Production, Manufacturing and Logistics A note on competitive supply chains with generalised supply costs q Derek Atkins a , Liping Liang b, * a Sauder School of Business, University of British Columbia, 2053 Main Mall, Vancouver, BC, Canada V6T 1Z2 b Department of Computing and Decision Sciences, Lingnan University, Tuen Mun, N.T., Hong Kong article info Article history: Received 1 December 2009 Accepted 9 July 2010 Available online 7 August 2010 Keywords: Marketing Supply chain outsourcing Channel competition abstract This note generalises models from two influential papers in the theory of supply chain outsourcing under competition: McGuire and Staelin (1983) and Cachon and Harker (2002). The first paper studies the impact of competitive intensity on the outsourcing decision from the supplier’s point of view for linear supply cost; the second paper examines the impact of supply economies of scale from the retailer’s point of view when selling perfectly substitutable products. By considering competitive intensity and supply economies of scale simultaneously, we find that equilibrium channel structures are primarily determined by the competitive intensity, which is true even under supply diseconomies of scale; the key message in the second paper of scale economies driving retailer’s outsourcing supply decision is highly dependent on the assumption of perfect substitutes. Our finding has no qualitative difference when either the suppliers or the retailers are modeled as the channel leader and make the outsourcing decisions. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Economies/diseconomies of scale in production widely exist in practice, but a linear cost is commonly used in the supply chain outsourcing and channel structure literature to simplify the analy- sis. McGuire and Staelin (1983) and Cachon and Harker (2002) (hereafter MS and CH) separately consider equilibrium channel structures for competitive supply chains in terms of a single prime driver: competitive intensity in the first case, and supply econo- mies of scale in the latter. But are the insights from these two influ- ential papers different if these two drivers are considered simultaneously? Are the insights dependent on which channel member has the power and acts as the leader? This note addresses these questions by generalising these two papers and studying the impact of both factors as well as supply diseconomies of scale on equilibrium channel structures from both the supplier’s and the re- tailer’s point of view. Both MS and CH are concerned with two competing supply chains each consisting of a supplier or manufac- turer providing one product (service) to a downstream retailer (service provider). We shall use supplier and retailer for simplicity. The retailers set the retail prices and sell the items which compete as substitutes. The concern of both papers is whether the channels should be integrated: leaving both supply and retailing ‘in-house’, or whether supply/retailing should be outsourced. Actually MS concern a supplier outsourcing to a retailer, but their methodology can easily be used for the reverse. We also take liberties with CH, for example they take a common supplier to both chains but with production costs that do not overlap. In addition, instead of a wholesale price, they use a contractual arrangement (through negotiation) to ensure suppliers are not worse off. None of these is- sues distorts their key messages, and in order to integrate the two results we have had to unify them. The structure and results of the two papers appear to mark them as distinct, but we shall present their essential features as two special cases of a single model, a model that also allows for some further generalisations not offered in the originals. What marks the two papers as distinct and what characteristics are similar are important, but before going into details it is conve- nient to present the key message from each. The message from MS is that, other things being equal, the fiercer the competition the more likely that retailing should be outsourced. In their own words, ‘‘If the retail market is highly competitive (in the sense that the demands are sufficiently interdependent), manufacturers in a duopoly are better off if they can shield themselves from this envi- ronment by inserting privately–owned profit maximizers between themselves and the ultimate retail markets even though they lose control of retail price.” The message from CH is that, other things being equal, supply economies of scale encourage the outsourcing of supply. This is not because scale economies can be gained by supplying many retailers, which is not allowed in the model. Rather, outsourcing a concave supply cost allows for supply costs to be ‘seen’ as linear through the action of the wholesale price. This relieves pressure on the downstream to exploit scale economies. Such pressure depresses retail prices and increases demand. This 0377-2217/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2010.07.012 q The authors are grateful to the editor and two anonymous referees for their insightful comments that helped improve this note. * Corresponding author. Tel.: +852 2616 8103; fax: +852 2892 2442. E-mail addresses: derek.atkins@sauder.ubc.ca (D. Atkins), lipingliang@ln.edu.hk (L. Liang). European Journal of Operational Research 207 (2010) 1316–1320 Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor