjust covered For the manufacturer given that the dominantretailerrsquos optimal retail price the optimal wholesale price is119908

T= (1 minus 120573)(119881 minus 119905) Since the manufacturer produces

the product at a constant unit (marginal) cost which isnormalized to zero and the market is just covered that is thesize of the market is one the profit for the manufacturer isprod

T119898= (1minus120573)(119881minus119905) Accordingly the profit for the dominant

retailer isprodT119903= 120573(119881 minus 119905)

(2) In RD-channel only the dominant retailer opens anInternet store (RIS) If a consumer locates at a distance fromphysical store (PS) he will get a net utility of by purchasingthe product from PS and a net utility of by purchasing theproduct from RIS To ensure the full market coverage thedominant retailer charges the monopoly price 119881 minus 120575 acrosshis two stores and sells the product to all consumers Forthe manufacturer given the dominant retailerrsquos optimal retailprice the optimal wholesale price is 119908RD

= (1 minus 120573)(119881 minus 120575)Since the manufacturer produces the product at a constantunit (marginal) cost which is normalized to zero and 119905 thesize of the market is one the profits for the manufacturer anddominant retailer are prodRD

119898= (1 minus 120573)(119881 minus 120575) and prod

RD119903

=

120573(119881 minus 120575) respectively(3) In MD-channel the manufacturer opens an Internet

store but dominant retailer does not So consumers canhave convenient access to the product through the dominantretailerrsquos physical store (PS) at price 119901

119903or the manufacturerrsquos

Internet store (MIS) at price 119901119898 their decision about which

store to buy revolves around the comparison of their net

12 Mathematical Problems in Engineering

utility derived fromPS119880PS = 119881minus119901119903minus119905119909 and119880MIS = 119881minus119901119898minus120575by buying the product from MIS Therefore the marginalconsumers are located at 119909 = (119901

119898minus 119901119903+ 120575)119905 So the profit

functions for the manufacturer and dominant retailer can bewritten as

prod

119898

= 119908[

(119901119898minus 119901119903+ 120575)

119905

] + 119901119898[

(119901119903minus 119901119898+ 119905 minus 120575)

119905

] minus 119865119898

(A1)

prod

119903

= (119901119903minus 119908) [

(119901119898minus 119901119903+ 120575)

119905

] (A2)

Under the assumption proposed in Section 3 the dom-inant retailer is the price leader and the manufacturer isthe follower As before the game is solved backwards Inthis market we firstly need to calculate the manufacturerrsquosoptimal price given any dominant retailerrsquos price

Themanufacturerrsquos reaction function can be derived fromthe first-order condition

120597prod119898

120597119901119898

=

[(2 minus 120573) 119901119903minus 2119901119898+ 119905 minus 120575]

119905

= 0

that is 119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A3)

Substituting (A3) into (A2) we get

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

(A4)

Taking the first-order derivative of (A4) with respect to119901119903and letting the derivative be zero we have

119901MD119903

=

(119905 + 120575)

2120573

(A5)

Given the wholesale price bargaining process we canobtain the manufacturerrsquos optimal wholesale price 119908MD

=

(1 minus 120573)(119905 + 120575)2120573 and substituting (A5) into (A3) we getthe manufacturerrsquos optimal retail price

119901MD119898

=

(2 + 120573) 119905 + (2 minus 3120573) 120575

4120573

(A6)

Substituting (A5) and (A6) into (A1) and (A2) wecan obtain the equilibrium profits for the manufacturers anddominant retailer respectively

MDprod

119898

=

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus 119865119898

MDprod

119903

=

(119905 + 120575)2

8119905

(A7)

Proof of Lemma 7 In the M-channel both the manufacturerand dominant retailer simultaneously open their own Inter-net stores then customers are able to purchase a product

either from the dominant retailerrsquos physical store (PS) or fromthe alternative Internet stores (MISRIS) They can get a netutility of 119880PS = 119881 minus 119901

119903minus 119905119909 by buying the product from PS

and a net utility of 119880MIS = 119881 minus 119901119898minus 120575 by buying the product

fromMIS and a net utility of119880RIS = 119881minus 119901119903minus 120575 by buying the

product from RISAccording to the basicmodel we know that the dominant

retailer firstmakes pricing decision as the price leader and themanufacturer is the follower If the dominant retailer chargesa price higher than the manufacturerrsquos price (119901

119903gt 119901119898) then

no consumer will buy the product from his Internet storeUnder this condition the dominant retailer makes no sale inhis Internet store and makes a profit of minus119865

119903 Therefore the

demand functions for the manufacturerrsquos Internet store anddominant retailerrsquos physical store are given respectively asfollows

119863MIS =(119901119903minus 119901119898+ 119905 minus 120575)

119905

(A8)

119863PS =(119901119898minus 119901119903+ 120575)

119905

(A9)

Hence the manufacturerrsquos profit function can be written as

prod

119898

=

[119908 (119901119898minus 119901119903+ 120575) + 119901

119898(119901119903minus 119901119898+ 119905 minus 120575)]

119905

minus 119865119898

(A10)

From the first-order condition we have

119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A11)

Given the condition of 119901119903gt 119901119898 this implies that 119901

119903gt (119905 minus

120575)120573 However when 119901119903le (119905 minus 120575)120573 and 119901

119903gt 119901119898 we always

have 120597prodM119898120597119901119898= [(2 minus 120573)119901

119903minus 2119901119898+ 119905 minus 120575]119905 gt 0

Therefore the manufacturer optimally sets its price at119901119898= 119901119903 and her optimal pricing schedule is as follows

119901119898=

119901119903 119901

119903le

119905 minus 120575

120572

(2 minus 120573) 119901119903+ 119905 minus 120575

2

119901119903gt

119905 minus 120575

120572

(A12)

Given the manufacturerrsquos pricing schedule the dominantretailerrsquos profit is given as follows

prod

119903

=

(119901119903minus 119908)

120575

119905

minus 119865119903 119901

119903le

119905 minus 120575

120573

(119901119903minus 119908)

119905 + 120575 minus 120573119901119903

2119905

minus 119865119903 119901119903gt

119905 minus 120575

120573

(A13)

Under the condition of 119901119903gt (119905 minus 120575)120573 the dominant

retailerrsquos profit is

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

minus 119865119903 (A14)

Taking the first-order derivative of (A14) with respect to 119901119903

and letting the derivative be zero we have 119901M119903= (119905 + 120575)2120573

Mathematical Problems in Engineering 13

Submitting it into (A11) we get the manufacturerrsquos optimalprice in her Internet store 119901M

119898= [(2 + 120573)119905 + (2 minus 3120573)120575]4120573

Hence the manufacturer and dominant retailerrsquos optimalprofits are prodM

119898= (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus 119865119898

andprodM119903= (119905 + 120575)

2

8119905 minus 119865119903 respectively

According to the previous assumption 119901119903gt (119905 minus 120575)120573

which implies that (119905 + 120575)2120573 gt (119905 minus 120575)120573 120575must satisfy 120575 gt1199053 However when 120575 lt 1199053 we always have

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](minus)

gt 0

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](+)

lt 0 (A15)

So the dominant retailerrsquos optimal retail price in the M-channel is 119901M

119903= (119905 minus 120575)120573 Therefore the manufacturer and

dominant retailerrsquos optimal profits areprodM119898= (119905 minus 120575)120573 minus [(119905 minus

120575)120575]119905 minus 119865119898andprodM

119903= [(119905 minus 120575)120575]119905 minus 119865

119903 respectively

B Strategic Conditions forOpening an Internet Store

Proofs of Proposition 8 and Corollary 9 From Lemma 6 weanalyse the equilibrium profits for the dominant retailerbetween the T-channel and RD-channel and note that onlywhen 119865

119903lt 120573(119905 minus 120575) then prodRD

119903gt prod

T119903 This implies that as

long as the setup cost of opening an Internet store satisfies119865119903

lt 120573(119905 minus 120575) ≜ 1198611 it is always optimal to open an

Internet store for the dominant retailer In addition we notethat 120597119861

1120597120575 = minus120573 lt 0 So the dominant retailerrsquos strategic

motive for opening an Internet store would be weakened byincreasing consumersrsquo disutility of purchasing a product fromInternet store

Proofs of Proposition 10 and Corollary 11 From Lemma 6 weanalyse the equilibrium profits for the manufacturer betweenthe T-channel and MD-channel and note that only when thesetup cost of opening an Internet store satisfies 119865

119898lt (119905 +

120575)2120573+[(119905minus120575)2

minus12119905120575]16119905minus(1minus120573)(119881minus119905) ≜ 1198612 thenprodMD

119898gt

prodT119898 In addition we note that 120597119861

2120597120575 = [4119905 minus 120573(7119905 minus 120575)]8120573119905

and find when 0 lt 120573 lt 4119905(7119905 minus 120575) then 1205971198612120597120575 gt 0 and

when 4119905(7119905 minus 120575) lt 120573 lt 1 then 1205971198612120597120575 lt 0

Proofs of Proposition 12 and Corollary 13 FromLemmas 6 and7 we analyse the equilibriumprofits for themanufacturer anddominant retailer between the T-channel andM-channel wenote that under the condition of 120575 lt 1199053 only when the setupcosts of opening an Internet store for the manufacturer anddominant retailer simultaneously satisfy

119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198613

119865119903lt

[(119905 minus 120575) 120575]

119905

minus 120573 (119881 minus 119905) ≜ 1198614

(B1)

thenMprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B2)

Similarly under the condition of 120575 gt 1199053 only when thesetup costs of opening an Internet store for the manufacturerand dominant retailer simultaneously satisfy

119865119898lt

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198615

119865119903lt

(119905 + 120575)2

8119905

minus 120573 (119881 minus 119905) ≜ 1198616

(B3)

then

Mprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B4)

In addition we note that both 1205971198613120597120575 = minus[119905 + 120573(119905 minus

2120575)]120573119905 lt 0 and 1205971198614120597120575 = (119905 minus 2120575)119905 gt 0 are held under

the condition of 120575 lt 1199053 Furthermore under the conditionof 120575 gt 1199053 we also find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198615120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

5120597120575 lt 0

1205971198616120597120575 = 2(119905 + 120575)8119905 gt 0

Proofs of Proposition 14 and Corollary 15 From Lemmas 6and 7 we analyse the manufacturerrsquos equilibrium profits inthe RD-channel and M-channel we note that under thecondition of 120575 lt 1199053 only when the setup cost of opening anInternet store for her satisfies 119865

119898lt (119905 minus 120575)120573 minus [(119905 minus 120575)120575]119905 minus

(1 minus 120573)(119881 minus 120575) ≜ 1198617 thenprodM

119898gt prod

RD119898 In addition we find

1205971198617120597120575 = minus[(1 + 120573

2

)119905 minus 2120573120575]120573119905 lt 0But under the condition of 120575 gt 1199053 only when the setup

cost of opening an Internet store for her satisfies 119865119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 120575) ≜ 1198618 then

prodM119898gt prod

RD119898 In addition 120597119861

8120597120575 = [120573(119905+120575)+4119905(1minus2120573

2

)]8120573119905

we find that when 0 lt 120573 lt [(119905 + 120575) + radic(119905 + 120575)2

+ 1281199052]16119905

then 1205971198618120597120575 gt 0 andwhen [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905 lt

120573 lt 1 then 1205971198618120597120575 lt 0

Proofs of Proposition 16 From Lemmas 6 and 7 we analysethe dominant retailerrsquos equilibriumprofits in theMD-channeland M-channel and note that when 120575 lt 1199053 then prod

M119903minus

prodMD119903

= minus(119905 minus 3120575)2

8119905 minus 119865119903lt 0 and when 120575 gt 1199053

then prodM119903minus prod

MD119903

= minus119865119903lt 0 These imply that when the

manufacturer has operated an Internet store the best choicefor dominant retailer is not to open an Internet store

Proofs of Proposition 17 and Corollary 18 From Lemmas 6and 7 we analyse the dominant retailerrsquos equilibrium profitsin the MD-channel and M-channel and note that under thecondition of 120575 lt 1199053 thenprodM

119898minus prod

MD119898

= [8119905(119905 minus 3120575) minus 120573[(119905 +

120575)2

minus 161205752

]8119905]16120573119905 This implies that the manufacturer willopen her Internet store when the dominant retailer opens an

14 Mathematical Problems in Engineering

Internet store and the setup costs of opening an Internet storefor her satisfies

1198619≜

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

lt 119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

≜ 11986110

(B5)

In addition we find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198619120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

9120597120575 lt 0

and 12059711986110120597120575 = minus[119905 + 120573(119905 minus 2120575)]120573119905 lt 0

C The ManufacturerDominantRetailers Pricing Policies

Proof of Proposition 19 In the MD-channel we respectivelydifferentiate between119901MD

119898and119901MD

119903with respect to 120573 and find

that 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0 For any given120573 differentiating between 119901MD

119898and 119901MD

119903with respect to 120575 we

have 120597119901MD119903

120597120575 = 12120573 gt 0 and 120597119901MD119898

120597120575 = (2 minus 3120573)4120573and if 120573 isin (0 23) then 120597119901MD

119898120597120575 gt 0 if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 In addition we find that 119901MD119898

minus 119901MD119903

= (119905 minus

3120575)4 it is obvious that when 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

when 120575 = 1199053 then 119901MD

119898= 119901

MD119903

and when 120575 gt 1199053 then119901MD119898

lt 119901MD119903

Proof of Proposition 20 In the M-channel we respectivelydifferentiate between 119901M

119898and 119901M

119903with respect to 120573 and find

that when 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0

and when 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 For any given 120573 we respectively differentiate between 119901M119898

and 119901M119903with respect to 120575 and find that when 120575 lt 1199053 then

120597119901M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0 when 120575 gt 1199053 then

120597119901M119898120597120575 = (2 minus 3120573)4120573 and 120597119901M

119903120597120575 = 12120573 gt 0

It is easy to note that when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0

but when 120573 isin (23 1) then 120597119901M119898120597120575 lt 0

Proof of Proposition 21 From Lemmas 6 and 7 we note that120597119908

RD120597120575 = minus(1 minus 120573) lt 0 and 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0In addition if 120575 lt 1199053 then 120597119908M

120597120575 = minus(1 minus 120573)120573 lt 0 if120575 gt 1199053 then 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0

Proof of Proposition 22 From the proofs of Propositions 19and 20 we note that when 120575 lt 1199053 if 120573 isin (0 23) then120597119901

MD119898

120597120575 gt 0 120597119901M119898120597120575 lt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 120597119901M119898120597120575 lt 0 when 120575 gt 1199053 if 120573 isin (0 23)

then 120597119901MD119898

120597120575 = 120597119901M119898120597120575 gt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 = 120597119901M119898120597120575 lt 0

Proof of Proposition 23 From Lemmas 6 and 7 we note that120597119901

RD119903120597120575 = minus1 lt 0 and 120597119901MD

119903120597120575 = 12120572 gt 0 In addition if

120575 lt 1199053 then 120597119901M119903120597120575 = minus1120572 lt 0 if 120575 gt 1199053 then 120597119901M

119903120597120575 =

12120572 gt 0

Abbreviations

UK The consumerrsquos utility of purchasing theproduct from K storeK isin PSRISMIS

119881 The value of consumers willing to payfor the product

120575 The consumersrsquo disutility of purchasingthe product from Internet store(MISRIS)

119905 The per unit transportation cost ofpurchasing the product from physicalstore (PS)

120573 The dominant retailerrsquos bargainingpower in the distribution channel

119908j The manufacturerrsquos wholesale price in

the j-channel j isin TRDMDM

119901j119903 The dominant retailerrsquos price in the

j-channel j isin TRDMDM

119901j119898 The manufacturerrsquos price in the

j-channel j isin MDM

119865119898119865119903 The setup cost of opening an Internetstore by the manufacturerdominantretailer

Πj119898Πj119903 The manufacturerdominant retailerrsquosprofit in the j-channelj isin TRDMDM

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been supported by theNational Natural Sci-ence Foundation of China (71271225) Chongqingrsquos NaturalScience Foundation (cstc2012jjA1404) and the Open Fund ofChongqing Key Laboratory of Logistics (CQKLL12001)

References

[1] L Hsiao and Y-J Chen ldquoStrategic motive for introducinginternet channels in a supply chainrdquo Production and OperationsManagement vol 23 no 1 pp 36ndash47 2014

[2] I Geyskens K Gielens and M G Dekimpe ldquoThe marketvaluation of Internet channel additionsrdquo Journal of Marketingvol 66 no 2 pp 102ndash119 2002

[3] 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

[4] S-H Chun and J-C Kim ldquoPricing strategies in B2C electroniccommerce analytical and empirical approachesrdquo Decision Sup-port Systems vol 40 no 2 pp 375ndash388 2005

[5] S K Mukhopadhyay X Zhu and X Yue ldquoOptimal contractdesign for mixed channels under information asymmetryrdquoProduction and Operations Management vol 17 no 6 pp 641ndash650 2008

Mathematical Problems in Engineering 15

[6] G S Cai ldquoChannel selection and coordination in dual-channelsupply chainsrdquo Journal of Retailing vol 86 no 1 pp 22ndash36 2010

[7] K Takahashi T Aoi D Hirotani and K Morikawa ldquoInventorycontrol in a two-echelon dual-channel supply chain with setupof production and deliveryrdquo International Journal of ProductionEconomics vol 133 no 1 pp 403ndash415 2011

[8] D W Carlton and J A Chevalier ldquoFree riding and salesstrategies for the Internetrdquo Journal of Industrial Economics vol49 no 4 pp 441ndash461 2001

[9] K D Antia M Bergen and S Dutta ldquoCompeting with graymarketsrdquoMIT SloanManagement Review vol 46 no 1 pp 63ndash69 2004

[10] J Shin ldquoHow does free riding on customer service affectcompetitionrdquo Marketing Science vol 26 no 4 pp 488ndash5032007

[11] G Iyer and J M Villas-Boas ldquoA bargaining theory of distribu-tion channelsrdquo Journal of Marketing Research vol 40 no 1 pp80ndash100 2003

[12] A Dukes and Y Liu ldquoIn-store media and distribution channelcoordinationrdquoMarketing Science vol 29 no 1 pp 94ndash107 2010

[13] H Ahn I Duenyas and R Zhang ldquoPrice competition betweenretailers and manufacturer-owned storesrdquoWorking Paper Uni-versity of California at Berkeley 2002

[14] K Cattani W Gilland H S Heese and J SwaminathanldquoBoiling frogs pricing strategies for a manufacturer addinga direct channel that competes with the traditional channelrdquoProduction and Operations Management vol 15 no 1 pp 40ndash56 2006

[15] K-Y Chen M Kaya and O Ozer ldquoDual sales channel man-agement with service competitionrdquo Manufacturing and ServiceOperations Management vol 10 no 4 pp 654ndash675 2008

[16] G Hua S Wang and T C E Cheng ldquoPrice and lead timedecisions in dual-channel supply chainsrdquo European Journal ofOperational Research vol 205 no 1 pp 113ndash126 2010

[17] W S Yoo andE Lee ldquoInternet channel entry a strategic analysisof mixed channel structuresrdquo Marketing Science vol 30 no 1pp 29ndash41 2011

[18] Y Xiong W Yan K Fernandes Z-K Xiong and N GuoldquoldquoBricks vs clicksrdquo the impact of manufacturer encroachmentwith a dealer leasing and selling of durable goodsrdquo EuropeanJournal of Operational Research vol 217 no 1 pp 75ndash83 2012

[19] Q Lu and N Liu ldquoPricing games of mixed conventional ande-commerce distribution channelsrdquo Computers and IndustrialEngineering vol 64 no 1 pp 122ndash132 2013

[20] Q Xu Z Liu and B Shen ldquoThe impact of price comparisonservice on pricing strategy in a dual-channel supply chainrdquoMathematical Problems in Engineering vol 2013 Article ID613528 13 pages 2013

[21] C A Ingene and M E Parry ldquoChannel coordination whenretailers competerdquoMarketing Science vol 14 no 4 pp 360ndash3771995

[22] 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

[23] J Raju and Z J Zhang ldquoChannel coordination in the presenceof a dominant retailerrdquoMarketing Science vol 24 no 2 pp 254ndash262 2005

[24] K L Webb and C J Lambe ldquoInternal multi-channel conflictan exploratory investigation and conceptual frameworkrdquo Indus-trial Marketing Management vol 36 no 1 pp 29ndash43 2007

[25] S K Mukhopadhyay D-Q Yao and X Yue ldquoInformationsharing of value-adding retailer in a mixed channel hi-techsupply chainrdquo Journal of Business Research vol 61 no 9 pp950ndash958 2008

[26] R Yan ldquoManaging channel coordination in a multi-channelmanufacturer-retailer supply chainrdquo Industrial Marketing Man-agement vol 40 no 4 pp 636ndash642 2011

[27] E Cao YMa CWan andM Lai ldquoContracting with asymmet-ric cost information in a dual-channel supply chainrdquoOperationsResearch Letters vol 41 no 4 pp 410ndash414 2013

[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] Y Liu S Gupta and Z J Zhang ldquoNote on self-restraint as anonline entry-deterrence strategyrdquoManagement Science vol 52no 11 pp 1799ndash1809 2006

[30] Z Cheng and B R Nault ldquoInternet channel entry retailcoverage and entry cost advantagerdquo Information Technology andManagement vol 8 no 2 pp 111ndash132 2007

[31] X Zhang ldquoRetailersrsquo multichannel and price advertising strate-giesrdquoMarketing Science vol 28 no 6 pp 1080ndash1094 2009

[32] W Huang and J M Swaminathan ldquoIntroduction of a secondchannel implications for pricing and profitsrdquo European Journalof Operational Research vol 194 no 1 pp 258ndash279 2009

[33] H Hotelling ldquoStability in competitionrdquo The Economic Journalvol 39 no 153 pp 41ndash57 1929

[34] J Zhang ldquoThe perils of behavior-based personalizationrdquo Mar-keting Science vol 30 no 1 pp 170ndash186 2011

[35] T Kabiraj and C Lee ldquoLicensing contracts in hotelling struc-turerdquoTheoretical Economics Letters vol 1 no 3 pp 57ndash62 2011

[36] HWang andTNariu ldquoDistribution channelmanagement in aninternet age equilibrium and social welfarerdquo Journal of IndustryCompetition and Trade vol 12 no 3 pp 285ndash298 2012

[37] M Lijesen ldquoHotellingrsquos webshoprdquo Journal of Economics vol 109no 2 pp 193ndash200 2013

[38] R Gulati and J Garino ldquoGet the right mix of bricks amp clicksrdquoHarvard Business Review vol 78 no 3 pp 107ndash214 2000

[39] K-J Chung S-D Lin and H M Srivastava ldquoThe completesolution procedures for the mathematical analysis of somefamilies of optimal inventorymodels with order-size dependenttrade credit and deterministic and constant demandrdquo AppliedMathematics and Computation vol 219 no 1 pp 142ndash157 2012

[40] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels under conditional trade credit in a supply chain systemrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 24 pp10036ndash10052 2013

[41] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels for deteriorating items in the discounted cash-flowsapproach under conditional trade credit and cash discount ina supply chain systemrdquo Applied Mathematics and InformationSciences vol 8 no 5 pp 2103ndash2111 2014

[42] J Luo and Q Zhang ldquoTrade credit a new mechanism tocoordinate supply chainrdquo Operations Research Letters vol 40no 5 pp 378ndash384 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

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Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Mathematical PhysicsAdvances in

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International Journal of

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Operations ResearchAdvances in

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Algebra

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Decision SciencesAdvances in

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 11

0 1 2 3 4 5 62

4

6

8

10

12

14

120575

pMDr

pRDr

pMr

Figure 11 Dominant retailerrsquos prices in different channels when 120573 =08

after they open their Internet stores and discuss the impactsof the dominant retailerrsquos bargaining power and consumersrsquodisutility of purchasing a product from Internet store onthe manufacturer and dominant retailerrsquos pricing strategiesFinally we conduct numerical examples to illustrate thetheoretical results

We obtain some new results differing from those inthe literature We find that the optimal choices for themanufacturer and dominant retailer to open an Internetstore are largely determined by their respective setup costswhich are closely related to the dominant retailerrsquos bargainingpower and consumersrsquo disutility of buying from Internetstore It is worth mentioning that multichannel retailing forthe dominant retailer is not necessarily the best strategyIn other words if the dominant retailer opens an Internetstore the marketing plan for him to attract more consumersby charging a lower price is impossible to achieve and hecan induce the manufacturer to open an Internet store tocompetewith himOnlywhen the setup cost for the dominantretailer to open an Internet store is sufficiently low then he isprofitable

What is more we also find that the manufacturerrsquosoptimal price at her Internet store is not always being lowerthan the dominant retailerrsquos For example if the consumersrsquodisutility of buying from Internet store is sufficiently highthe manufacturer must provide strong price incentives forconsumers to purchase the product from the Internet store

Although this research provides new insights for themanufacturer and dominant retailer to open an Internetstore and set prices in a supply chain there are severaldirections that could be extended First this study assumedthat all information is known to the manufacturer anddominant retailer in our model However information couldbe asymmetric in the supply chain since both players haveprivate information about their own internal variable costs

for example the setup cost of opening an Internet storecustomersrsquo purchase patterns and search costsTherefore wecan explore the competitive equilibrium under asymmetricinformation settings Second we assume that consumersrsquodisutility of buy from Internet store is independent of theunit transportation cost which can be relaxed in the futureresearch Third trade credit is widely used in practice andhas important impact on supply chain management [39ndash41] In recent years trade credit has become one of themajor transactions between suppliers and retailers in a valuechain For example Wal-Mart Carrefour and GOME (alarge Chinese home appliance chain retailer) even delayedpayments to their suppliers for as long as one year [42]Hence it is worthy to understand how the trade creditaffects supply channel configuration together with pricingstrategies in the E-commerce market A final issue worthyof investigation is how different types of customers affectthe manufacturer and dominant retailerrsquos channel selectionstrategies We leave these questions for future research

Appendices

A Equilibrium Outcome ofthe Four Channel Structures

Proof of Lemma 6 (1) In the T-channel both the manufac-turer and dominant retailer do not open their Internet storesThere is only the dominant retailerrsquos physical store in themarket So the dominant retailer acts as a monopolist andoptimally charges a price 119881 minus 119905 such that the market isjust covered For the manufacturer given that the dominantretailerrsquos optimal retail price the optimal wholesale price is119908

T= (1 minus 120573)(119881 minus 119905) Since the manufacturer produces

the product at a constant unit (marginal) cost which isnormalized to zero and the market is just covered that is thesize of the market is one the profit for the manufacturer isprod

T119898= (1minus120573)(119881minus119905) Accordingly the profit for the dominant

retailer isprodT119903= 120573(119881 minus 119905)

(2) In RD-channel only the dominant retailer opens anInternet store (RIS) If a consumer locates at a distance fromphysical store (PS) he will get a net utility of by purchasingthe product from PS and a net utility of by purchasing theproduct from RIS To ensure the full market coverage thedominant retailer charges the monopoly price 119881 minus 120575 acrosshis two stores and sells the product to all consumers Forthe manufacturer given the dominant retailerrsquos optimal retailprice the optimal wholesale price is 119908RD

= (1 minus 120573)(119881 minus 120575)Since the manufacturer produces the product at a constantunit (marginal) cost which is normalized to zero and 119905 thesize of the market is one the profits for the manufacturer anddominant retailer are prodRD

119898= (1 minus 120573)(119881 minus 120575) and prod

RD119903

=

120573(119881 minus 120575) respectively(3) In MD-channel the manufacturer opens an Internet

store but dominant retailer does not So consumers canhave convenient access to the product through the dominantretailerrsquos physical store (PS) at price 119901

119903or the manufacturerrsquos

Internet store (MIS) at price 119901119898 their decision about which

store to buy revolves around the comparison of their net

12 Mathematical Problems in Engineering

utility derived fromPS119880PS = 119881minus119901119903minus119905119909 and119880MIS = 119881minus119901119898minus120575by buying the product from MIS Therefore the marginalconsumers are located at 119909 = (119901

119898minus 119901119903+ 120575)119905 So the profit

functions for the manufacturer and dominant retailer can bewritten as

prod

119898

= 119908[

(119901119898minus 119901119903+ 120575)

119905

] + 119901119898[

(119901119903minus 119901119898+ 119905 minus 120575)

119905

] minus 119865119898

(A1)

prod

119903

= (119901119903minus 119908) [

(119901119898minus 119901119903+ 120575)

119905

] (A2)

Under the assumption proposed in Section 3 the dom-inant retailer is the price leader and the manufacturer isthe follower As before the game is solved backwards Inthis market we firstly need to calculate the manufacturerrsquosoptimal price given any dominant retailerrsquos price

Themanufacturerrsquos reaction function can be derived fromthe first-order condition

120597prod119898

120597119901119898

=

[(2 minus 120573) 119901119903minus 2119901119898+ 119905 minus 120575]

119905

= 0

that is 119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A3)

Substituting (A3) into (A2) we get

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

(A4)

Taking the first-order derivative of (A4) with respect to119901119903and letting the derivative be zero we have

119901MD119903

=

(119905 + 120575)

2120573

(A5)

Given the wholesale price bargaining process we canobtain the manufacturerrsquos optimal wholesale price 119908MD

=

(1 minus 120573)(119905 + 120575)2120573 and substituting (A5) into (A3) we getthe manufacturerrsquos optimal retail price

119901MD119898

=

(2 + 120573) 119905 + (2 minus 3120573) 120575

4120573

(A6)

Substituting (A5) and (A6) into (A1) and (A2) wecan obtain the equilibrium profits for the manufacturers anddominant retailer respectively

MDprod

119898

=

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus 119865119898

MDprod

119903

=

(119905 + 120575)2

8119905

(A7)

Proof of Lemma 7 In the M-channel both the manufacturerand dominant retailer simultaneously open their own Inter-net stores then customers are able to purchase a product

either from the dominant retailerrsquos physical store (PS) or fromthe alternative Internet stores (MISRIS) They can get a netutility of 119880PS = 119881 minus 119901

119903minus 119905119909 by buying the product from PS

and a net utility of 119880MIS = 119881 minus 119901119898minus 120575 by buying the product

fromMIS and a net utility of119880RIS = 119881minus 119901119903minus 120575 by buying the

product from RISAccording to the basicmodel we know that the dominant

retailer firstmakes pricing decision as the price leader and themanufacturer is the follower If the dominant retailer chargesa price higher than the manufacturerrsquos price (119901

119903gt 119901119898) then

no consumer will buy the product from his Internet storeUnder this condition the dominant retailer makes no sale inhis Internet store and makes a profit of minus119865

119903 Therefore the

demand functions for the manufacturerrsquos Internet store anddominant retailerrsquos physical store are given respectively asfollows

119863MIS =(119901119903minus 119901119898+ 119905 minus 120575)

119905

(A8)

119863PS =(119901119898minus 119901119903+ 120575)

119905

(A9)

Hence the manufacturerrsquos profit function can be written as

prod

119898

=

[119908 (119901119898minus 119901119903+ 120575) + 119901

119898(119901119903minus 119901119898+ 119905 minus 120575)]

119905

minus 119865119898

(A10)

From the first-order condition we have

119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A11)

Given the condition of 119901119903gt 119901119898 this implies that 119901

119903gt (119905 minus

120575)120573 However when 119901119903le (119905 minus 120575)120573 and 119901

119903gt 119901119898 we always

have 120597prodM119898120597119901119898= [(2 minus 120573)119901

119903minus 2119901119898+ 119905 minus 120575]119905 gt 0

Therefore the manufacturer optimally sets its price at119901119898= 119901119903 and her optimal pricing schedule is as follows

119901119898=

119901119903 119901

119903le

119905 minus 120575

120572

(2 minus 120573) 119901119903+ 119905 minus 120575

2

119901119903gt

119905 minus 120575

120572

(A12)

Given the manufacturerrsquos pricing schedule the dominantretailerrsquos profit is given as follows

prod

119903

=

(119901119903minus 119908)

120575

119905

minus 119865119903 119901

119903le

119905 minus 120575

120573

(119901119903minus 119908)

119905 + 120575 minus 120573119901119903

2119905

minus 119865119903 119901119903gt

119905 minus 120575

120573

(A13)

Under the condition of 119901119903gt (119905 minus 120575)120573 the dominant

retailerrsquos profit is

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

minus 119865119903 (A14)

Taking the first-order derivative of (A14) with respect to 119901119903

and letting the derivative be zero we have 119901M119903= (119905 + 120575)2120573

Mathematical Problems in Engineering 13

Submitting it into (A11) we get the manufacturerrsquos optimalprice in her Internet store 119901M

119898= [(2 + 120573)119905 + (2 minus 3120573)120575]4120573

Hence the manufacturer and dominant retailerrsquos optimalprofits are prodM

119898= (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus 119865119898

andprodM119903= (119905 + 120575)

2

8119905 minus 119865119903 respectively

According to the previous assumption 119901119903gt (119905 minus 120575)120573

which implies that (119905 + 120575)2120573 gt (119905 minus 120575)120573 120575must satisfy 120575 gt1199053 However when 120575 lt 1199053 we always have

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](minus)

gt 0

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](+)

lt 0 (A15)

So the dominant retailerrsquos optimal retail price in the M-channel is 119901M

119903= (119905 minus 120575)120573 Therefore the manufacturer and

dominant retailerrsquos optimal profits areprodM119898= (119905 minus 120575)120573 minus [(119905 minus

120575)120575]119905 minus 119865119898andprodM

119903= [(119905 minus 120575)120575]119905 minus 119865

119903 respectively

B Strategic Conditions forOpening an Internet Store

Proofs of Proposition 8 and Corollary 9 From Lemma 6 weanalyse the equilibrium profits for the dominant retailerbetween the T-channel and RD-channel and note that onlywhen 119865

119903lt 120573(119905 minus 120575) then prodRD

119903gt prod

T119903 This implies that as

long as the setup cost of opening an Internet store satisfies119865119903

lt 120573(119905 minus 120575) ≜ 1198611 it is always optimal to open an

Internet store for the dominant retailer In addition we notethat 120597119861

1120597120575 = minus120573 lt 0 So the dominant retailerrsquos strategic

motive for opening an Internet store would be weakened byincreasing consumersrsquo disutility of purchasing a product fromInternet store

Proofs of Proposition 10 and Corollary 11 From Lemma 6 weanalyse the equilibrium profits for the manufacturer betweenthe T-channel and MD-channel and note that only when thesetup cost of opening an Internet store satisfies 119865

119898lt (119905 +

120575)2120573+[(119905minus120575)2

minus12119905120575]16119905minus(1minus120573)(119881minus119905) ≜ 1198612 thenprodMD

119898gt

prodT119898 In addition we note that 120597119861

2120597120575 = [4119905 minus 120573(7119905 minus 120575)]8120573119905

and find when 0 lt 120573 lt 4119905(7119905 minus 120575) then 1205971198612120597120575 gt 0 and

when 4119905(7119905 minus 120575) lt 120573 lt 1 then 1205971198612120597120575 lt 0

Proofs of Proposition 12 and Corollary 13 FromLemmas 6 and7 we analyse the equilibriumprofits for themanufacturer anddominant retailer between the T-channel andM-channel wenote that under the condition of 120575 lt 1199053 only when the setupcosts of opening an Internet store for the manufacturer anddominant retailer simultaneously satisfy

119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198613

119865119903lt

[(119905 minus 120575) 120575]

119905

minus 120573 (119881 minus 119905) ≜ 1198614

(B1)

thenMprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B2)

Similarly under the condition of 120575 gt 1199053 only when thesetup costs of opening an Internet store for the manufacturerand dominant retailer simultaneously satisfy

119865119898lt

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198615

119865119903lt

(119905 + 120575)2

8119905

minus 120573 (119881 minus 119905) ≜ 1198616

(B3)

then

Mprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B4)

In addition we note that both 1205971198613120597120575 = minus[119905 + 120573(119905 minus

2120575)]120573119905 lt 0 and 1205971198614120597120575 = (119905 minus 2120575)119905 gt 0 are held under

the condition of 120575 lt 1199053 Furthermore under the conditionof 120575 gt 1199053 we also find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198615120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

5120597120575 lt 0

1205971198616120597120575 = 2(119905 + 120575)8119905 gt 0

Proofs of Proposition 14 and Corollary 15 From Lemmas 6and 7 we analyse the manufacturerrsquos equilibrium profits inthe RD-channel and M-channel we note that under thecondition of 120575 lt 1199053 only when the setup cost of opening anInternet store for her satisfies 119865

119898lt (119905 minus 120575)120573 minus [(119905 minus 120575)120575]119905 minus

(1 minus 120573)(119881 minus 120575) ≜ 1198617 thenprodM

119898gt prod

RD119898 In addition we find

1205971198617120597120575 = minus[(1 + 120573

2

)119905 minus 2120573120575]120573119905 lt 0But under the condition of 120575 gt 1199053 only when the setup

cost of opening an Internet store for her satisfies 119865119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 120575) ≜ 1198618 then

prodM119898gt prod

RD119898 In addition 120597119861

8120597120575 = [120573(119905+120575)+4119905(1minus2120573

2

)]8120573119905

we find that when 0 lt 120573 lt [(119905 + 120575) + radic(119905 + 120575)2

+ 1281199052]16119905

then 1205971198618120597120575 gt 0 andwhen [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905 lt

120573 lt 1 then 1205971198618120597120575 lt 0

Proofs of Proposition 16 From Lemmas 6 and 7 we analysethe dominant retailerrsquos equilibriumprofits in theMD-channeland M-channel and note that when 120575 lt 1199053 then prod

M119903minus

prodMD119903

= minus(119905 minus 3120575)2

8119905 minus 119865119903lt 0 and when 120575 gt 1199053

then prodM119903minus prod

MD119903

= minus119865119903lt 0 These imply that when the

manufacturer has operated an Internet store the best choicefor dominant retailer is not to open an Internet store

Proofs of Proposition 17 and Corollary 18 From Lemmas 6and 7 we analyse the dominant retailerrsquos equilibrium profitsin the MD-channel and M-channel and note that under thecondition of 120575 lt 1199053 thenprodM

119898minus prod

MD119898

= [8119905(119905 minus 3120575) minus 120573[(119905 +

120575)2

minus 161205752

]8119905]16120573119905 This implies that the manufacturer willopen her Internet store when the dominant retailer opens an

14 Mathematical Problems in Engineering

Internet store and the setup costs of opening an Internet storefor her satisfies

1198619≜

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

lt 119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

≜ 11986110

(B5)

In addition we find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198619120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

9120597120575 lt 0

and 12059711986110120597120575 = minus[119905 + 120573(119905 minus 2120575)]120573119905 lt 0

C The ManufacturerDominantRetailers Pricing Policies

Proof of Proposition 19 In the MD-channel we respectivelydifferentiate between119901MD

119898and119901MD

119903with respect to 120573 and find

that 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0 For any given120573 differentiating between 119901MD

119898and 119901MD

119903with respect to 120575 we

have 120597119901MD119903

120597120575 = 12120573 gt 0 and 120597119901MD119898

120597120575 = (2 minus 3120573)4120573and if 120573 isin (0 23) then 120597119901MD

119898120597120575 gt 0 if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 In addition we find that 119901MD119898

minus 119901MD119903

= (119905 minus

3120575)4 it is obvious that when 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

when 120575 = 1199053 then 119901MD

119898= 119901

MD119903

and when 120575 gt 1199053 then119901MD119898

lt 119901MD119903

Proof of Proposition 20 In the M-channel we respectivelydifferentiate between 119901M

119898and 119901M

119903with respect to 120573 and find

that when 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0

and when 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 For any given 120573 we respectively differentiate between 119901M119898

and 119901M119903with respect to 120575 and find that when 120575 lt 1199053 then

120597119901M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0 when 120575 gt 1199053 then

120597119901M119898120597120575 = (2 minus 3120573)4120573 and 120597119901M

119903120597120575 = 12120573 gt 0

It is easy to note that when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0

but when 120573 isin (23 1) then 120597119901M119898120597120575 lt 0

Proof of Proposition 21 From Lemmas 6 and 7 we note that120597119908

RD120597120575 = minus(1 minus 120573) lt 0 and 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0In addition if 120575 lt 1199053 then 120597119908M

120597120575 = minus(1 minus 120573)120573 lt 0 if120575 gt 1199053 then 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0

Proof of Proposition 22 From the proofs of Propositions 19and 20 we note that when 120575 lt 1199053 if 120573 isin (0 23) then120597119901

MD119898

120597120575 gt 0 120597119901M119898120597120575 lt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 120597119901M119898120597120575 lt 0 when 120575 gt 1199053 if 120573 isin (0 23)

then 120597119901MD119898

120597120575 = 120597119901M119898120597120575 gt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 = 120597119901M119898120597120575 lt 0

Proof of Proposition 23 From Lemmas 6 and 7 we note that120597119901

RD119903120597120575 = minus1 lt 0 and 120597119901MD

119903120597120575 = 12120572 gt 0 In addition if

120575 lt 1199053 then 120597119901M119903120597120575 = minus1120572 lt 0 if 120575 gt 1199053 then 120597119901M

119903120597120575 =

12120572 gt 0

Abbreviations

UK The consumerrsquos utility of purchasing theproduct from K storeK isin PSRISMIS

119881 The value of consumers willing to payfor the product

120575 The consumersrsquo disutility of purchasingthe product from Internet store(MISRIS)

119905 The per unit transportation cost ofpurchasing the product from physicalstore (PS)

120573 The dominant retailerrsquos bargainingpower in the distribution channel

119908j The manufacturerrsquos wholesale price in

the j-channel j isin TRDMDM

119901j119903 The dominant retailerrsquos price in the

j-channel j isin TRDMDM

119901j119898 The manufacturerrsquos price in the

j-channel j isin MDM

119865119898119865119903 The setup cost of opening an Internetstore by the manufacturerdominantretailer

Πj119898Πj119903 The manufacturerdominant retailerrsquosprofit in the j-channelj isin TRDMDM

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been supported by theNational Natural Sci-ence Foundation of China (71271225) Chongqingrsquos NaturalScience Foundation (cstc2012jjA1404) and the Open Fund ofChongqing Key Laboratory of Logistics (CQKLL12001)

References

[1] L Hsiao and Y-J Chen ldquoStrategic motive for introducinginternet channels in a supply chainrdquo Production and OperationsManagement vol 23 no 1 pp 36ndash47 2014

[2] I Geyskens K Gielens and M G Dekimpe ldquoThe marketvaluation of Internet channel additionsrdquo Journal of Marketingvol 66 no 2 pp 102ndash119 2002

[3] 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

[4] S-H Chun and J-C Kim ldquoPricing strategies in B2C electroniccommerce analytical and empirical approachesrdquo Decision Sup-port Systems vol 40 no 2 pp 375ndash388 2005

[5] S K Mukhopadhyay X Zhu and X Yue ldquoOptimal contractdesign for mixed channels under information asymmetryrdquoProduction and Operations Management vol 17 no 6 pp 641ndash650 2008

Mathematical Problems in Engineering 15

[6] G S Cai ldquoChannel selection and coordination in dual-channelsupply chainsrdquo Journal of Retailing vol 86 no 1 pp 22ndash36 2010

[7] K Takahashi T Aoi D Hirotani and K Morikawa ldquoInventorycontrol in a two-echelon dual-channel supply chain with setupof production and deliveryrdquo International Journal of ProductionEconomics vol 133 no 1 pp 403ndash415 2011

[8] D W Carlton and J A Chevalier ldquoFree riding and salesstrategies for the Internetrdquo Journal of Industrial Economics vol49 no 4 pp 441ndash461 2001

[9] K D Antia M Bergen and S Dutta ldquoCompeting with graymarketsrdquoMIT SloanManagement Review vol 46 no 1 pp 63ndash69 2004

[10] J Shin ldquoHow does free riding on customer service affectcompetitionrdquo Marketing Science vol 26 no 4 pp 488ndash5032007

[11] G Iyer and J M Villas-Boas ldquoA bargaining theory of distribu-tion channelsrdquo Journal of Marketing Research vol 40 no 1 pp80ndash100 2003

[12] A Dukes and Y Liu ldquoIn-store media and distribution channelcoordinationrdquoMarketing Science vol 29 no 1 pp 94ndash107 2010

[13] H Ahn I Duenyas and R Zhang ldquoPrice competition betweenretailers and manufacturer-owned storesrdquoWorking Paper Uni-versity of California at Berkeley 2002

[14] K Cattani W Gilland H S Heese and J SwaminathanldquoBoiling frogs pricing strategies for a manufacturer addinga direct channel that competes with the traditional channelrdquoProduction and Operations Management vol 15 no 1 pp 40ndash56 2006

[15] K-Y Chen M Kaya and O Ozer ldquoDual sales channel man-agement with service competitionrdquo Manufacturing and ServiceOperations Management vol 10 no 4 pp 654ndash675 2008

[16] G Hua S Wang and T C E Cheng ldquoPrice and lead timedecisions in dual-channel supply chainsrdquo European Journal ofOperational Research vol 205 no 1 pp 113ndash126 2010

[17] W S Yoo andE Lee ldquoInternet channel entry a strategic analysisof mixed channel structuresrdquo Marketing Science vol 30 no 1pp 29ndash41 2011

[18] Y Xiong W Yan K Fernandes Z-K Xiong and N GuoldquoldquoBricks vs clicksrdquo the impact of manufacturer encroachmentwith a dealer leasing and selling of durable goodsrdquo EuropeanJournal of Operational Research vol 217 no 1 pp 75ndash83 2012

[19] Q Lu and N Liu ldquoPricing games of mixed conventional ande-commerce distribution channelsrdquo Computers and IndustrialEngineering vol 64 no 1 pp 122ndash132 2013

[20] Q Xu Z Liu and B Shen ldquoThe impact of price comparisonservice on pricing strategy in a dual-channel supply chainrdquoMathematical Problems in Engineering vol 2013 Article ID613528 13 pages 2013

[21] C A Ingene and M E Parry ldquoChannel coordination whenretailers competerdquoMarketing Science vol 14 no 4 pp 360ndash3771995

[22] 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

[23] J Raju and Z J Zhang ldquoChannel coordination in the presenceof a dominant retailerrdquoMarketing Science vol 24 no 2 pp 254ndash262 2005

[24] K L Webb and C J Lambe ldquoInternal multi-channel conflictan exploratory investigation and conceptual frameworkrdquo Indus-trial Marketing Management vol 36 no 1 pp 29ndash43 2007

[25] S K Mukhopadhyay D-Q Yao and X Yue ldquoInformationsharing of value-adding retailer in a mixed channel hi-techsupply chainrdquo Journal of Business Research vol 61 no 9 pp950ndash958 2008

[26] R Yan ldquoManaging channel coordination in a multi-channelmanufacturer-retailer supply chainrdquo Industrial Marketing Man-agement vol 40 no 4 pp 636ndash642 2011

[27] E Cao YMa CWan andM Lai ldquoContracting with asymmet-ric cost information in a dual-channel supply chainrdquoOperationsResearch Letters vol 41 no 4 pp 410ndash414 2013

[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] Y Liu S Gupta and Z J Zhang ldquoNote on self-restraint as anonline entry-deterrence strategyrdquoManagement Science vol 52no 11 pp 1799ndash1809 2006

[30] Z Cheng and B R Nault ldquoInternet channel entry retailcoverage and entry cost advantagerdquo Information Technology andManagement vol 8 no 2 pp 111ndash132 2007

[31] X Zhang ldquoRetailersrsquo multichannel and price advertising strate-giesrdquoMarketing Science vol 28 no 6 pp 1080ndash1094 2009

[32] W Huang and J M Swaminathan ldquoIntroduction of a secondchannel implications for pricing and profitsrdquo European Journalof Operational Research vol 194 no 1 pp 258ndash279 2009

[33] H Hotelling ldquoStability in competitionrdquo The Economic Journalvol 39 no 153 pp 41ndash57 1929

[34] J Zhang ldquoThe perils of behavior-based personalizationrdquo Mar-keting Science vol 30 no 1 pp 170ndash186 2011

[35] T Kabiraj and C Lee ldquoLicensing contracts in hotelling struc-turerdquoTheoretical Economics Letters vol 1 no 3 pp 57ndash62 2011

[36] HWang andTNariu ldquoDistribution channelmanagement in aninternet age equilibrium and social welfarerdquo Journal of IndustryCompetition and Trade vol 12 no 3 pp 285ndash298 2012

[37] M Lijesen ldquoHotellingrsquos webshoprdquo Journal of Economics vol 109no 2 pp 193ndash200 2013

[38] R Gulati and J Garino ldquoGet the right mix of bricks amp clicksrdquoHarvard Business Review vol 78 no 3 pp 107ndash214 2000

[39] K-J Chung S-D Lin and H M Srivastava ldquoThe completesolution procedures for the mathematical analysis of somefamilies of optimal inventorymodels with order-size dependenttrade credit and deterministic and constant demandrdquo AppliedMathematics and Computation vol 219 no 1 pp 142ndash157 2012

[40] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels under conditional trade credit in a supply chain systemrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 24 pp10036ndash10052 2013

[41] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels for deteriorating items in the discounted cash-flowsapproach under conditional trade credit and cash discount ina supply chain systemrdquo Applied Mathematics and InformationSciences vol 8 no 5 pp 2103ndash2111 2014

[42] J Luo and Q Zhang ldquoTrade credit a new mechanism tocoordinate supply chainrdquo Operations Research Letters vol 40no 5 pp 378ndash384 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 Mathematical Problems in Engineering

utility derived fromPS119880PS = 119881minus119901119903minus119905119909 and119880MIS = 119881minus119901119898minus120575by buying the product from MIS Therefore the marginalconsumers are located at 119909 = (119901

119898minus 119901119903+ 120575)119905 So the profit

functions for the manufacturer and dominant retailer can bewritten as

prod

119898

= 119908[

(119901119898minus 119901119903+ 120575)

119905

] + 119901119898[

(119901119903minus 119901119898+ 119905 minus 120575)

119905

] minus 119865119898

(A1)

prod

119903

= (119901119903minus 119908) [

(119901119898minus 119901119903+ 120575)

119905

] (A2)

Under the assumption proposed in Section 3 the dom-inant retailer is the price leader and the manufacturer isthe follower As before the game is solved backwards Inthis market we firstly need to calculate the manufacturerrsquosoptimal price given any dominant retailerrsquos price

Themanufacturerrsquos reaction function can be derived fromthe first-order condition

120597prod119898

120597119901119898

=

[(2 minus 120573) 119901119903minus 2119901119898+ 119905 minus 120575]

119905

= 0

that is 119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A3)

Substituting (A3) into (A2) we get

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

(A4)

Taking the first-order derivative of (A4) with respect to119901119903and letting the derivative be zero we have

119901MD119903

=

(119905 + 120575)

2120573

(A5)

Given the wholesale price bargaining process we canobtain the manufacturerrsquos optimal wholesale price 119908MD

=

(1 minus 120573)(119905 + 120575)2120573 and substituting (A5) into (A3) we getthe manufacturerrsquos optimal retail price

119901MD119898

=

(2 + 120573) 119905 + (2 minus 3120573) 120575

4120573

(A6)

Substituting (A5) and (A6) into (A1) and (A2) wecan obtain the equilibrium profits for the manufacturers anddominant retailer respectively

MDprod

119898

=

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus 119865119898

MDprod

119903

=

(119905 + 120575)2

8119905

(A7)

Proof of Lemma 7 In the M-channel both the manufacturerand dominant retailer simultaneously open their own Inter-net stores then customers are able to purchase a product

either from the dominant retailerrsquos physical store (PS) or fromthe alternative Internet stores (MISRIS) They can get a netutility of 119880PS = 119881 minus 119901

119903minus 119905119909 by buying the product from PS

and a net utility of 119880MIS = 119881 minus 119901119898minus 120575 by buying the product

fromMIS and a net utility of119880RIS = 119881minus 119901119903minus 120575 by buying the

product from RISAccording to the basicmodel we know that the dominant

retailer firstmakes pricing decision as the price leader and themanufacturer is the follower If the dominant retailer chargesa price higher than the manufacturerrsquos price (119901

119903gt 119901119898) then

no consumer will buy the product from his Internet storeUnder this condition the dominant retailer makes no sale inhis Internet store and makes a profit of minus119865

119903 Therefore the

demand functions for the manufacturerrsquos Internet store anddominant retailerrsquos physical store are given respectively asfollows

119863MIS =(119901119903minus 119901119898+ 119905 minus 120575)

119905

(A8)

119863PS =(119901119898minus 119901119903+ 120575)

119905

(A9)

Hence the manufacturerrsquos profit function can be written as

prod

119898

=

[119908 (119901119898minus 119901119903+ 120575) + 119901

119898(119901119903minus 119901119898+ 119905 minus 120575)]

119905

minus 119865119898

(A10)

From the first-order condition we have

119901119898=

[(2 minus 120573) 119901119903+ 119905 minus 120575]

2

(A11)

Given the condition of 119901119903gt 119901119898 this implies that 119901

119903gt (119905 minus

120575)120573 However when 119901119903le (119905 minus 120575)120573 and 119901

119903gt 119901119898 we always

have 120597prodM119898120597119901119898= [(2 minus 120573)119901

119903minus 2119901119898+ 119905 minus 120575]119905 gt 0

Therefore the manufacturer optimally sets its price at119901119898= 119901119903 and her optimal pricing schedule is as follows

119901119898=

119901119903 119901

119903le

119905 minus 120575

120572

(2 minus 120573) 119901119903+ 119905 minus 120575

2

119901119903gt

119905 minus 120575

120572

(A12)

Given the manufacturerrsquos pricing schedule the dominantretailerrsquos profit is given as follows

prod

119903

=

(119901119903minus 119908)

120575

119905

minus 119865119903 119901

119903le

119905 minus 120575

120573

(119901119903minus 119908)

119905 + 120575 minus 120573119901119903

2119905

minus 119865119903 119901119903gt

119905 minus 120575

120573

(A13)

Under the condition of 119901119903gt (119905 minus 120575)120573 the dominant

retailerrsquos profit is

prod

119903

=

[120573119901119903(119905 + 120575 minus 120573119901

119903)]

2119905

minus 119865119903 (A14)

Taking the first-order derivative of (A14) with respect to 119901119903

and letting the derivative be zero we have 119901M119903= (119905 + 120575)2120573

Mathematical Problems in Engineering 13

Submitting it into (A11) we get the manufacturerrsquos optimalprice in her Internet store 119901M

119898= [(2 + 120573)119905 + (2 minus 3120573)120575]4120573

Hence the manufacturer and dominant retailerrsquos optimalprofits are prodM

119898= (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus 119865119898

andprodM119903= (119905 + 120575)

2

8119905 minus 119865119903 respectively

According to the previous assumption 119901119903gt (119905 minus 120575)120573

which implies that (119905 + 120575)2120573 gt (119905 minus 120575)120573 120575must satisfy 120575 gt1199053 However when 120575 lt 1199053 we always have

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](minus)

gt 0

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](+)

lt 0 (A15)

So the dominant retailerrsquos optimal retail price in the M-channel is 119901M

119903= (119905 minus 120575)120573 Therefore the manufacturer and

dominant retailerrsquos optimal profits areprodM119898= (119905 minus 120575)120573 minus [(119905 minus

120575)120575]119905 minus 119865119898andprodM

119903= [(119905 minus 120575)120575]119905 minus 119865

119903 respectively

B Strategic Conditions forOpening an Internet Store

Proofs of Proposition 8 and Corollary 9 From Lemma 6 weanalyse the equilibrium profits for the dominant retailerbetween the T-channel and RD-channel and note that onlywhen 119865

119903lt 120573(119905 minus 120575) then prodRD

119903gt prod

T119903 This implies that as

long as the setup cost of opening an Internet store satisfies119865119903

lt 120573(119905 minus 120575) ≜ 1198611 it is always optimal to open an

Internet store for the dominant retailer In addition we notethat 120597119861

1120597120575 = minus120573 lt 0 So the dominant retailerrsquos strategic

motive for opening an Internet store would be weakened byincreasing consumersrsquo disutility of purchasing a product fromInternet store

Proofs of Proposition 10 and Corollary 11 From Lemma 6 weanalyse the equilibrium profits for the manufacturer betweenthe T-channel and MD-channel and note that only when thesetup cost of opening an Internet store satisfies 119865

119898lt (119905 +

120575)2120573+[(119905minus120575)2

minus12119905120575]16119905minus(1minus120573)(119881minus119905) ≜ 1198612 thenprodMD

119898gt

prodT119898 In addition we note that 120597119861

2120597120575 = [4119905 minus 120573(7119905 minus 120575)]8120573119905

and find when 0 lt 120573 lt 4119905(7119905 minus 120575) then 1205971198612120597120575 gt 0 and

when 4119905(7119905 minus 120575) lt 120573 lt 1 then 1205971198612120597120575 lt 0

Proofs of Proposition 12 and Corollary 13 FromLemmas 6 and7 we analyse the equilibriumprofits for themanufacturer anddominant retailer between the T-channel andM-channel wenote that under the condition of 120575 lt 1199053 only when the setupcosts of opening an Internet store for the manufacturer anddominant retailer simultaneously satisfy

119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198613

119865119903lt

[(119905 minus 120575) 120575]

119905

minus 120573 (119881 minus 119905) ≜ 1198614

(B1)

thenMprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B2)

Similarly under the condition of 120575 gt 1199053 only when thesetup costs of opening an Internet store for the manufacturerand dominant retailer simultaneously satisfy

119865119898lt

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198615

119865119903lt

(119905 + 120575)2

8119905

minus 120573 (119881 minus 119905) ≜ 1198616

(B3)

then

Mprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B4)

In addition we note that both 1205971198613120597120575 = minus[119905 + 120573(119905 minus

2120575)]120573119905 lt 0 and 1205971198614120597120575 = (119905 minus 2120575)119905 gt 0 are held under

the condition of 120575 lt 1199053 Furthermore under the conditionof 120575 gt 1199053 we also find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198615120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

5120597120575 lt 0

1205971198616120597120575 = 2(119905 + 120575)8119905 gt 0

Proofs of Proposition 14 and Corollary 15 From Lemmas 6and 7 we analyse the manufacturerrsquos equilibrium profits inthe RD-channel and M-channel we note that under thecondition of 120575 lt 1199053 only when the setup cost of opening anInternet store for her satisfies 119865

119898lt (119905 minus 120575)120573 minus [(119905 minus 120575)120575]119905 minus

(1 minus 120573)(119881 minus 120575) ≜ 1198617 thenprodM

119898gt prod

RD119898 In addition we find

1205971198617120597120575 = minus[(1 + 120573

2

)119905 minus 2120573120575]120573119905 lt 0But under the condition of 120575 gt 1199053 only when the setup

cost of opening an Internet store for her satisfies 119865119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 120575) ≜ 1198618 then

prodM119898gt prod

RD119898 In addition 120597119861

8120597120575 = [120573(119905+120575)+4119905(1minus2120573

2

)]8120573119905

we find that when 0 lt 120573 lt [(119905 + 120575) + radic(119905 + 120575)2

+ 1281199052]16119905

then 1205971198618120597120575 gt 0 andwhen [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905 lt

120573 lt 1 then 1205971198618120597120575 lt 0

Proofs of Proposition 16 From Lemmas 6 and 7 we analysethe dominant retailerrsquos equilibriumprofits in theMD-channeland M-channel and note that when 120575 lt 1199053 then prod

M119903minus

prodMD119903

= minus(119905 minus 3120575)2

8119905 minus 119865119903lt 0 and when 120575 gt 1199053

then prodM119903minus prod

MD119903

= minus119865119903lt 0 These imply that when the

manufacturer has operated an Internet store the best choicefor dominant retailer is not to open an Internet store

Proofs of Proposition 17 and Corollary 18 From Lemmas 6and 7 we analyse the dominant retailerrsquos equilibrium profitsin the MD-channel and M-channel and note that under thecondition of 120575 lt 1199053 thenprodM

119898minus prod

MD119898

= [8119905(119905 minus 3120575) minus 120573[(119905 +

120575)2

minus 161205752

]8119905]16120573119905 This implies that the manufacturer willopen her Internet store when the dominant retailer opens an

14 Mathematical Problems in Engineering

Internet store and the setup costs of opening an Internet storefor her satisfies

1198619≜

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

lt 119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

≜ 11986110

(B5)

In addition we find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198619120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

9120597120575 lt 0

and 12059711986110120597120575 = minus[119905 + 120573(119905 minus 2120575)]120573119905 lt 0

C The ManufacturerDominantRetailers Pricing Policies

Proof of Proposition 19 In the MD-channel we respectivelydifferentiate between119901MD

119898and119901MD

119903with respect to 120573 and find

that 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0 For any given120573 differentiating between 119901MD

119898and 119901MD

119903with respect to 120575 we

have 120597119901MD119903

120597120575 = 12120573 gt 0 and 120597119901MD119898

120597120575 = (2 minus 3120573)4120573and if 120573 isin (0 23) then 120597119901MD

119898120597120575 gt 0 if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 In addition we find that 119901MD119898

minus 119901MD119903

= (119905 minus

3120575)4 it is obvious that when 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

when 120575 = 1199053 then 119901MD

119898= 119901

MD119903

and when 120575 gt 1199053 then119901MD119898

lt 119901MD119903

Proof of Proposition 20 In the M-channel we respectivelydifferentiate between 119901M

119898and 119901M

119903with respect to 120573 and find

that when 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0

and when 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 For any given 120573 we respectively differentiate between 119901M119898

and 119901M119903with respect to 120575 and find that when 120575 lt 1199053 then

120597119901M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0 when 120575 gt 1199053 then

120597119901M119898120597120575 = (2 minus 3120573)4120573 and 120597119901M

119903120597120575 = 12120573 gt 0

It is easy to note that when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0

but when 120573 isin (23 1) then 120597119901M119898120597120575 lt 0

Proof of Proposition 21 From Lemmas 6 and 7 we note that120597119908

RD120597120575 = minus(1 minus 120573) lt 0 and 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0In addition if 120575 lt 1199053 then 120597119908M

120597120575 = minus(1 minus 120573)120573 lt 0 if120575 gt 1199053 then 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0

Proof of Proposition 22 From the proofs of Propositions 19and 20 we note that when 120575 lt 1199053 if 120573 isin (0 23) then120597119901

MD119898

120597120575 gt 0 120597119901M119898120597120575 lt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 120597119901M119898120597120575 lt 0 when 120575 gt 1199053 if 120573 isin (0 23)

then 120597119901MD119898

120597120575 = 120597119901M119898120597120575 gt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 = 120597119901M119898120597120575 lt 0

Proof of Proposition 23 From Lemmas 6 and 7 we note that120597119901

RD119903120597120575 = minus1 lt 0 and 120597119901MD

119903120597120575 = 12120572 gt 0 In addition if

120575 lt 1199053 then 120597119901M119903120597120575 = minus1120572 lt 0 if 120575 gt 1199053 then 120597119901M

119903120597120575 =

12120572 gt 0

Abbreviations

UK The consumerrsquos utility of purchasing theproduct from K storeK isin PSRISMIS

119881 The value of consumers willing to payfor the product

120575 The consumersrsquo disutility of purchasingthe product from Internet store(MISRIS)

119905 The per unit transportation cost ofpurchasing the product from physicalstore (PS)

120573 The dominant retailerrsquos bargainingpower in the distribution channel

119908j The manufacturerrsquos wholesale price in

the j-channel j isin TRDMDM

119901j119903 The dominant retailerrsquos price in the

j-channel j isin TRDMDM

119901j119898 The manufacturerrsquos price in the

j-channel j isin MDM

119865119898119865119903 The setup cost of opening an Internetstore by the manufacturerdominantretailer

Πj119898Πj119903 The manufacturerdominant retailerrsquosprofit in the j-channelj isin TRDMDM

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been supported by theNational Natural Sci-ence Foundation of China (71271225) Chongqingrsquos NaturalScience Foundation (cstc2012jjA1404) and the Open Fund ofChongqing Key Laboratory of Logistics (CQKLL12001)

References

[1] L Hsiao and Y-J Chen ldquoStrategic motive for introducinginternet channels in a supply chainrdquo Production and OperationsManagement vol 23 no 1 pp 36ndash47 2014

[2] I Geyskens K Gielens and M G Dekimpe ldquoThe marketvaluation of Internet channel additionsrdquo Journal of Marketingvol 66 no 2 pp 102ndash119 2002

[3] 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

[4] S-H Chun and J-C Kim ldquoPricing strategies in B2C electroniccommerce analytical and empirical approachesrdquo Decision Sup-port Systems vol 40 no 2 pp 375ndash388 2005

[5] S K Mukhopadhyay X Zhu and X Yue ldquoOptimal contractdesign for mixed channels under information asymmetryrdquoProduction and Operations Management vol 17 no 6 pp 641ndash650 2008

Mathematical Problems in Engineering 15

[6] G S Cai ldquoChannel selection and coordination in dual-channelsupply chainsrdquo Journal of Retailing vol 86 no 1 pp 22ndash36 2010

[7] K Takahashi T Aoi D Hirotani and K Morikawa ldquoInventorycontrol in a two-echelon dual-channel supply chain with setupof production and deliveryrdquo International Journal of ProductionEconomics vol 133 no 1 pp 403ndash415 2011

[8] D W Carlton and J A Chevalier ldquoFree riding and salesstrategies for the Internetrdquo Journal of Industrial Economics vol49 no 4 pp 441ndash461 2001

[9] K D Antia M Bergen and S Dutta ldquoCompeting with graymarketsrdquoMIT SloanManagement Review vol 46 no 1 pp 63ndash69 2004

[10] J Shin ldquoHow does free riding on customer service affectcompetitionrdquo Marketing Science vol 26 no 4 pp 488ndash5032007

[11] G Iyer and J M Villas-Boas ldquoA bargaining theory of distribu-tion channelsrdquo Journal of Marketing Research vol 40 no 1 pp80ndash100 2003

[12] A Dukes and Y Liu ldquoIn-store media and distribution channelcoordinationrdquoMarketing Science vol 29 no 1 pp 94ndash107 2010

[13] H Ahn I Duenyas and R Zhang ldquoPrice competition betweenretailers and manufacturer-owned storesrdquoWorking Paper Uni-versity of California at Berkeley 2002

[14] K Cattani W Gilland H S Heese and J SwaminathanldquoBoiling frogs pricing strategies for a manufacturer addinga direct channel that competes with the traditional channelrdquoProduction and Operations Management vol 15 no 1 pp 40ndash56 2006

[15] K-Y Chen M Kaya and O Ozer ldquoDual sales channel man-agement with service competitionrdquo Manufacturing and ServiceOperations Management vol 10 no 4 pp 654ndash675 2008

[16] G Hua S Wang and T C E Cheng ldquoPrice and lead timedecisions in dual-channel supply chainsrdquo European Journal ofOperational Research vol 205 no 1 pp 113ndash126 2010

[17] W S Yoo andE Lee ldquoInternet channel entry a strategic analysisof mixed channel structuresrdquo Marketing Science vol 30 no 1pp 29ndash41 2011

[18] Y Xiong W Yan K Fernandes Z-K Xiong and N GuoldquoldquoBricks vs clicksrdquo the impact of manufacturer encroachmentwith a dealer leasing and selling of durable goodsrdquo EuropeanJournal of Operational Research vol 217 no 1 pp 75ndash83 2012

[19] Q Lu and N Liu ldquoPricing games of mixed conventional ande-commerce distribution channelsrdquo Computers and IndustrialEngineering vol 64 no 1 pp 122ndash132 2013

[20] Q Xu Z Liu and B Shen ldquoThe impact of price comparisonservice on pricing strategy in a dual-channel supply chainrdquoMathematical Problems in Engineering vol 2013 Article ID613528 13 pages 2013

[21] C A Ingene and M E Parry ldquoChannel coordination whenretailers competerdquoMarketing Science vol 14 no 4 pp 360ndash3771995

[22] 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

[23] J Raju and Z J Zhang ldquoChannel coordination in the presenceof a dominant retailerrdquoMarketing Science vol 24 no 2 pp 254ndash262 2005

[24] K L Webb and C J Lambe ldquoInternal multi-channel conflictan exploratory investigation and conceptual frameworkrdquo Indus-trial Marketing Management vol 36 no 1 pp 29ndash43 2007

[25] S K Mukhopadhyay D-Q Yao and X Yue ldquoInformationsharing of value-adding retailer in a mixed channel hi-techsupply chainrdquo Journal of Business Research vol 61 no 9 pp950ndash958 2008

[26] R Yan ldquoManaging channel coordination in a multi-channelmanufacturer-retailer supply chainrdquo Industrial Marketing Man-agement vol 40 no 4 pp 636ndash642 2011

[27] E Cao YMa CWan andM Lai ldquoContracting with asymmet-ric cost information in a dual-channel supply chainrdquoOperationsResearch Letters vol 41 no 4 pp 410ndash414 2013

[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] Y Liu S Gupta and Z J Zhang ldquoNote on self-restraint as anonline entry-deterrence strategyrdquoManagement Science vol 52no 11 pp 1799ndash1809 2006

[30] Z Cheng and B R Nault ldquoInternet channel entry retailcoverage and entry cost advantagerdquo Information Technology andManagement vol 8 no 2 pp 111ndash132 2007

[31] X Zhang ldquoRetailersrsquo multichannel and price advertising strate-giesrdquoMarketing Science vol 28 no 6 pp 1080ndash1094 2009

[32] W Huang and J M Swaminathan ldquoIntroduction of a secondchannel implications for pricing and profitsrdquo European Journalof Operational Research vol 194 no 1 pp 258ndash279 2009

[33] H Hotelling ldquoStability in competitionrdquo The Economic Journalvol 39 no 153 pp 41ndash57 1929

[34] J Zhang ldquoThe perils of behavior-based personalizationrdquo Mar-keting Science vol 30 no 1 pp 170ndash186 2011

[35] T Kabiraj and C Lee ldquoLicensing contracts in hotelling struc-turerdquoTheoretical Economics Letters vol 1 no 3 pp 57ndash62 2011

[36] HWang andTNariu ldquoDistribution channelmanagement in aninternet age equilibrium and social welfarerdquo Journal of IndustryCompetition and Trade vol 12 no 3 pp 285ndash298 2012

[37] M Lijesen ldquoHotellingrsquos webshoprdquo Journal of Economics vol 109no 2 pp 193ndash200 2013

[38] R Gulati and J Garino ldquoGet the right mix of bricks amp clicksrdquoHarvard Business Review vol 78 no 3 pp 107ndash214 2000

[39] K-J Chung S-D Lin and H M Srivastava ldquoThe completesolution procedures for the mathematical analysis of somefamilies of optimal inventorymodels with order-size dependenttrade credit and deterministic and constant demandrdquo AppliedMathematics and Computation vol 219 no 1 pp 142ndash157 2012

[40] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels under conditional trade credit in a supply chain systemrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 24 pp10036ndash10052 2013

[41] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels for deteriorating items in the discounted cash-flowsapproach under conditional trade credit and cash discount ina supply chain systemrdquo Applied Mathematics and InformationSciences vol 8 no 5 pp 2103ndash2111 2014

[42] J Luo and Q Zhang ldquoTrade credit a new mechanism tocoordinate supply chainrdquo Operations Research Letters vol 40no 5 pp 378ndash384 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

Mathematical Problems in Engineering 13

Submitting it into (A11) we get the manufacturerrsquos optimalprice in her Internet store 119901M

119898= [(2 + 120573)119905 + (2 minus 3120573)120575]4120573

Hence the manufacturer and dominant retailerrsquos optimalprofits are prodM

119898= (119905 + 120575)2120573 + [(119905 minus 120575)

2

minus 12119905120575]16119905 minus 119865119898

andprodM119903= (119905 + 120575)

2

8119905 minus 119865119903 respectively

According to the previous assumption 119901119903gt (119905 minus 120575)120573

which implies that (119905 + 120575)2120573 gt (119905 minus 120575)120573 120575must satisfy 120575 gt1199053 However when 120575 lt 1199053 we always have

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](minus)

gt 0

120597prod119903

120597119901119903

10038161003816100381610038161003816100381610038161003816[(119905minus120575)120573](+)

lt 0 (A15)

So the dominant retailerrsquos optimal retail price in the M-channel is 119901M

119903= (119905 minus 120575)120573 Therefore the manufacturer and

dominant retailerrsquos optimal profits areprodM119898= (119905 minus 120575)120573 minus [(119905 minus

120575)120575]119905 minus 119865119898andprodM

119903= [(119905 minus 120575)120575]119905 minus 119865

119903 respectively

B Strategic Conditions forOpening an Internet Store

Proofs of Proposition 8 and Corollary 9 From Lemma 6 weanalyse the equilibrium profits for the dominant retailerbetween the T-channel and RD-channel and note that onlywhen 119865

119903lt 120573(119905 minus 120575) then prodRD

119903gt prod

T119903 This implies that as

long as the setup cost of opening an Internet store satisfies119865119903

lt 120573(119905 minus 120575) ≜ 1198611 it is always optimal to open an

Internet store for the dominant retailer In addition we notethat 120597119861

1120597120575 = minus120573 lt 0 So the dominant retailerrsquos strategic

motive for opening an Internet store would be weakened byincreasing consumersrsquo disutility of purchasing a product fromInternet store

Proofs of Proposition 10 and Corollary 11 From Lemma 6 weanalyse the equilibrium profits for the manufacturer betweenthe T-channel and MD-channel and note that only when thesetup cost of opening an Internet store satisfies 119865

119898lt (119905 +

120575)2120573+[(119905minus120575)2

minus12119905120575]16119905minus(1minus120573)(119881minus119905) ≜ 1198612 thenprodMD

119898gt

prodT119898 In addition we note that 120597119861

2120597120575 = [4119905 minus 120573(7119905 minus 120575)]8120573119905

and find when 0 lt 120573 lt 4119905(7119905 minus 120575) then 1205971198612120597120575 gt 0 and

when 4119905(7119905 minus 120575) lt 120573 lt 1 then 1205971198612120597120575 lt 0

Proofs of Proposition 12 and Corollary 13 FromLemmas 6 and7 we analyse the equilibriumprofits for themanufacturer anddominant retailer between the T-channel andM-channel wenote that under the condition of 120575 lt 1199053 only when the setupcosts of opening an Internet store for the manufacturer anddominant retailer simultaneously satisfy

119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198613

119865119903lt

[(119905 minus 120575) 120575]

119905

minus 120573 (119881 minus 119905) ≜ 1198614

(B1)

thenMprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B2)

Similarly under the condition of 120575 gt 1199053 only when thesetup costs of opening an Internet store for the manufacturerand dominant retailer simultaneously satisfy

119865119898lt

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

minus (1 minus 120573) (119881 minus 119905) ≜ 1198615

119865119903lt

(119905 + 120575)2

8119905

minus 120573 (119881 minus 119905) ≜ 1198616

(B3)

then

Mprod

119898

gt

Tprod

119898

Mprod

119903

gt

Tprod

119903

(B4)

In addition we note that both 1205971198613120597120575 = minus[119905 + 120573(119905 minus

2120575)]120573119905 lt 0 and 1205971198614120597120575 = (119905 minus 2120575)119905 gt 0 are held under

the condition of 120575 lt 1199053 Furthermore under the conditionof 120575 gt 1199053 we also find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198615120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

5120597120575 lt 0

1205971198616120597120575 = 2(119905 + 120575)8119905 gt 0

Proofs of Proposition 14 and Corollary 15 From Lemmas 6and 7 we analyse the manufacturerrsquos equilibrium profits inthe RD-channel and M-channel we note that under thecondition of 120575 lt 1199053 only when the setup cost of opening anInternet store for her satisfies 119865

119898lt (119905 minus 120575)120573 minus [(119905 minus 120575)120575]119905 minus

(1 minus 120573)(119881 minus 120575) ≜ 1198617 thenprodM

119898gt prod

RD119898 In addition we find

1205971198617120597120575 = minus[(1 + 120573

2

)119905 minus 2120573120575]120573119905 lt 0But under the condition of 120575 gt 1199053 only when the setup

cost of opening an Internet store for her satisfies 119865119898lt (119905 +

120575)2120573 + [(119905 minus 120575)2

minus 12119905120575]16119905 minus (1 minus 120573)(119881 minus 120575) ≜ 1198618 then

prodM119898gt prod

RD119898 In addition 120597119861

8120597120575 = [120573(119905+120575)+4119905(1minus2120573

2

)]8120573119905

we find that when 0 lt 120573 lt [(119905 + 120575) + radic(119905 + 120575)2

+ 1281199052]16119905

then 1205971198618120597120575 gt 0 andwhen [(119905+120575)+radic(119905 + 120575)2 + 1281199052]16119905 lt

120573 lt 1 then 1205971198618120597120575 lt 0

Proofs of Proposition 16 From Lemmas 6 and 7 we analysethe dominant retailerrsquos equilibriumprofits in theMD-channeland M-channel and note that when 120575 lt 1199053 then prod

M119903minus

prodMD119903

= minus(119905 minus 3120575)2

8119905 minus 119865119903lt 0 and when 120575 gt 1199053

then prodM119903minus prod

MD119903

= minus119865119903lt 0 These imply that when the

manufacturer has operated an Internet store the best choicefor dominant retailer is not to open an Internet store

Proofs of Proposition 17 and Corollary 18 From Lemmas 6and 7 we analyse the dominant retailerrsquos equilibrium profitsin the MD-channel and M-channel and note that under thecondition of 120575 lt 1199053 thenprodM

119898minus prod

MD119898

= [8119905(119905 minus 3120575) minus 120573[(119905 +

120575)2

minus 161205752

]8119905]16120573119905 This implies that the manufacturer willopen her Internet store when the dominant retailer opens an

14 Mathematical Problems in Engineering

Internet store and the setup costs of opening an Internet storefor her satisfies

1198619≜

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

lt 119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

≜ 11986110

(B5)

In addition we find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198619120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

9120597120575 lt 0

and 12059711986110120597120575 = minus[119905 + 120573(119905 minus 2120575)]120573119905 lt 0

C The ManufacturerDominantRetailers Pricing Policies

Proof of Proposition 19 In the MD-channel we respectivelydifferentiate between119901MD

119898and119901MD

119903with respect to 120573 and find

that 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0 For any given120573 differentiating between 119901MD

119898and 119901MD

119903with respect to 120575 we

have 120597119901MD119903

120597120575 = 12120573 gt 0 and 120597119901MD119898

120597120575 = (2 minus 3120573)4120573and if 120573 isin (0 23) then 120597119901MD

119898120597120575 gt 0 if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 In addition we find that 119901MD119898

minus 119901MD119903

= (119905 minus

3120575)4 it is obvious that when 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

when 120575 = 1199053 then 119901MD

119898= 119901

MD119903

and when 120575 gt 1199053 then119901MD119898

lt 119901MD119903

Proof of Proposition 20 In the M-channel we respectivelydifferentiate between 119901M

119898and 119901M

119903with respect to 120573 and find

that when 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0

and when 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 For any given 120573 we respectively differentiate between 119901M119898

and 119901M119903with respect to 120575 and find that when 120575 lt 1199053 then

120597119901M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0 when 120575 gt 1199053 then

120597119901M119898120597120575 = (2 minus 3120573)4120573 and 120597119901M

119903120597120575 = 12120573 gt 0

It is easy to note that when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0

but when 120573 isin (23 1) then 120597119901M119898120597120575 lt 0

Proof of Proposition 21 From Lemmas 6 and 7 we note that120597119908

RD120597120575 = minus(1 minus 120573) lt 0 and 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0In addition if 120575 lt 1199053 then 120597119908M

120597120575 = minus(1 minus 120573)120573 lt 0 if120575 gt 1199053 then 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0

Proof of Proposition 22 From the proofs of Propositions 19and 20 we note that when 120575 lt 1199053 if 120573 isin (0 23) then120597119901

MD119898

120597120575 gt 0 120597119901M119898120597120575 lt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 120597119901M119898120597120575 lt 0 when 120575 gt 1199053 if 120573 isin (0 23)

then 120597119901MD119898

120597120575 = 120597119901M119898120597120575 gt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 = 120597119901M119898120597120575 lt 0

Proof of Proposition 23 From Lemmas 6 and 7 we note that120597119901

RD119903120597120575 = minus1 lt 0 and 120597119901MD

119903120597120575 = 12120572 gt 0 In addition if

120575 lt 1199053 then 120597119901M119903120597120575 = minus1120572 lt 0 if 120575 gt 1199053 then 120597119901M

119903120597120575 =

12120572 gt 0

Abbreviations

UK The consumerrsquos utility of purchasing theproduct from K storeK isin PSRISMIS

119881 The value of consumers willing to payfor the product

120575 The consumersrsquo disutility of purchasingthe product from Internet store(MISRIS)

119905 The per unit transportation cost ofpurchasing the product from physicalstore (PS)

120573 The dominant retailerrsquos bargainingpower in the distribution channel

119908j The manufacturerrsquos wholesale price in

the j-channel j isin TRDMDM

119901j119903 The dominant retailerrsquos price in the

j-channel j isin TRDMDM

119901j119898 The manufacturerrsquos price in the

j-channel j isin MDM

119865119898119865119903 The setup cost of opening an Internetstore by the manufacturerdominantretailer

Πj119898Πj119903 The manufacturerdominant retailerrsquosprofit in the j-channelj isin TRDMDM

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been supported by theNational Natural Sci-ence Foundation of China (71271225) Chongqingrsquos NaturalScience Foundation (cstc2012jjA1404) and the Open Fund ofChongqing Key Laboratory of Logistics (CQKLL12001)

References

[1] L Hsiao and Y-J Chen ldquoStrategic motive for introducinginternet channels in a supply chainrdquo Production and OperationsManagement vol 23 no 1 pp 36ndash47 2014

[2] I Geyskens K Gielens and M G Dekimpe ldquoThe marketvaluation of Internet channel additionsrdquo Journal of Marketingvol 66 no 2 pp 102ndash119 2002

[3] 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

[4] S-H Chun and J-C Kim ldquoPricing strategies in B2C electroniccommerce analytical and empirical approachesrdquo Decision Sup-port Systems vol 40 no 2 pp 375ndash388 2005

[5] S K Mukhopadhyay X Zhu and X Yue ldquoOptimal contractdesign for mixed channels under information asymmetryrdquoProduction and Operations Management vol 17 no 6 pp 641ndash650 2008

Mathematical Problems in Engineering 15

[6] G S Cai ldquoChannel selection and coordination in dual-channelsupply chainsrdquo Journal of Retailing vol 86 no 1 pp 22ndash36 2010

[7] K Takahashi T Aoi D Hirotani and K Morikawa ldquoInventorycontrol in a two-echelon dual-channel supply chain with setupof production and deliveryrdquo International Journal of ProductionEconomics vol 133 no 1 pp 403ndash415 2011

[8] D W Carlton and J A Chevalier ldquoFree riding and salesstrategies for the Internetrdquo Journal of Industrial Economics vol49 no 4 pp 441ndash461 2001

[9] K D Antia M Bergen and S Dutta ldquoCompeting with graymarketsrdquoMIT SloanManagement Review vol 46 no 1 pp 63ndash69 2004

[10] J Shin ldquoHow does free riding on customer service affectcompetitionrdquo Marketing Science vol 26 no 4 pp 488ndash5032007

[11] G Iyer and J M Villas-Boas ldquoA bargaining theory of distribu-tion channelsrdquo Journal of Marketing Research vol 40 no 1 pp80ndash100 2003

[12] A Dukes and Y Liu ldquoIn-store media and distribution channelcoordinationrdquoMarketing Science vol 29 no 1 pp 94ndash107 2010

[13] H Ahn I Duenyas and R Zhang ldquoPrice competition betweenretailers and manufacturer-owned storesrdquoWorking Paper Uni-versity of California at Berkeley 2002

[14] K Cattani W Gilland H S Heese and J SwaminathanldquoBoiling frogs pricing strategies for a manufacturer addinga direct channel that competes with the traditional channelrdquoProduction and Operations Management vol 15 no 1 pp 40ndash56 2006

[15] K-Y Chen M Kaya and O Ozer ldquoDual sales channel man-agement with service competitionrdquo Manufacturing and ServiceOperations Management vol 10 no 4 pp 654ndash675 2008

[16] G Hua S Wang and T C E Cheng ldquoPrice and lead timedecisions in dual-channel supply chainsrdquo European Journal ofOperational Research vol 205 no 1 pp 113ndash126 2010

[17] W S Yoo andE Lee ldquoInternet channel entry a strategic analysisof mixed channel structuresrdquo Marketing Science vol 30 no 1pp 29ndash41 2011

[18] Y Xiong W Yan K Fernandes Z-K Xiong and N GuoldquoldquoBricks vs clicksrdquo the impact of manufacturer encroachmentwith a dealer leasing and selling of durable goodsrdquo EuropeanJournal of Operational Research vol 217 no 1 pp 75ndash83 2012

[19] Q Lu and N Liu ldquoPricing games of mixed conventional ande-commerce distribution channelsrdquo Computers and IndustrialEngineering vol 64 no 1 pp 122ndash132 2013

[20] Q Xu Z Liu and B Shen ldquoThe impact of price comparisonservice on pricing strategy in a dual-channel supply chainrdquoMathematical Problems in Engineering vol 2013 Article ID613528 13 pages 2013

[21] C A Ingene and M E Parry ldquoChannel coordination whenretailers competerdquoMarketing Science vol 14 no 4 pp 360ndash3771995

[22] 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

[23] J Raju and Z J Zhang ldquoChannel coordination in the presenceof a dominant retailerrdquoMarketing Science vol 24 no 2 pp 254ndash262 2005

[24] K L Webb and C J Lambe ldquoInternal multi-channel conflictan exploratory investigation and conceptual frameworkrdquo Indus-trial Marketing Management vol 36 no 1 pp 29ndash43 2007

[25] S K Mukhopadhyay D-Q Yao and X Yue ldquoInformationsharing of value-adding retailer in a mixed channel hi-techsupply chainrdquo Journal of Business Research vol 61 no 9 pp950ndash958 2008

[26] R Yan ldquoManaging channel coordination in a multi-channelmanufacturer-retailer supply chainrdquo Industrial Marketing Man-agement vol 40 no 4 pp 636ndash642 2011

[27] E Cao YMa CWan andM Lai ldquoContracting with asymmet-ric cost information in a dual-channel supply chainrdquoOperationsResearch Letters vol 41 no 4 pp 410ndash414 2013

[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] Y Liu S Gupta and Z J Zhang ldquoNote on self-restraint as anonline entry-deterrence strategyrdquoManagement Science vol 52no 11 pp 1799ndash1809 2006

[30] Z Cheng and B R Nault ldquoInternet channel entry retailcoverage and entry cost advantagerdquo Information Technology andManagement vol 8 no 2 pp 111ndash132 2007

[31] X Zhang ldquoRetailersrsquo multichannel and price advertising strate-giesrdquoMarketing Science vol 28 no 6 pp 1080ndash1094 2009

[32] W Huang and J M Swaminathan ldquoIntroduction of a secondchannel implications for pricing and profitsrdquo European Journalof Operational Research vol 194 no 1 pp 258ndash279 2009

[33] H Hotelling ldquoStability in competitionrdquo The Economic Journalvol 39 no 153 pp 41ndash57 1929

[34] J Zhang ldquoThe perils of behavior-based personalizationrdquo Mar-keting Science vol 30 no 1 pp 170ndash186 2011

[35] T Kabiraj and C Lee ldquoLicensing contracts in hotelling struc-turerdquoTheoretical Economics Letters vol 1 no 3 pp 57ndash62 2011

[36] HWang andTNariu ldquoDistribution channelmanagement in aninternet age equilibrium and social welfarerdquo Journal of IndustryCompetition and Trade vol 12 no 3 pp 285ndash298 2012

[37] M Lijesen ldquoHotellingrsquos webshoprdquo Journal of Economics vol 109no 2 pp 193ndash200 2013

[38] R Gulati and J Garino ldquoGet the right mix of bricks amp clicksrdquoHarvard Business Review vol 78 no 3 pp 107ndash214 2000

[39] K-J Chung S-D Lin and H M Srivastava ldquoThe completesolution procedures for the mathematical analysis of somefamilies of optimal inventorymodels with order-size dependenttrade credit and deterministic and constant demandrdquo AppliedMathematics and Computation vol 219 no 1 pp 142ndash157 2012

[40] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels under conditional trade credit in a supply chain systemrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 24 pp10036ndash10052 2013

[41] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels for deteriorating items in the discounted cash-flowsapproach under conditional trade credit and cash discount ina supply chain systemrdquo Applied Mathematics and InformationSciences vol 8 no 5 pp 2103ndash2111 2014

[42] J Luo and Q Zhang ldquoTrade credit a new mechanism tocoordinate supply chainrdquo Operations Research Letters vol 40no 5 pp 378ndash384 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 Mathematical Problems in Engineering

Internet store and the setup costs of opening an Internet storefor her satisfies

1198619≜

(119905 + 120575)

2120573

+

[(119905 minus 120575)2

minus 12119905120575]

16119905

lt 119865119898lt

(119905 minus 120575)

120573

minus

[(119905 minus 120575) 120575]

119905

≜ 11986110

(B5)

In addition we find that when 0 lt 120573 lt 4119905(7119905 minus 120575) then1205971198619120597120575 gt 0 and when 4119905(7119905 minus 120575) lt 120573 lt 1 then 120597119861

9120597120575 lt 0

and 12059711986110120597120575 = minus[119905 + 120573(119905 minus 2120575)]120573119905 lt 0

C The ManufacturerDominantRetailers Pricing Policies

Proof of Proposition 19 In the MD-channel we respectivelydifferentiate between119901MD

119898and119901MD

119903with respect to 120573 and find

that 120597119901MD119898

120597120573 = 120597119901MD119903

120597120573 = minus(119905 + 120575)21205732

lt 0 For any given120573 differentiating between 119901MD

119898and 119901MD

119903with respect to 120575 we

have 120597119901MD119903

120597120575 = 12120573 gt 0 and 120597119901MD119898

120597120575 = (2 minus 3120573)4120573and if 120573 isin (0 23) then 120597119901MD

119898120597120575 gt 0 if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 In addition we find that 119901MD119898

minus 119901MD119903

= (119905 minus

3120575)4 it is obvious that when 120575 lt 1199053 then 119901MD119898

gt 119901MD119903

when 120575 = 1199053 then 119901MD

119898= 119901

MD119903

and when 120575 gt 1199053 then119901MD119898

lt 119901MD119903

Proof of Proposition 20 In the M-channel we respectivelydifferentiate between 119901M

119898and 119901M

119903with respect to 120573 and find

that when 120575 lt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 minus 120575)120573

2

lt 0

and when 120575 gt 1199053 then 120597119901M119898120597120573 = 120597119901

M119903120597120573 = minus(119905 + 120575)2120573

2

lt

0 For any given 120573 we respectively differentiate between 119901M119898

and 119901M119903with respect to 120575 and find that when 120575 lt 1199053 then

120597119901M119898120597120575 = 120597119901

M119903120597120575 = minus1120573 lt 0 when 120575 gt 1199053 then

120597119901M119898120597120575 = (2 minus 3120573)4120573 and 120597119901M

119903120597120575 = 12120573 gt 0

It is easy to note that when 120573 isin (0 23) then 120597119901M119898120597120575 gt 0

but when 120573 isin (23 1) then 120597119901M119898120597120575 lt 0

Proof of Proposition 21 From Lemmas 6 and 7 we note that120597119908

RD120597120575 = minus(1 minus 120573) lt 0 and 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0In addition if 120575 lt 1199053 then 120597119908M

120597120575 = minus(1 minus 120573)120573 lt 0 if120575 gt 1199053 then 120597119908MD

120597120575 = (1 minus 120573)2120573 gt 0

Proof of Proposition 22 From the proofs of Propositions 19and 20 we note that when 120575 lt 1199053 if 120573 isin (0 23) then120597119901

MD119898

120597120575 gt 0 120597119901M119898120597120575 lt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 lt 0 120597119901M119898120597120575 lt 0 when 120575 gt 1199053 if 120573 isin (0 23)

then 120597119901MD119898

120597120575 = 120597119901M119898120597120575 gt 0 but if 120573 isin (23 1) then

120597119901MD119898

120597120575 = 120597119901M119898120597120575 lt 0

Proof of Proposition 23 From Lemmas 6 and 7 we note that120597119901

RD119903120597120575 = minus1 lt 0 and 120597119901MD

119903120597120575 = 12120572 gt 0 In addition if

120575 lt 1199053 then 120597119901M119903120597120575 = minus1120572 lt 0 if 120575 gt 1199053 then 120597119901M

119903120597120575 =

12120572 gt 0

Abbreviations

UK The consumerrsquos utility of purchasing theproduct from K storeK isin PSRISMIS

119881 The value of consumers willing to payfor the product

120575 The consumersrsquo disutility of purchasingthe product from Internet store(MISRIS)

119905 The per unit transportation cost ofpurchasing the product from physicalstore (PS)

120573 The dominant retailerrsquos bargainingpower in the distribution channel

119908j The manufacturerrsquos wholesale price in

the j-channel j isin TRDMDM

119901j119903 The dominant retailerrsquos price in the

j-channel j isin TRDMDM

119901j119898 The manufacturerrsquos price in the

j-channel j isin MDM

119865119898119865119903 The setup cost of opening an Internetstore by the manufacturerdominantretailer

Πj119898Πj119903 The manufacturerdominant retailerrsquosprofit in the j-channelj isin TRDMDM

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been supported by theNational Natural Sci-ence Foundation of China (71271225) Chongqingrsquos NaturalScience Foundation (cstc2012jjA1404) and the Open Fund ofChongqing Key Laboratory of Logistics (CQKLL12001)

References

[1] L Hsiao and Y-J Chen ldquoStrategic motive for introducinginternet channels in a supply chainrdquo Production and OperationsManagement vol 23 no 1 pp 36ndash47 2014

[2] I Geyskens K Gielens and M G Dekimpe ldquoThe marketvaluation of Internet channel additionsrdquo Journal of Marketingvol 66 no 2 pp 102ndash119 2002

[3] 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

[4] S-H Chun and J-C Kim ldquoPricing strategies in B2C electroniccommerce analytical and empirical approachesrdquo Decision Sup-port Systems vol 40 no 2 pp 375ndash388 2005

[5] S K Mukhopadhyay X Zhu and X Yue ldquoOptimal contractdesign for mixed channels under information asymmetryrdquoProduction and Operations Management vol 17 no 6 pp 641ndash650 2008

Mathematical Problems in Engineering 15

[6] G S Cai ldquoChannel selection and coordination in dual-channelsupply chainsrdquo Journal of Retailing vol 86 no 1 pp 22ndash36 2010

[7] K Takahashi T Aoi D Hirotani and K Morikawa ldquoInventorycontrol in a two-echelon dual-channel supply chain with setupof production and deliveryrdquo International Journal of ProductionEconomics vol 133 no 1 pp 403ndash415 2011

[8] D W Carlton and J A Chevalier ldquoFree riding and salesstrategies for the Internetrdquo Journal of Industrial Economics vol49 no 4 pp 441ndash461 2001

[9] K D Antia M Bergen and S Dutta ldquoCompeting with graymarketsrdquoMIT SloanManagement Review vol 46 no 1 pp 63ndash69 2004

[10] J Shin ldquoHow does free riding on customer service affectcompetitionrdquo Marketing Science vol 26 no 4 pp 488ndash5032007

[11] G Iyer and J M Villas-Boas ldquoA bargaining theory of distribu-tion channelsrdquo Journal of Marketing Research vol 40 no 1 pp80ndash100 2003

[12] A Dukes and Y Liu ldquoIn-store media and distribution channelcoordinationrdquoMarketing Science vol 29 no 1 pp 94ndash107 2010

[13] H Ahn I Duenyas and R Zhang ldquoPrice competition betweenretailers and manufacturer-owned storesrdquoWorking Paper Uni-versity of California at Berkeley 2002

[14] K Cattani W Gilland H S Heese and J SwaminathanldquoBoiling frogs pricing strategies for a manufacturer addinga direct channel that competes with the traditional channelrdquoProduction and Operations Management vol 15 no 1 pp 40ndash56 2006

[15] K-Y Chen M Kaya and O Ozer ldquoDual sales channel man-agement with service competitionrdquo Manufacturing and ServiceOperations Management vol 10 no 4 pp 654ndash675 2008

[16] G Hua S Wang and T C E Cheng ldquoPrice and lead timedecisions in dual-channel supply chainsrdquo European Journal ofOperational Research vol 205 no 1 pp 113ndash126 2010

[17] W S Yoo andE Lee ldquoInternet channel entry a strategic analysisof mixed channel structuresrdquo Marketing Science vol 30 no 1pp 29ndash41 2011

[18] Y Xiong W Yan K Fernandes Z-K Xiong and N GuoldquoldquoBricks vs clicksrdquo the impact of manufacturer encroachmentwith a dealer leasing and selling of durable goodsrdquo EuropeanJournal of Operational Research vol 217 no 1 pp 75ndash83 2012

[19] Q Lu and N Liu ldquoPricing games of mixed conventional ande-commerce distribution channelsrdquo Computers and IndustrialEngineering vol 64 no 1 pp 122ndash132 2013

[20] Q Xu Z Liu and B Shen ldquoThe impact of price comparisonservice on pricing strategy in a dual-channel supply chainrdquoMathematical Problems in Engineering vol 2013 Article ID613528 13 pages 2013

[21] C A Ingene and M E Parry ldquoChannel coordination whenretailers competerdquoMarketing Science vol 14 no 4 pp 360ndash3771995

[22] 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

[23] J Raju and Z J Zhang ldquoChannel coordination in the presenceof a dominant retailerrdquoMarketing Science vol 24 no 2 pp 254ndash262 2005

[24] K L Webb and C J Lambe ldquoInternal multi-channel conflictan exploratory investigation and conceptual frameworkrdquo Indus-trial Marketing Management vol 36 no 1 pp 29ndash43 2007

[25] S K Mukhopadhyay D-Q Yao and X Yue ldquoInformationsharing of value-adding retailer in a mixed channel hi-techsupply chainrdquo Journal of Business Research vol 61 no 9 pp950ndash958 2008

[26] R Yan ldquoManaging channel coordination in a multi-channelmanufacturer-retailer supply chainrdquo Industrial Marketing Man-agement vol 40 no 4 pp 636ndash642 2011

[27] E Cao YMa CWan andM Lai ldquoContracting with asymmet-ric cost information in a dual-channel supply chainrdquoOperationsResearch Letters vol 41 no 4 pp 410ndash414 2013

[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] Y Liu S Gupta and Z J Zhang ldquoNote on self-restraint as anonline entry-deterrence strategyrdquoManagement Science vol 52no 11 pp 1799ndash1809 2006

[30] Z Cheng and B R Nault ldquoInternet channel entry retailcoverage and entry cost advantagerdquo Information Technology andManagement vol 8 no 2 pp 111ndash132 2007

[31] X Zhang ldquoRetailersrsquo multichannel and price advertising strate-giesrdquoMarketing Science vol 28 no 6 pp 1080ndash1094 2009

[32] W Huang and J M Swaminathan ldquoIntroduction of a secondchannel implications for pricing and profitsrdquo European Journalof Operational Research vol 194 no 1 pp 258ndash279 2009

[33] H Hotelling ldquoStability in competitionrdquo The Economic Journalvol 39 no 153 pp 41ndash57 1929

[34] J Zhang ldquoThe perils of behavior-based personalizationrdquo Mar-keting Science vol 30 no 1 pp 170ndash186 2011

[35] T Kabiraj and C Lee ldquoLicensing contracts in hotelling struc-turerdquoTheoretical Economics Letters vol 1 no 3 pp 57ndash62 2011

[36] HWang andTNariu ldquoDistribution channelmanagement in aninternet age equilibrium and social welfarerdquo Journal of IndustryCompetition and Trade vol 12 no 3 pp 285ndash298 2012

[37] M Lijesen ldquoHotellingrsquos webshoprdquo Journal of Economics vol 109no 2 pp 193ndash200 2013

[38] R Gulati and J Garino ldquoGet the right mix of bricks amp clicksrdquoHarvard Business Review vol 78 no 3 pp 107ndash214 2000

[39] K-J Chung S-D Lin and H M Srivastava ldquoThe completesolution procedures for the mathematical analysis of somefamilies of optimal inventorymodels with order-size dependenttrade credit and deterministic and constant demandrdquo AppliedMathematics and Computation vol 219 no 1 pp 142ndash157 2012

[40] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels under conditional trade credit in a supply chain systemrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 24 pp10036ndash10052 2013

[41] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels for deteriorating items in the discounted cash-flowsapproach under conditional trade credit and cash discount ina supply chain systemrdquo Applied Mathematics and InformationSciences vol 8 no 5 pp 2103ndash2111 2014

[42] J Luo and Q Zhang ldquoTrade credit a new mechanism tocoordinate supply chainrdquo Operations Research Letters vol 40no 5 pp 378ndash384 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

Mathematical Problems in Engineering 15

[6] G S Cai ldquoChannel selection and coordination in dual-channelsupply chainsrdquo Journal of Retailing vol 86 no 1 pp 22ndash36 2010

[7] K Takahashi T Aoi D Hirotani and K Morikawa ldquoInventorycontrol in a two-echelon dual-channel supply chain with setupof production and deliveryrdquo International Journal of ProductionEconomics vol 133 no 1 pp 403ndash415 2011

[8] D W Carlton and J A Chevalier ldquoFree riding and salesstrategies for the Internetrdquo Journal of Industrial Economics vol49 no 4 pp 441ndash461 2001

[9] K D Antia M Bergen and S Dutta ldquoCompeting with graymarketsrdquoMIT SloanManagement Review vol 46 no 1 pp 63ndash69 2004

[10] J Shin ldquoHow does free riding on customer service affectcompetitionrdquo Marketing Science vol 26 no 4 pp 488ndash5032007

[11] G Iyer and J M Villas-Boas ldquoA bargaining theory of distribu-tion channelsrdquo Journal of Marketing Research vol 40 no 1 pp80ndash100 2003

[12] A Dukes and Y Liu ldquoIn-store media and distribution channelcoordinationrdquoMarketing Science vol 29 no 1 pp 94ndash107 2010

[13] H Ahn I Duenyas and R Zhang ldquoPrice competition betweenretailers and manufacturer-owned storesrdquoWorking Paper Uni-versity of California at Berkeley 2002

[14] K Cattani W Gilland H S Heese and J SwaminathanldquoBoiling frogs pricing strategies for a manufacturer addinga direct channel that competes with the traditional channelrdquoProduction and Operations Management vol 15 no 1 pp 40ndash56 2006

[15] K-Y Chen M Kaya and O Ozer ldquoDual sales channel man-agement with service competitionrdquo Manufacturing and ServiceOperations Management vol 10 no 4 pp 654ndash675 2008

[16] G Hua S Wang and T C E Cheng ldquoPrice and lead timedecisions in dual-channel supply chainsrdquo European Journal ofOperational Research vol 205 no 1 pp 113ndash126 2010

[17] W S Yoo andE Lee ldquoInternet channel entry a strategic analysisof mixed channel structuresrdquo Marketing Science vol 30 no 1pp 29ndash41 2011

[18] Y Xiong W Yan K Fernandes Z-K Xiong and N GuoldquoldquoBricks vs clicksrdquo the impact of manufacturer encroachmentwith a dealer leasing and selling of durable goodsrdquo EuropeanJournal of Operational Research vol 217 no 1 pp 75ndash83 2012

[19] Q Lu and N Liu ldquoPricing games of mixed conventional ande-commerce distribution channelsrdquo Computers and IndustrialEngineering vol 64 no 1 pp 122ndash132 2013

[20] Q Xu Z Liu and B Shen ldquoThe impact of price comparisonservice on pricing strategy in a dual-channel supply chainrdquoMathematical Problems in Engineering vol 2013 Article ID613528 13 pages 2013

[21] C A Ingene and M E Parry ldquoChannel coordination whenretailers competerdquoMarketing Science vol 14 no 4 pp 360ndash3771995

[22] 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

[23] J Raju and Z J Zhang ldquoChannel coordination in the presenceof a dominant retailerrdquoMarketing Science vol 24 no 2 pp 254ndash262 2005

[24] K L Webb and C J Lambe ldquoInternal multi-channel conflictan exploratory investigation and conceptual frameworkrdquo Indus-trial Marketing Management vol 36 no 1 pp 29ndash43 2007

[25] S K Mukhopadhyay D-Q Yao and X Yue ldquoInformationsharing of value-adding retailer in a mixed channel hi-techsupply chainrdquo Journal of Business Research vol 61 no 9 pp950ndash958 2008

[26] R Yan ldquoManaging channel coordination in a multi-channelmanufacturer-retailer supply chainrdquo Industrial Marketing Man-agement vol 40 no 4 pp 636ndash642 2011

[27] E Cao YMa CWan andM Lai ldquoContracting with asymmet-ric cost information in a dual-channel supply chainrdquoOperationsResearch Letters vol 41 no 4 pp 410ndash414 2013

[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] Y Liu S Gupta and Z J Zhang ldquoNote on self-restraint as anonline entry-deterrence strategyrdquoManagement Science vol 52no 11 pp 1799ndash1809 2006

[30] Z Cheng and B R Nault ldquoInternet channel entry retailcoverage and entry cost advantagerdquo Information Technology andManagement vol 8 no 2 pp 111ndash132 2007

[31] X Zhang ldquoRetailersrsquo multichannel and price advertising strate-giesrdquoMarketing Science vol 28 no 6 pp 1080ndash1094 2009

[32] W Huang and J M Swaminathan ldquoIntroduction of a secondchannel implications for pricing and profitsrdquo European Journalof Operational Research vol 194 no 1 pp 258ndash279 2009

[33] H Hotelling ldquoStability in competitionrdquo The Economic Journalvol 39 no 153 pp 41ndash57 1929

[34] J Zhang ldquoThe perils of behavior-based personalizationrdquo Mar-keting Science vol 30 no 1 pp 170ndash186 2011

[35] T Kabiraj and C Lee ldquoLicensing contracts in hotelling struc-turerdquoTheoretical Economics Letters vol 1 no 3 pp 57ndash62 2011

[36] HWang andTNariu ldquoDistribution channelmanagement in aninternet age equilibrium and social welfarerdquo Journal of IndustryCompetition and Trade vol 12 no 3 pp 285ndash298 2012

[37] M Lijesen ldquoHotellingrsquos webshoprdquo Journal of Economics vol 109no 2 pp 193ndash200 2013

[38] R Gulati and J Garino ldquoGet the right mix of bricks amp clicksrdquoHarvard Business Review vol 78 no 3 pp 107ndash214 2000

[39] K-J Chung S-D Lin and H M Srivastava ldquoThe completesolution procedures for the mathematical analysis of somefamilies of optimal inventorymodels with order-size dependenttrade credit and deterministic and constant demandrdquo AppliedMathematics and Computation vol 219 no 1 pp 142ndash157 2012

[40] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels under conditional trade credit in a supply chain systemrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 24 pp10036ndash10052 2013

[41] K-J Chung S-D Lin and H M Srivastava ldquoThe inventorymodels for deteriorating items in the discounted cash-flowsapproach under conditional trade credit and cash discount ina supply chain systemrdquo Applied Mathematics and InformationSciences vol 8 no 5 pp 2103ndash2111 2014

[42] J Luo and Q Zhang ldquoTrade credit a new mechanism tocoordinate supply chainrdquo Operations Research Letters vol 40no 5 pp 378ndash384 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