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MANAGEMENT SCIENCEArticles in Advance, pp. 1–12
http://pubsonline.informs.org/journal/mnsc ISSN 0025-1909 (print), ISSN 1526-5501 (online)
Demand Pooling in Omnichannel OperationsMing Hu,a Xiaolin Xu,b Weili Xue,c Yi Yangd
aRotman School of Management, University of Toronto, Toronto, Ontario M5S3E6, Canada; b School of Business, Nanjing University,Nanjing 210093, China; c School of Economics and Management, Southeast University, Nanjing 210093, China; d School of Management,Zhejiang University, Hangzhou 310058, ChinaContact: [email protected], https://orcid.org/0000-0003-0900-7631 (MH); [email protected],
https://orcid.org/0000-0003-0598-657X (XX); [email protected], https://orcid.org/0000-0002-2258-9579 (WX); [email protected],https://orcid.org/0000-0001-5161-991X (YY)
Received: June 13, 2020Revised: October 8, 2020; December 14, 2020Accepted: December 21, 2020Published Online in Articles in Advance:March 23, 2021
https://doi.org/10.1287/mnsc.2021.3964
Copyright: © 2021 INFORMS
Abstract. Both traditional retailers and e-tailers have been implementing omnichannelstrategies such as buy online, pick up at store (BOPS). We build a stylized model to in-vestigate the impact of the BOPS initiative on store operations from an inventory per-spective. We consider two segments of customers, namely store-only customers who onlymake purchases offline and omni-customers who strategically choose between offline andonline channels. We show that BOPS may either benefit or hurt the retailer depending ontwo fundamental system primitives: the store visiting cost and the online waiting cost. Ifthe online waiting cost is relatively low and the store visiting cost is even lower, BOPS caninduce omni-customers to migrate from online buying to BOPS, leading to demand poolingat the brick-and-mortar (B&M) store. Such demand pooling provides two benefits forthe retailer: it reduces the overstocking cost, and after inventory reoptimization, it resultsin a higher fill rate at the B&M store, which benefits existing customers and potentiallyattracts more customers to the store. In contrast, if both store visiting and online waitingcosts are relatively high with the latter even higher, introducing BOPS can result in demanddepooling as a result of the migration of the omni-customers from offline purchasingto BOPS. This leads to a lower fill rate after inventory reoptimization, likely the result of alower profit margin under BOPS, which turns away store-only customers and hurtsthe retailer.
History: Accepted by Charles Corbett, operations management.Funding: M. Hu was supported by the Natural Sciences and Engineering Research Council of Canada
[Grant RGPIN-2015-06757]. X. Xu is grateful for financial support by the National Natural Sci-ence Foundation of China [Grant 71871114]. W. Xue is grateful for the financial support of theNational Natural Science Foundation of China [Grant 71822103]. Y. Yang is grateful for the financialsupport of the National Natural Science Foundation of China [Grants 71871198, 71931009, and71821002].
Supplemental Material: The online appendices are available at https://doi.org/10.1287/mnsc.2021.3964.
Keywords: omnichannel • retail operations • channel management • inventory management
1. IntroductionHeated debates emerged a decade ago about wherethe future of retailing lies–online or offline channels?The answer seems more apparent now as the linesbetween digital and physical stores become blurrier.The future of retailing looks like a hybrid of physicalstores and online ordering channels with each com-pany striving to achieve the same goal from differentstarting points. Amazon andWalmart, for example, areeach trying to becomemore like the other—Walmart byinvesting heavily in its technology and acquiringonline retailers such as Jet and Bonobos and Ama-zon by opening physical bookstores and buying thephysical supermarket Whole Foods.
The omnichannel environment presents equal op-portunities for both “traditional” retailers (e.g., Wal-mart), which began businesswith physical stores, and“new” retailers (e.g., Warby Parker), which started
out by selling online (Bell et al. 2014). However,finding ways to manage inventory at a local store,which may serve multiple streams of customers in agiven omnichannel strategy, becomes a key challengeto retailers. On the one hand, inventory plays a vi-tal role under different omnichannel strategies be-cause of its effect on the service levels experiencedby customers. To cater to both online and in-storeshoppers at the same time, Target improved its brick-and-mortar (B&M) in-stock performance by 20% inthe fourth quarter of 2015 (Chao 2016). On the otherhand, inventory is often the most significant costcomponent for retailers (as a percentage of sales).As mentioned, one solution for traditional retailers isto use the merchandise in their stores, ideally af-ter inventory reoptimization, to fulfill online orders;however, that strategy may not be as efficient asthe centralized distribution centers that e-tailers use
1
(Kapner 2015). With more inventory at stores to meetthe in-store pickup demand, retailers also face a riskof being stuck with excess inventory (Bose 2014).
In this paper, we study a representative omni-channel strategy, that is, buy online, pick up atstore (BOPS). In fulfilling customer demand underBOPS, the B&M store plays the critical role of a mini-warehouse and pickup location. We build a stylizedmodel for a retailer with two segments of customers:store-only customers who only consider purchasingthe product at the B&M store and omni-customerswho consider buying the product through all chan-nels provided by the retailer. As a benchmark, wefirst analyze a BASE model in which no omnichannelstrategy is implemented and online and offline channelsare operated independently. Without considering theimplication of inventory, it is intuitive that the intro-duction of a new omnichannel strategy expands themarket while simultaneously cannibalizing the exist-ing online and offline channels.However, the story canbe very different ifwe consider the strategic interactionbetween the retailer’s inventory decision and cus-tomers’ purchasing behavior. Hence inventory iscritical to determiningwhether BOPSmight be a goodstrategy for a retailer.
Assuming that customers’ online base surplus (i.e.,valuationminus price) is higher than their offline basesurplus1 and that the profit margin of online sales islower than that of offline sales,2 we find that BOPSmay either benefit or hurt the retailer depending ontwo fundamental system primitives: the store visitingcost and the online waiting cost. If store visiting andonline waiting costs are both low with the formereven lower3, the introduction of BOPS can incentivizeomni-customers to migrate from the online channelto BOPS, which not only gives local inventory in-formation, but also provides a new purchase channelfor omni-customers. Thus, BOPS can lead to demandpooling at the B&M store; that is, the local inventorycan be used to fulfill orders from two customer seg-ments. Demand pooling has two benefits for the re-tailer. First, it allows higher utilization of the localinventory and saves overstocking cost (referred toas the “utilization enhancement effect”). Second, af-ter inventory reoptimization, it results in a higher fillrate at the B&M store (referred to as the “availabilityimprovement effect”), which benefits the existingcustomers and potentially attracts more customersto visit. However, the opposite of demand poolingcan also happen. If store visiting and online waitingcosts are both high with the latter even higher,4 BOPScan hurt the retailer as well as the customers. Thedamage is due to a demand depooling effect: thoseomni-customers who would shop offline in theBASEmodel nowmigrate to BOPS, inwhich the profitmargin is lower than in the offline channel. After
inventory reoptimization, the fill rate is reduced atthe B&M store, which then deters the store-only andomni-customers from visiting the store. That is, al-though omni-customers who adopt BOPS are stillmainly fulfilled by the B&M store, demand depoolingoccurs after inventory reoptimization because theprofit margin of BOPS sales is lower than that ofonline sales. Therefore, BOPS may hurt both the re-tailer and those two segments of customers.
2. Literature ReviewWe study the joint management of online and offlinechannels under an omnichannel strategy and exploreits pros and cons by considering the interactions ofmultiple channels through the endogenized inventorydecisions. There are two closely related streams ofliterature: omnichannel and multichannel manage-ment. The more closely related is omnichannel man-agement, which has recently gained traction. One partof this stream investigates the impact of omnichannelson customers’ choice behavior among channels. Forexample, Konus et al. (2008) and De Keyser et al. (2015)use survey data to identify various segments of mul-tichannel shoppers. Chintagunta et al. (2012) empir-ically quantify the relative transaction costs whenhouseholds choose between the online and offlinechannels of grocery stores. These empirical papersprovide a better understanding of customers’ channelchoice behavior and market segmentation. Anotherpart of this stream of literature investigates the prac-tical implications of implementing an omnichannelstrategy. Gallino and Moreno (2014) empirically ex-amine the impact of BOPS on a retailer’s sales volumein both online and offline channels and find that theimplementation of BOPS results in a reduction inonline sales and an increase in store sales and traffic.Gallino et al. (2017) analyze the data from a leadingU.S. retailer that introduced the ship-to-store option(BOSS) to customers and demonstrate that BOSS canincrease sales dispersion among various products inthe B&M stores. Bell et al. (2018) empirically showthat offline showrooms not only increase online andoverall sales, but also improve operational efficiency.Existing analytical models of omnichannel man-
agement focus on investigating how omnichannelstrategies affect a retailer’s operational decisions andprofitability. Cao et al. (2016) show that BOPS pro-vides customers with a new purchasing option and,thus, can attract more customers, which may benefitthe retailer. However, BOPS may be detrimentalbecause of the profitmargin loss fromoperating BOPS(when customersmigrate from the offline channel, thepurchase price could be lower, and there is an extrahandling cost when customers migrate from eitherthe offline or online channel). We identify a positivepooling effect and a negative depooling effect of
Hu et al.: Demand Pooling in Omnichannel Operations2 Management Science, Articles in Advance, pp. 1–12, © 2021 INFORMS
BOPS in addition to its market expansion effect andpossible profit margin loss.
In this stream of analytical models, a trilogy by Gaoand Su is closely related to our model. Gao and Su(2017b) study how retailers can effectively deliveronline and offline information to omni-customers bycomparing three information mechanisms: physicalshowrooms, virtual showrooms, and availability in-formation disclosure. Different mechanisms result indifferent customer valuation revelations, leading todifferent channel choice behavior. In particular, theyshow that physical showroomsmay prompt a retailerto lower the store inventory level because a segmentof customers decides not to buy after learning viashowrooming that their valuation turns out to be low.The reduced inventory level pushes the other segmentof customers who have a high realized valuation tomigrate to the online channel. As a result, in equi-librium, both segments migrate to the online channelas they are homogeneous ex ante. Such an interac-tion, via the B&M inventory, between the two ex postdifferent segments of customers who are ex antehomogeneous is analogous to that between the two exante different segments of customers—omnichanneland store-only customers—in our paper.
Moreover, as we do, Gao and Su (2017a) also studyan omnichannel strategy with the BOPS option andexamine the impact of the BOPS initiative on storeoperations. One of their main findings is that BOPSmay benefit or hurt the retailer, depending on theproduct characteristics. The benefits of BOPS aretwofold. First, BOPS as an additional option enablesthe retailer to reach new customers (i.e., a marketexpansion effect) by inventory information disclo-sure. Second, BOPS can generate extra cross-selling rev-enue for theB&M store by inducing omni-customers tovisit the store. On the other hand, Gao and Su (2017a)also reveal an adverse effect of BOPS, which mayreduce the cross-selling revenue in the B&M store.That is, customers can learn the real-time inventoryinformation via BOPS andwill not visit the B&M storeonce the desired item is out of stock. Furthermore,they extend their results to the case in which thereare two segments of customers —store-only andomni-customers— who proportionally share a ran-dom demand size. Our model has some similarity buttwo essential differences: (1) store-only customers inour model are strategic in the sense that they antici-pate the in-store fill rate before heading out to thestore, and (2) we separatelymodel the sizes of the twosegments using two random variables. These twodifferences enable us to identify another benefit ofBOPS from the inventory perspective (even withoutthe cross-selling effect), that is, the demand poolingeffect, which leads to an increase in the fill rate of theB&M store after inventory reoptimization and then
attracts more store-only customers to purchase. Theyalso enable us to identify another drawback of BOPS,that is, the demand depooling effect, operating in thereverse direction of the pooling effect.Finally, in the context of a service system, Gao and
Su (2018) examine the effects of both online and offlineself-ordering technologies on customer demand, em-ployment levels, and the firm’s profit. The authorsinvestigate the interaction, through the staffing level,between employee-served (offline channel) and self-serving (online self-ordering channel) customers. In adrastically different context, we consider the interac-tion, through the local inventory, between store-onlyand omni-customers who can strategically choose thepurchase channel as well as how their orders are ful-filled and obtain a different set of managerial insights.
3. Model DescriptionWe consider a retailer that sells a product to cus-tomers through two channels: online and offline. Asin Cao et al. (2016), we assume there are two types ofcustomers: one intending to shop only offline, re-ferred to as store-only customers and the other con-templating both the online and offline channels, re-ferred to as omni-customers.5 This classification is alsoconsistent with several empirical studies. For exam-ple, De Keyser et al. (2015) demonstrate that theproportion of store-only customers is around 18% bysurvey data from a Dutch telecom retailer, whereasthat of multichannel customers is about 52%. Suchsegmentation can be predicted by both demographicsand psychographics (see Konus et al. 2008): store-onlycustomers are those who are not tech-savvy and prefertraditional shopping or those who enjoy shopping in thephysical stores, whereas omni-customers are those whoprefer to try new and different products, seek new ex-periences, and are typically young and well educated.6
We assume that the market sizes of omnichannel andstore-only customers, denoted by Dm and Ds, re-spectively, follow the normal distributionswithmeanand variance, (μm, σ2m) and (μs, σ2s ), respectively. Tosimplify the analysis, we also assume they have thesame coefficient of variation, that is, σm/μm � σs/μs.Moreover, the market sizes of the two segments areassumed to be correlated with a general coefficient ofρ to show that our results are robust to any demandcorrelation between the two streams of customers.The customer segmentationmentioned is based on the
channel choices a customer faces when making a pur-chase decision. We refer to those customers who even-tually choose to purchase offline (respectively, online)as the offline (online) demand. The online demand,if any, consists of omni-customers only, who wouldotherwise choose to purchase offline or exit themarket, whereas the offline demand, if any, consistsof store-only customers, omni-customers, or both.
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The retailer can hold inventory in the local B&Mstore or the distribution center (DC). The offline de-mand can be satisfied only by the B&M inventory. Incontrast, the online demand can be fulfilled by bothsources, depending on the omnichannel strategyemployed by the retailer and the resulting choicesmade by customers. In particular, we consider thefollowing two strategies observed from the practice,with the former as a benchmark and the latter being atypical omnichannel strategy that is widely adoptedin the retailing industry.
Independent online and offline channels (BASE): Inthe BASE model, the retailer uses the DC inventory tofulfill the online demand, and online and offlinechannels operate independently.
Buy online, pick up at store (BOPS): In the BOPSmodel, the retailer uses the B&M store inventory tosatisfy those online customers who choose the localpickup option.
We assume that omni-customers who eventuallychoose BOPSfirst check online for the store inventory;if the store is out of stock, they then switch to theonline channel with DC fulfillment if the utility ofdoing so is positive (seeGao and Su 2017a). For ease ofexposition, we assume that the DC has unlimited in-ventory capacity. (Our main results also hold whenthe inventory level in the DC is endogenized.) Thisassumption is reasonable when the retailer can makean emergency replenishment from another DC or asupplier with a relatively short lead time comparedwith that from the DC to customers. As a result, theonline purchases, regardless of how they are fulfilled,can be fully satisfied in time. Therefore, the retailerfocuses on deciding how much inventory to stock inthe B&M store before random demands are realized.In addition, customers are lost if they choose to visit thelocal store only to discover that their desired productis out of stock. The latter is consistent with the ob-servation in Haddon (2018) that “when [walk-in] cus-tomers do not immediately find the items theywant, 70%switch to another brand or store, or stop their order.”
In the BASE model, we assume that store-only cus-tomers and omni-customers who purchase offlinehave equal chances of being satisfied by the local in-ventory as the retailer has no way of differentiatingthe two segments of customers when they visit theB&M store. In contrast, BOPS enables the retailer totell omni-customers from store-only customers and toimplement different fulfillment priorities. Alishahet al. (2016) show that the optimal inventory alloca-tion policy aims to satisfy the store-only customersfirst. Based on this, we assume that store-only cus-tomers have a higher fulfillment priority than omni-customers who purchase from BOPS and are alsosatisfied from the local inventory. That is, the retailersatisfies store-only customers first and then satisfies
the BOPS demand as much as possible by usingthe remaining inventory in the B&M store. This as-sumption, adopted by Govindarajan et al. (2020) aswell, is consistent with the notion that store-onlycustomers tend to represent a higher profit marginor a greater loss of goodwill in the event of a stockoutthan omni-customers, who tend to have more pur-chase options. In reality, customers from differentsegments may come in sequentially, and the retailercould use a sophisticated inventory rationing policy.Nevertheless, our model serves as a good approxi-mation of the practical situation in which the retailerreserves inventory for store-only customers.We denote by co and cb the unit fulfillment costs of
the DC and the B&M store, respectively. The fulfill-ment cost includes the procurement cost, the logisticscost incurred in shipping from the DC to the cus-tomer’s doorstep, and the inventory holding andhandling costs at the DC or B&M store. We assumethat co ≤ cb, which is consistent with the observationthat the inventory holding and handling costs at theB&M store are much higher than those at the DC(Kapner 2015).Given the retailer’s channel strategy, customers
choose the purchase option that maximizes theirexpected utility, which consists of at most threeelements—the expected base surplus of consumingthe product, the store visiting cost, and the onlinewaiting cost—and is expressed as
E utility[ ] � E base surplus
[ ] − store visiting cost(if any) − online waiting cost (if any).
Expected Base SurplusCustomers’ expected base surplus � fill rate × (basevaluation − selling price), where the fill rate is basedon customers’ belief or actual information about thein-stock probability. The selling prices for online andoffline channels, denoted by po and pb, are assumed tobe exogenous. For simplicity, we assume that cus-tomers are homogeneous in their valuation of theproduct in the online and offline channels, denoted byvo and vb, respectively. The comparison of vo and vbcan go either way. On the one hand, customers canaccurately value the offline product after inspection,and online customers without firsthand experiencemay risk having only partial knowledge on which tobase their valuation. Thus, customers may view theonline product as being inferior to its offline coun-terpart, that is, vo < vb (Chiang et al. 2003). On theother hand, customers may find online purchasesmore appealing because of the abundant review in-formation and easy comparison shopping availableonline, which can lead to vo ≥ vb. Moreover, the fillrate for the online channel is equal to one because we
Hu et al.: Demand Pooling in Omnichannel Operations4 Management Science, Articles in Advance, pp. 1–12, © 2021 INFORMS
assume that its demand can always be fulfilled,whereas the offline demand may face a stockout risk,depending on the inventory level in the B&M store.
Store Visiting CostCustomers who visit the B&M store incur a positivevisiting cost k, which might depend on the averagedriving distance. From the retailer’s perspective, k canbe a measure of the density of its B&M stores. Here, alower value of k means a higher density of B&Mstores. For simplicity, we assume that this cost isidentical for all customers.
Online Waiting CostThe online waiting cost, denoted by t, is the (per-ceived) waiting cost associated with processing anddelivery of online orders as opposed to no waiting ifthe customers can buy the product offline. From theretailer’s perspective, the higher the value of t, the lessdelivery efficiency the retailer has. From the cus-tomers’ perspective, t can also be interpreted as ameasure of their patience level, depending on the typeof product. For instance, people may be less patientwith the delivery of perishable products than withthat of durable ones.
The sequence of the game between the retailer andcustomers is as follows. Under a specific channelstrategy, the retailer first forms a belief in the pro-portion(s) of customers whowill purchase offline andthen decides the inventory level in the B&M store.Customers who cannot observe the inventory level inthe B&M store form a belief about the fill rate, andwhen the BOPS option is available, omni-customers candeterminewhether their online purchase is available forlocal pickup. Based on the belief/information, cus-tomers choose the option that yields the highest, non-negative, expected utility among all available purchaseoptions or choose to exit the market generating zerosurpluses. Throughout the paper, we adopt the notionof rational expectation (RE) equilibrium (see, e.g., Suand Zhang 2008, Cachon and Swinney 2009). The REequilibrium (REE) requires that beliefs must be con-sistent with actual outcomes. Here, the retailer’s be-lief must be identical to the actual proportion(s) ofcustomers who purchase offline, whereas customers’beliefs about the fill rate of the offline channel mustagree with the actual expected in-stock probability.We denote the base surpluses from online and offlinechannels by uo and ub, respectively, without consid-ering the fill rate of the offline channel. Hence, uo �vo − po and ub � vb − pb. For ease of exposition, wemake the following two assumptions with one on thedemand side about customer utilities and the other onthe supply side about the profit margins.
Assumption 1. uo ≥ max(t,ub).
Assumption 1 requires that customers’ base sur-plus from the online channel (i.e., uo − t) is nonneg-ative, ensuring that the online channel is always apotential choice. It holds when the online waitingcost is relatively low. Assumption 1 also requires theonline base surplus to be higher than the offline basesurplus. This assumption is merely for ease of explora-tion; with it relaxed, our main insights on demand (de)pooling still hold (see Online Appendices B and C).LetΦ(·) be the cumulative distribution function of a
standard normal distribution and Φ−1(·) its inversefunction. Then, we define
ε∗ ≡ Φ−1 1 − cb/pb( )
and
Δ ≡̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅σ2s + σ2m + 2ρσsσm
√− σs
( ) ∫ ε∗−∞
εdΦ ε( )/μm,
where ε∗ corresponds to the critical fractile for anewsvendor and Δ measures a scaled risk associatedwith going to the B&M store because of its lim-ited inventory.
Assumption 2. po − co ≤ pb − cb + Δ.
Assumption 2 rules out the existence of multiplenon–Pareto-dominant equilibria. We note that thisassumption can be less restrictive than po − co ≤ pb − cb,adopted by Gao and Su (2017a), when Δ ≥ 0. Thecondition Δ ≥ 0 can hold when the two streams ofdemand are sufficiently negatively correlated (notingthat
∫ ε∗−∞ εdΦ(ε) < 0). IfΔ < 0, for example, when ρ ≥ 0,
Assumption 2 implies that the profit margin of onlinesales is sufficiently lower than that of offline sales.Moreover, when Assumption 2 is relaxed, the sameinsights hold for at least one of the equilibria.Next, we use UZ
X,Y to denote customers’ expectedutility, where X represents the type of customers, Yspecifies the fulfillment channel, and Z reflects themodel setting. Specifically, X ∈ {m, s}, where m de-notes omni-customers and s represents store-onlycustomers; Y ∈ {b, o, ob}, where b and o represent thetraditional offline and online channels, respectively,and obmeans the BOPS channel; andZ ∈ {B,P}, whereB and P correspond to the BASE and BOPS settings,respectively.
4. Model AnalysisIn this section, we analyze two different types ofomnichannel strategies, namely BASE and BOPS,and characterize the Pareto-dominant RE equilibriumunder each strategy.
4.1. Separate Online and Off-line Channels (BASE)As mentioned, customers who purchase via the offlinechannel may face a stockout. Without knowing the ex-act inventory in the B&M store, customers first forma belief ζ̂ on the in-stock probability before making
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their purchase decision. Based on this belief, cus-tomers’ utilities from offline and online channels, re-spectively, can be expressed as
UBs,b � UB
m,b � ζ̂ub − k, UBm,o � uo − t. (1)
Store-only customers purchase the product ifUBs,b ≥ 0;
otherwise, they exit the market. Assumption 1 en-sures that UB
m,o is always nonnegative. Hence, omni-customers never choose to exit the market. In par-ticular, omni-customers purchase the product fromthe offline channel if and only if UB
m,b ≥UBm,o and from
the online channel if and only if UBm,o > UB
m,b.Next, we consider the retailer’s decision problem.
First, the retailer anticipates that a fraction φ̂m ofomni-customers and a fraction φ̂s of store-only cus-tomers purchase through the offline channel, andthus, the aggregated offline demand is φ̂mDm + φ̂sDs.Given that customers do not have inventory infor-mation for the B&M store in BASE, as mentioned, weassume that those omni-customers who visit the storeand experience a stockout will not switch back to theonline purchase and, hence, will be lost. This is incontrast to the BOPS case in which omni-customerscan check the local inventory before heading to thestore and, in the event of a stockout, can easily switch toonline purchase with DC fulfillment. The remainingfraction (1 − φ̂m) of omni-customers choose to pur-chase through the online channel as its utility is al-ways nonnegative. That is, the online demand canbe expressed as (1 − φ̂m)Dm. Therefore, the retailer’sexpected profit function can be expressed as
πB q( ) � pbE min φ̂mDm + φ̂sDs, q
( )[ ] − cbq⏟̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅⏞⏞̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅⏟Profit from Offline Channel
+ po − co( )
E 1 − φ̂m
( )Dm
[ ].⏟̅̅̅̅̅̅̅̅̅̅̅̅ ⏞⏞̅̅̅̅̅̅̅̅̅̅̅̅ ⏟
Profit from Online Channel
(2)
The first two terms and the last term in (2) representthe expected profits from the offline and onlinechannels, respectively. Without loss of generality, wenormalize the unit salvage value to zero. Given thebeliefs φ̂m and φ̂s, the retailer chooses the orderquantity q to maximize the expected total profit. Unlikethe classic newsvendor problem, here in equilibrium,the demand also depends on the fill rate, which, in turn,depends on the order quantity. To derive the RE equi-librium, we must characterize how the retailer’s or-der quantity and the market size affect the fill rateof the B&M store and then the customer belief.According to Deneckere and Peck (1995), this fill rateis given by E[min{D, q}]/E[D], where D and q rep-resent the random demand and the inventory level inthe B&M store, respectively.
We first explore how demand aggregation affectsthe fill rate by comparing two scenarios that could
possibly sustain in an RE equilibrium. In scenario I,only store-only customers choose the offline chan-nel, that is, (φ̂m, φ̂s) � (0, 1), and in scenario II, bothstore-only customers and omni-customers purchaseoffline, that is, (φ̂m, φ̂s) � (1, 1). Let qs and qsm bethe optimal order quantity maximizing (2) underscenarios I and II, respectively. Consequently, thecorresponding fill rates can be calculated as ζs �E[min(Ds, qs)]/E[Ds] and ζsm � E[min(Dm +Ds, qsm)]/E[Dm +Ds].Lemma 1. ζsm ≥ ζs.
Lemma 1 shows that demand aggregation fromdifferent customer streams (scenario II) leads to ahigher fill rate of the B&M store than just a singlestream of store-only customers (scenario I). This re-sult indicates the potential benefit of demandpooling,which we explore later for BOPS. With Lemma 1, thefollowing proposition characterizes the RE equilib-rium for the BASE model.
Proposition 1 (REE in BASE). At the RE equilibrium, theinventory level in the B&M store and customers’ channelchoices in the offline channel are as follows:i. If k ≤ ζsmub − (uo − t), qB � qsm and (φB
s ,φBm) � (1, 1).
ii. If ζsmub − (uo − t) < k ≤ ζsub, qB � qs and (φBs ,
φBm) � (1, 0).iii. If k > max (ζsub, ζsmub − (uo − t)), qB � 0 and (φB
s ,φBm) � (0, 0).A fraction (1 − φB
m) of omni-customers purchase throughthe online channel.
Proposition 1 shows that, if the store visiting cost islow enough, both store-only customers and omni-customers choose to purchase through the offlinechannel. If the store visiting cost is in an intermedi-ate range, omni-customers switch to the online chan-nel because the utility of purchasing online is higherthan offline, whereas store-only customers stick to theoffline channel as the associated utility is still positive.If the store visiting cost is high enough, no customersvisit the B&M store. Moreover, those omni-customerswhodo not choose the offline channel purchase onlinebecause of Assumption 1.
4.2. Buy Online, Pick Up at Store (BOPS)Now, we analyze the BOPS model, in which the re-tailer can use the B&M store inventory to fulfill ordersfrom both store-only customers and omni-customerswho choose BOPS. As in the BASE model, store-onlycustomers can either purchase through the offlinechannel or exit the market, depending on the utilityUP
s,b � ζ̂ub − k, where ζ̂ is the belief about the fill rate inthe B&M store. However, when BOPS is a viableoption, omni-customers face a choice of one of fouralternatives: purchase online with DC fulfillment,purchase offline, choose BOPS, or exit the market.
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Moreover, as in Gao and Su (2017a), we assume thatomni-customers can always check the inventory viaBOPS before going to the store. This means that BOPSplays the role of disclosing inventory information.Hence, given that the offline inventory informationis taken into account, omni-customers’ utilities ofpurchasing from different channels are given by
UPm,b � ub − k, UP
m,o � uo − t, UPm,ob � uo − k. (3)
Given that uo ≥ t (see Assumption 1), omni-customersalways earn a nonnegative utility from the onlinechannel, and thus, they never choose to exit themarket. Figure 1 illustrates the omni-customers’ de-cision tree. Specifically, an incoming omni-customeralways checks the inventory availability at the B&Mstore first via BOPS. If the B&M store is out of stock,this omni-customer purchases from an online channelor leaves the market, depending on the customer’sutility UP
m,o. If the inventory is available, the customercompares utilities from each option, given in (3), tochoose the one that maximizes the customer’s utilityand generates a nonnegative surplus.
As uo ≥ ub (see alsoAssumption 1), an omni-customeralways prefers the BOPS channel over purchasingoffline. Therefore, the omni-customer chooses eitherthe online channel or the BOPS channel. In particular,the customer chooses the BOPS channel if UP
m,ob ≥ UPm,o
(i.e., k ≤ t) and, otherwise, the online channel. Overall,1{k≤t}Dm and 1{k>t}Dm represent the numbers of omni-customers who prefer BOPS and those who prefer theonline channel, respectively, where 1{·} is an indica-tor function.
Next, we derive the sales volumes from differentchannels. Notably, omni-customers’ channel choicesonly depend on parameters that are assumed to becommon knowledge. Therefore, unlike in the BASEmodel, the retailer can predict omni-customers’ de-cisions with only a belief φ̂s about the proportion ofstore-only customers who would purchase throughthe offline channel. Recall that we assume the store-only customers to have fulfillment priority. Afterfulfilling orders from the store-only customers, theB&M store has the remaining inventory at the level
of (q − φ̂sDs)+. Given that thenumberof omni-customerswho prefer the BOPS channel is 1{k≤t}Dm, the salesvolume of BOPS ismin(1{k≤t}Dm, (q − φ̂sDs)+). The salesvolume in the online channel includes the onlinedemand 1{k>t}Dm and the unsatisfied BOPS demand(1{k≤t}Dm − (q − φ̂sDs)+)+. Therefore, given the beliefφ̂s, the retailer’s expected profit can be expressed as
πP q( )� pbE min φ̂sDs,q
( )[ ]⏟̅̅̅̅̅̅̅̅ ⏞⏞̅̅̅̅̅̅̅̅ ⏟
Revenue from Store-Only Customers
+ poE min 1 k≤t{ }Dm, q− φ̂sDs( )+( )[ ]
⏟̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅⏞⏞̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅⏟Revenue from BOPS Channel
−cbq
+ po− co( )
E 1 k>t{ }Dm + 1 k≤t{ }Dm
([− q − φ̂sDs( )+)+]
.⏟̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅⏞⏞̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅⏟Profit fromOnline Channel
(4)In (4), the first term represents the expected revenuefrom store-only customers, the second term is therevenue from omni-customers who purchase throughthe BOPS channel, the third term is the inventoryprocurement cost of the B&M store, and the last termis the profit from those omni-customerswho purchasethrough the online channel with DC fulfillment.To better understand the effect of BOPS on the fill
rate of the B&M store, we first consider a special caseof k ≤ t, in which omni-customers always chooseto purchase via BOPS if available. We denote by qpthe optimal order quantity that maximizes (4) withφ̂s � 1. The corresponding fill rate for store-only cus-tomers is given by ζp � E[min(Ds, qp)]/E[Ds]. The fol-lowing lemma illustrates how the BOPS strategymight affect the fill rate of the off-line channel.
Lemma 2. qsm ≥ qp ≥ qs and ζp ≥ ζs. Moreover, ζsm can begreater or less than ζp.
Recall that qs and ζs (see Lemma 1) are the retailer’soptimal order quantity and the corresponding fill rateof the offline channel in the BASEmodel when just thestore-only customers purchase offline.With the BOPSstrategy, the B&M store inventory can be used tofulfill orders from both store-only and BOPS cus-tomers. Therefore, BOPS decreases the overstockingrisk for the local store inventory. This incentivizes theretailer to order more local inventory, which, in turn,leads to a higher fill rate, that is, qp ≥ qs and ζp ≥ ζs,thereby benefiting store-only customers in the pa-rameter subspace in which the B&M store sells only tostore-only customers. However, in the parametersubspace in which omni-customers who used to shopoffline have now switched to BOPS, the resulting fillrate for store-only customers could decrease or in-crease after inventory reoptimization. This is be-cause, compared with BASE, BOPS leads to a lowerunderstocking cost because unsatisfied omni-customers
Figure 1. The Decision Tree of Omni-Customers Underthe BOPS
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who choose BOPS are recaptured by the online channel.This incentivizes the retailer to order less and reduce theoverallfill rateat theB&Mstore under BOPS.However,as store-only customers have higher fulfillment pri-ority under BOPS than under BASE, in which theyshare the inventory with omni-customers, even if theinventory level may be lower under BOPS, it is stillpossible for the fill rate for store-only customersunder BOPS to be higher.
Next, we formally characterize the RE equilibriumunder BOPS.
Proposition 2 (REE Under BOPS). At the RE equilibrium,the retailer’s optimal inventory level in the B&M store andcustomers’ optimal channel choices are as follows:
i. If k ≤ min(t, ζpub), qP � qp, φPs � 1, and omni-
customers choose BOPS (and spill over to the onlinechannel in the event of stockout).
ii. If t < k ≤ ζsub, qP � qs, φPs � 1, and omni-customers
purchase through the online channel.iii. If k > max (min(t, ζpub), ζsub), qP � 0, φP
s � 0, andomni-customers purchase through the online channel.
Figure 2 illustrates the RE equilibrium in differentparameter regions depending on the store visitingcost k and the online waiting cost t. We discuss theequilibrium by considering two cases: k ≥ t and k < t,which correspond to two separate regions divided bythe 45° line in Figure 2. In the former case (k ≥ t),wherein the store visiting cost is higher than theonline waiting cost, omni-customers always choosethe online channel. As the store visiting cost increases,store-only customers switch from originally choosingthe offline channel (area III) to exiting the market (seethe part of area II above the 45° line). In the latter case(k < t), omni-customers may prefer BOPS over the
online channel.When the store visiting cost k is below athreshold (area I), store-only customers prefer to shopoffline (as opposed to exiting the market). In this case,it is beneficial for the retailer to serve both demandstreams through the B&M store. However, when thestore visiting cost exceeds the threshold (see the partof area II below the 45° line), store-only customers exitthe market. This also affects the incentive of the re-tailer to serve omni-customers. With only omni-customers, it is more profitable for the retailer toserve them through the online channel instead ofBOPS because the same price is charged but co ≤ cb.Therefore, even though omni-customers may preferBOPS, the retailer shuts down this channel to forcethese customers to buy online. This highlights howthe interaction of the store-only and omni-customerscould influence the optimal omnichannel design; seefurther discussion in the following section.
5. Strategy Comparison: BOPS vs. BASEThe introduction of the BOPS strategy may yield thefollowing effects, which are essentially two sides ofthe same coin.
Demand Pooling EffectCompared with the BASE model, the introductionof BOPS may motivate omni-customers who pur-chase online under BASE to switch from the onlinechannel to BOPS as the latter option provides a highersurplus. As a result, demand pooling occurs in thesense that the retailer uses the local inventory to serveboth BOPS and store-only customers. Lemma 2 showsthat demand pooling can lead to a higher fill rate(i.e., ζp ≥ ζs), which, in turn, attracts more store-onlycustomers ex ante and satisfies more of them ex postand, thus, can benefit the retailer.
Demand Depooling EffectThe demand depooling effect is the opposite of thedemand pooling effect. Consider that, under BASE,omni-customers may prefer purchasing offline as itprovides a higher surplus than that from the onlinechannel, for example, when the store visiting cost islow. When BOPS becomes a viable option, omni-customers have a strong incentive to switch fromoffline to BOPS because the store visiting cost appliesto both the offline purchase option and BOPS, butBOPS generates more surplus under Assumption 1.Though the store inventory serves both BOPS andstore-only customers, the profit margin under BOPScan be sufficiently lower than that of the offlinechannel under Assumption 2.7 Hence, the introduc-tion of BOPS can incentivize the retailer to reduce thein-store inventory level, leading to a lower fill rate,which turns away store-only customers ex ante or expost and, thus, can hurt the retailer.
Figure 2. (Color online) Customer Choice BehaviorUnder BOPS
Note. (·, ·) represents the equilibrium, at which the former and latterarguments denote the equilibrium channel choices of store-onlycustomers and omni-customers, respectively.
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With the REE under BASE and BOPS characterizedin Propositions 1 and 2, we now formally compare thetwo strategies for the retailer; see Figure 3 for an il-lustration. For areas III, II-2, and II-3, the two strat-egies have the same profitability. We explain this intwo separate cases: (i) areas III and II-2 (inwhich k ≥ t)and (ii) area II-3 (in which k < t). Although the out-comes are identical, the reasons behind those re-sults are different. In the former regions, that is, wherethe store visiting cost is higher than the onlinewaitingcost (k ≥ t), the omni-customers do not choose theBOPS channel. That is, BOPS does not affect cus-tomers’ channel choices and makes no difference tothe retailer’s optimal decision. We turn our atten-tion to area II-3. In the BASE model, store-only cus-tomers choose to exit the market, whereas omni-customers choose the online channel. With BOPS,omni-customers prefer BOPS over the online channelbecause the store visiting cost is lower than the onlinewaiting cost (k < t). In comparison, store-only cus-tomers would still prefer to exit the market. As the ful-fillment cost of the online channel is lower than that ofBOPS, serving only the BOPSdemandbyusing the B&Mstore inventory is not profitable for the retailer; hence,the retailer shuts down the BOPS channel, for ex-ample, by disclosing no local inventory. As a result, themarket equilibrium is the same as in the BASE model.
Next, we compare the two strategies for the remainingparameter space that is below the 45° line (i.e., k < t).Wefirst characterize the area in which BOPS benefits theretailer as follows.
Proposition 3 (Demand Pooling Effect). If the onlinewaiting cost is relatively low and the store visiting costis even lower as shown in areas I-2 and I-3 of Figure 3,that is, ζsmub − uo + t < k ≤ min(t, ζpub), BOPS benefitsthe retailer.
In this scenario, with BOPS introduced, omni-customers switch from the online channel to BOPS
as the latter provides a higher surplus. As a result,demand pooling occurs in the sense that the retailer usesthe local inventory to serve both BOPS and store-onlycustomers. Two benefits are associated with demandpooling. First, for the original inventory level, it al-lows higher utilization of the perishable inventory andsaves overstocking cost when the visiting cost is lowenough (area I-2). This phenomenon is called the uti-lization enhancement effect. Second, in anticipation ofthe pooled demand, the retailer reoptimizes the localinventory and sets a higher fill rate at the local store(areas I-2 and I-3). This is called the availability im-provement effect, which creates a win–win–win situ-ation that benefits the retailer and store-only andomni-customers. In particular, the improved productavailability locally under BOPS not only reduces theloss of sales to store-only customers ex post, but alsocan attract more of them (those customers who wouldotherwise shop elsewhere) ex ante to visit the store andlead to a market expansion for the retailer (area I-3).Thus, we provide here an alternative rationale for
the application of BOPS—demand pooling. This is incontrast to Cao et al. (2016), who show that the BOPSchannel could cannibalize the existing offline chan-nel. Our finding is consistent with the empirical ob-servation by Gallino and Moreno (2014), who arguethat the implementation of BOPS is associatedwith anincrease in store sales and traffic. We explain thisobservation from the perspective of demand poolingin addition to the benefit of information release byBOPS that is introduced in Gao and Su (2017a). Inpractice, on the one hand, in order to capture thebenefits of the pooling effect, traditional offline re-tailers, such as Walmart, Best Buy, Target, and IKEA,which have already built a strong B&M store net-work, now also use their offline stores as e-commercewarehouses (see, e.g., Chaudhuri 2016, Gottfried 2016,Nash 2016, Ziobro 2016). On the other hand, domi-nant e-tailers such as Amazon and TMall Alibaba inChina are now opening more B&M stores, hoping tocapture store-only customers in addition to theirexisting customers, who might adopt the BOPS op-tion. For example, Amazon has started opening aconvenience-style Go store and is slated to open largemultifunction stores with curbside pickup capability(Stevens and Safdar 2016).However, introducing BOPS may backfire and turn
away existing store-only customers, thus having a det-rimental impact on both the retailer and customers. Thisdemand depooling effect is illustrated by the followingextreme scenario in which the whole segment of store-only customers are “forced” out ex ante.
Proposition 4 (Demand Depooling Effect). If both the storevisiting cost and the online waiting cost are relativelyhigh with the latter even higher as in area II-1 of Figure 3,
Figure 3. (Color online) BOPS over BASE
Hu et al.: Demand Pooling in Omnichannel OperationsManagement Science, Articles in Advance, pp. 1–12, © 2021 INFORMS 9
that is, ζpub < k ≤ ζsmub − uo + t, store-only customers exitthe market after BOPS is implemented, and BOPS hurtsthe retailer.
In this scenario, both store-only and omni-customersin the BASE model choose the offline channel (whichimplies that omni-customers prefer the offline channelto online). If BOPS becomes a viable option, omni-customers have a strong incentive to switch from theoffline channel to BOPS because the store visiting costapplies toboth theofflinepurchaseoptionandBOPS, butBOPS generates more customer surplus because uo ≥ub (see Assumption 1). Under Assumption 2, whichholds, for example, when online sales have a lowermargin than offline sales, the B&M store has an in-centive to reduce the fill rate after BOPS is imple-mented. The lower fill rate makes the offline option nolonger attractive to store-only customers, and as such,they prefer to exit the market. In turn, such demanddepooling would hurt the retailer. Proposition 4 is anextreme case in which all store-only customers areturned away ex ante. Proposition 5 presents a middleground in which store-only customers could beturned away unsatisfied ex post because of a lowerfill rate.
The demand depooling effect is consistent withpractical observations. For example, to combat thepotential decrease in the fill rate at the B&M store afterintroducing BOPS, Target does not offer some of itsmost heavily advertised items through BOPS (Ziobro2015), whereas Toys “R” Us scaled back some onlinemarketing and eliminated other online deals entirelyduring the Christmas of 2016 in fear of shorting store-only customers on popular products (Ziobro 2016).
The effects of demand pooling and depooling ofBOPS are two sides of the same coin and may be inplay simultaneously as the following result implies.
Proposition 5 (Both Effects in Play). If the store visitingcost is low and the online waiting cost is high as in area I-1 ofFigure 3, that is, k ≤ min(ζpub, ζsmub − uo + t), both de-mand pooling and depooling effects apply. In that area, thereexists δS(co) such that
i. If the online price is low, that is, po < δS(co), thedemand depooling effect dominates, and BOPS hurtsthe retailer.
ii. If the online price is high, that is, po ≥ δS(co), thedemand pooling effect dominates, and BOPS benefitsthe retailer.
Proposition 5 shows that, when the store visitingcost is low and the online waiting cost is high as inarea I-1 of Figure 3, the effects of demand pooling anddepooling of BOPS are in play simultaneously. Forsuch a case in equilibriumunder the BASE, both store-only and omni-customers choose to visit the B&Mstore to make a purchase, and the retailer sets up arelatively high fill rate at ζsm. Now, we dissect the
migration process of omni-customers after the in-troduction of BOPS into two parts to illustrate howthe two effects of demand pooling and depoolingapply simultaneously:
Omni-Customers Migrate to BOPSUnder Assumption 2, the retailer has an incentive tostore less inventory at the B&M store, which maydeter store-only customers from visiting the store exante or leave more store-only customers unsatisfiedex post. This is the depooling effect.
Omni-Customers Pick up at StoreAfter checking the inventory via BOPS, a fraction ofomni-customers come to pick up their purchases,which are taken from the local inventory. With thesame pool of local inventory serving store-only cus-tomers and some omni-customers, the retailer mayhave an incentive to increase the fill rate of the offlinechannel. This is the pooling effect.With the cost parameters in area I-1, in equilibrium,
both depooling and pooling effects apply, and the fillrate at the local store may be lower or higher than thatin BASE (see Lemma 2). The pooling effect benefitsthe retailer, which reduces the understocking riskby using the inventory of both channels; that is, BOPSstrategy can serve all of those omni-customers whoare partially served in the BASE model. This is be-cause, in BASE, unsatisfied omni-customers who visitthe local store and experience stockout are lost, whereasunder BOPS, they are served either by the local inven-tory (if available) or by the DC inventory. However,the depooling effect that turns away store-only cus-tomers ex ante or ex post could offset the poolingeffect. The overall impact of demand depooling andpooling depends on the online price. In particular, ifthe online price is above a certain threshold, thedownside of demand depooling is limited and thebenefit of demand pooling is more significant; then,the combined effect of BOPS is positive for the retailerand vice versa.
6. Discussion and ConclusionOwing to the complexity of the problem, we adopt asimplified model to flush out the fundamental in-sights. Hence, examining whether these insights arerobust is critical. We fully investigate a set of exten-sions of the model in Online Appendices D and E anddiscuss two of them here.
6.1. Cross-Selling EffectCustomers who visit the B&M store (whether theyexperience a stockout or not) are likely to purchaseother products, which is the so-called cross-sellingeffect. Denote by r the expected cross-selling reve-nue brought by each customer who visits the store for
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the initially desired product. A positive cross-sellingeffect, that is, r > 0, could influence the retailer’s in-ventory decision, which then, in turn, affects thecustomers’ channel choice behavior. We discoverthe following.
First, the retailer can bemorewilling to adopt BOPSwith cross-selling than without. For example, whenthe online waiting cost is relatively high but lowerthan the store visiting cost, without cross-selling(r � 0), store-only customers choose to exit the mar-ket and omni-customers turn to the online channel.As a result, the retailer has no incentive to stock anyinventory at the local store. However, if the cross-selling effect is strong enough (r ≥ cb − co), it is ben-eficial for the retailer to stock some local inventory toentice omni-customers to make store visits via BOPS.
Second, the pooling effect is more likely to occur.Consider the situation in which, under BOPS withoutcross-selling, omni-customers switch from the onlinechannel to BOPS, resulting in the pooling effect from thecombined streams of store-only and omni-customers.With cross-selling, the stockout cost increases frompb − cb to pb − cb + r. Thus, the retailer has an incentiveto further increase the inventory level and the fill rateat the B&M store, which enhances the pooling effect.
Third, the negative effect of depooling could bestrengthened. When the store visiting cost is high butlower than the online waiting cost, omni-customerswho, under BASE, prefer visiting the B&M storemigrate to BOPS (for both cases of r � 0 and r > 0),resulting in a lower fill rate in the B&M store un-der BOPS because po ≤ pb. Consequently, store-onlycustomers are deterred from visiting the store, and inturn, the retailer suffers because of this depoolingeffect, not to mention the additional loss of cross-selling revenue from store-only customers.
6.2. Recourse Behavior of Omni-CustomersIn the BASEmodel, when store-visiting omni-customersexperience a stockout, they are assumed to be lost. Now,we relax this assumption. Suppose that those omni-customers who experience a stockout in store switchto the online channel. Comparedwith the lost sales case,the pooling/depooling effect could be strengthenedor weakened. As the explanations for the impact ofthe recourse behavior on pooling and depooling ef-fects are similar, herewe only discuss its impact on thepooling effect.
Consider the situation under BASE in which, withoutthe recourse behavior, omni-customers choose the onlinechannel, and store-only customers exit themarket. Here,without the recourse behavior, BOPS may trigger apooling effect (i.e., the retailer uses the local inventory toserve both BOPS and store-only customers, resulting in ahigher fill rate). However, the higher utility from therecourse behavior may incentivize omni-customers to
switch from theonline channel to the offlineunderBASE.That is, with the recourse behavior of omni-customers,both omni-customers and store-only customers canchoose the offline channel under BASE. Then BOPS doesnot necessarily lead to a pooling effect; that is, the re-course behavior may lessen the pooling effect.On the other hand, consider the situation in which,
without the recourse behavior of omni-customers,both store-only and omni-customers choose the offlinechannel under BASE; here, BOPS may not triggera pooling effect. The recourse behavior of omni-customers reduces the lost-sales cost at the B&Mstore. As a result, under BASE, the retailer orders lessinventory for the B&M store, resulting in a lowerfill rate, which forces omni-customers to choose theonline channel. Consequently, the introduction ofBOPS under the recourse behavior may bring omni-customers to visit the store, resulting in a poolingeffect; that is, the recourse behavior could amplify thepooling effect.
6.3. Concluding RemarksBOPS, as an omnichannel strategy, has been widelyadopted by traditional B&M retailers (e.g., Walmart)and e-tailers (e.g., Amazon). From the inventoryperspective, we develop a stylized model to inves-tigate the impact of BOPS on store operations. Wefind that BOPS can be a double-edged sword for theretailer: it may either benefit or hurt the retailerdepending on two fundamental system primitives,the store visiting and online waiting costs.Many directions are worthy of further exploration.
For example, our analysis suggests that omnichannelstrategies tend to benefit the retailer when the onlinewaiting cost is relatively low and the store visitingcost is even lower. However, it is difficult for retailersto push both capabilities to the desired level in a shorttime. Then, the cooperation between traditional offlineretailers and e-tailers may be another effective way toenjoy the benefit of deploying omnichannel strategiesquickly. Therefore, how to design an effective coop-eration mechanism that benefits both sides may provea vital problem for those online and offline firms whoare also competitors.
AcknowledgmentsThe authors thank the department editor, Charles Corbett; theassociate editor, and three anonymous reviewers for theirguidance and constructive comments. All authors have anequal contribution to the study. Both Yi Yang and Weili Xueserve as the corresponding authors.
Endnotes1Our main insights qualitatively carry over when this assumption isrelaxed. The analysis is available upon request.
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2Aweaker condition is adopted later (see Assumption 2). Even if thisweaker assumption is relaxed, the same insights hold for at least oneof the equilibria.3 See, for example, areas I-2 and I-3 in Figure 3 for an illustration.4 See, for example, area II-1 in Figure 3 for an illustration.5Gao and Su (2017a) only consider omni-customers. The introductionof store-only customers allows us to better study the interaction ofmultiple customer segments from the inventory perspective. Withoutstore-only customers, our model is reduced to theirs.6Though our model does not consider web-only customers, the mod-eling of such a segment would not change our insights. This is becauseour model focuses on the potential conflict of the offline inventory beingshared by both store-only customers and omni-customers. This inven-tory would not be shared with web-only customers.7 If the profit margin of online sales is higher than that of offline sales,Assumption 2 requires that the two demand segments have a suf-ficiently high negative correlation, which leads to a sufficiently highfill rate under BASE and a relatively lower fill rate under BOPS as theomni-customers can be recaptured by the online channel in the eventof a stockout.
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