Competition and Outsourcing With Scale Economies

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Competition and Outsourcing with Scale Economies¤ Gérard P. Cachon Patrick T. Harker The Wharton School ¢ University of Pennsylvania ¢ Philadelphia PA 19104 November 2001 Abstract Scale economies are commonplace in operations, yet, due to analytical challenges, relatively little is known about how …rms should compete in their presence. This paper presents a model
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  Competition and Outsourcing with Scale Economies ¤ Gérard P. Cachon Patrick T. Harker harker@opim.wharton.upenn.edu Wharton School ¢ University of Pennsylvania ¢ Philadelphia PA 19104November 2001 Abstract Scale economies are commonplace in operations, yet, due to analytical challenges, rel-atively little is known about how …rms should compete in their presence. This paperpresents a model of competition between two …rms that face scale economies; i.e., each…rm’s cost per unit of demand is decreasing in demand. A general framework is used,which incorporates competition between two service providers with price and time sensi-tive demand (a queuing game) and competition between two retailers with …xed orderingcosts and price sensitive consumers (an EOQ game). Reasonably general conditions areprovided under which there exists at most one equilibrium with both …rms participatingin the market. We demonstrate, in the context of the queuing game, that the lower cost…rm in equilibrium may have higher market share and a higher price, an enviable situa-tion. We also allow each …rm to outsource their production process to a supplier or totheir customers (e.g., co-production). Even if the supplier’s technology is no better thanthe …rms’ technology and the supplier is required to establish dedicated capacity (so thesupplier’s scale can be no greater than either …rm’s scale), we show that the …rms strictlyprefer to outsource. We conclude that scale economies provide a strong motivation foroutsourcing that has not previously been identi…ed in the literature. ¤ Thanks is extended to the seminar participants at the following universities: theDepartment of Operations Research, University of North Carolina; the Department of Industrial and Operations Engineering, Univeristy of Michigan; the Graduate School of Business, Stanford University; the Anderson School of Business, Univeristy of California atLos Angeles; the 1999 MIT Summer Camp, Sloan School of Business, MIT; the OperationsManagement Department, University of Michigan; and the Management Department, Uni-versity of Texas at Austin. Thanks is also extended to Philip Afeche, Frances Frei, NoahGans, Martin Lariviere and Erica Plambeck for their many helpful comments. The previ-ous version of this paper was titled “Service Competition, Outsourcing and Co-Productionin a Queuing Game.” An electronic copy is available from the …rst author’s web page.  Scales economies are commonplace in operations. But while there is a considerable opera-tions management literature that identi…es scale economies and develops strategies to exploitthem, relatively little is known about how …rms should compete in their presence. Even theeconomics literature on competition among …rms generally assumes constant or decreasingreturns to scale, so as to avoid the signi…cant analytical complications scale economies create(Vives, 1999). Nevertheless, research is needed on this challenge.This paper studies competition between two …rms that face scale economies; i.e., cost perunit of demand is decreasing in demand. A general framework is employed: it includes,among others, competition between service providers (i.e., a queuing game) and competitionbetween two retailers with …xed ordering costs (i.e., an Economic Order Quantity game).Firms compete for demand with two instruments: the explicit prices they charge consumersand the operational performance levels they deliver. An example of the latter in the contextof the queuing game is the …rm’s expected service time, where faster service means betteroperational performance.Competition with scale economies is brutal for two reasons. First, a …rm must capturea positive threshold of demand or else it is not pro…table (i.e., small players cannot be prof-itable). Second, scale economies increase price competition: a price cut increases demand,which lowers the average cost per unit of demand. As a result, an equilibrium may not exist,even with symmetric …rms (i.e., …rms with the same cost and demand). However, whenan equilibrium exists in which both …rms have positive demand, then it is unique, underreasonable conditions. Hence, competition in this setting does have some structure. Weshow that the low cost …rm always has a higher market share in equilibrium, which is notsurprising. What is unexpected is that the low cost …rm can also have the higher price,which is certainly an enviable position: the …rm uses its lower cost to dominate with oper-ational performance, which allows the …rm to charge a premium and capture more demandthan its rival. As an added bonus, the higher demand also allows the …rm to operate moree¢ciently than its rival. Furthermore, in low margin conditions a small cost advantagecan yield an enormous pro…t advantage even if it does not result in a large market sharedi¤erence.In this environment, …rms could bene…t from any strategy that mitigates price competi-tiveness. We show that outsourcing is one such strategy. We suppose that there exists a1  supplier with the same technology as the …rms. This supplier is able to manage either …rm’soperations and charges a constant fee per unit of demand for that service. The supplierestablishes dedicated capacity for each …rm that outsources, so the supplier is unable to pooldemand across …rms to gain e¢ciency. In other words, the supplier is operationally no moree¢cient than either …rm. Yet, we show that there are contracts that yield the supplier apositive pro…t and yield a higher pro…t to either …rm than if they insourced (i.e., did notoutsource with the supplier). Hence, all …rms are better o¤ with outsourcing. In thissetting, the …rms do not outsource because the supplier is cheaper (by assumption either…rm is able to generate exactly the same cost as the supplier without paying the supplier’smargin). Instead, they outsource because outsourcing dampens price competition. It isalso possible that a …rm can bene…t from a unilateral move to outsource, i.e., a …rm may…nd outsourcing pro…table even if its competitor does not outsource. These results do notoccur with a constant returns to scale technology. Hence, we conclude that in the presenceof scale economies …rms can bene…t from outsourcing even if their supplier is unable to gainany scale advantages.Outsourcing to another …rm is not the only way to change the nature of the productionprocess. If the …rm is o¤ering a service, then the …rm may be able to outsource some of theproduction process onto its customers; i.e., the …rms can make its customers co-producers.Again, we show that …rms may use co-production even if it increases a …rm’s cost; i.e., theprice discount the …rm must give consumers to compensate for their co-production is greaterthan the cost the …rm would incur if the …rm did the service itself.The next section reviews literature relevant to this work. §2 details our model. §3analyzes equilibrium behavior between two …rms. §4 considers the impact of outsourcing.The …nal section concludes. 1 Literature review The body of research related to this work can be divided into three broad sets. The …rstincludes papers that use queuing theory to study the delivery of services. The second setstudies competition between …rms that set inventory policies. The third is the literature onoutsourcing and vertical integration in operations management, marketing and economics.2  As mentioned in the introduction, competing queues is one of the games that falls intoour framework. There are many papers that investigate competition when customers aresensitive to time: Armory and Haviv (1998), Chayet and Hopp (1999), Davidson (1988), DeVany (1976), De Vany and Saving (1983), Gans (2000), Gilbert and Weng (1997), Kalai,Kamien and Rubinovitch (1992), Lederer and Li (1997), Li (1992), Li and Lee (1994), andLoch (1994). In most of these models …rms compete either with prices or with processingrates, but not both. 1 Those authors recognized that allowing for both decisions createssigni…cant analytical complications; in particular, the …rms’ pro…t functions are not wellbehaved (unimodal). Further, qualitative statements regarding competition in that settingare not possible since pure strategy equilibria do not exist. A second distinction is that inmany of those models customers wait in a single queue. 2 In our model, the …rms maintainseparate queues and customers are not able to jockey between. Further, with a singlequeue framework total market demand is constant (i.e., all customers join the queue andare eventually served). We allow for demand functions in which total market demand maydecrease.Deneckere and Peck (1995) and Reitman (1991) do consider a model in which …rms simul-taneously choose prices and processing rates, and customers choose …rms based on expectedutility maximization. However, there are no scale economies in their production processes,which is the main focus of this paper.Gans (2000,2002) and Hall and Porteus (2000) consider competition between …rms whencustomer chooses between …rms based on their past service encounters. In our model, 1 Li and Lee (1992) analyze a model with …xed processing rates and then discuss how themodel could be expanded to allow the …rms to choose prices as well. However, theyemphasize that the lack of pure strategy equilibria in that game imposes a signi…cantchallenge to the analysis of the expanded game. In Lederer and Li (1997), the …rmshave …xed overall production capacity, but they decide howto allocate that capacity acrossmultiple customerclasses. In the single class version of theirmodel, the …rms only competeon price. 2 Gilbert and Weng (1997) do consider a model with separate queues, however the arrivalprocess to each queue is set so that each …rm has the same expected waiting time.3
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