Abstract
The paper studies a stylized supply chain, consisting of a manufacturer who sells a particular product to an independent retailer. The aim is to study intertemporal coordination and contracting in the supply chain, using a franchise contract. A franchise contract includes as special cases a wholesale-price contract, a two-part tariff, and a revenue-sharing contract. The retailer determines her ordering rate and the consumer price while the manufacturer determines the production rate and the parameters of the franchise contract. Contract parameters are time-dependent and determined under two, alternative, objectives. First, the manufacturer wishes to achieve an outcome in which total supply chain profits are maximized. Second, the manufacturer seeks an outcome which maximizes its individual profits. The setup is a differential game played over a fixed and finite horizon.
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References
Cachon G (2003) Supply chain coordination with contracts. In: Graves S, de Kok T (eds) Handbooks in operations research and management science: supply chain management. Elsevier, Amsterdam
Cachon GP, Lariviere MA (2005) Supply chain coordination with revenue sharing contracts: strengths and limitations. Manag Sci 51:30–44
Desai VS (1992) Marketing-production decisions under independent and integrated channel structure. Ann Oper Res 34:275–306
Desai VS (1996) Interactions between members of a marketing-production channel under seasonal demand. Eur J Oper Res 90:115–141
Dockner EJ, Jørgensen S, Van Long N, Sorger G (2000) Differential games in economics and management science. Cambridge University Press, Cambridge
El Ouardighi F, Kim B (2010) Supply chain quality management with wholesale price and revenue-sharing contracts under horizontal competition. Eur J Oper Res 206:329–340
El Ouardighi F, Jørgensen S, Pasin F (2009) A dynamic game of operations and marketing management in a supply chain. Int Game Theory Rev 10:373–398
Eliashberg J, Steinberg R (1987) Marketing-production decisions in an industrial channel of distribution. Manag Sci 33:981–1000
Eliashberg J, Steinberg R (1991) Competitive strategies for two firms with asymmetric production cost structures. Manag Sci 37:1452–1473
Feichtinger G, Hartl RF (1986) Optimale kontrolle ökonomischer prozesse. Walter de Gruyter, Berlin
Foros Ø, Hagen KP, Kind HJ (2009) Price-dependent profit sharing as a channel coordination device. Manag Sci 55:1280–1291
Gaimon C (1998) The price-production problem: an operations and marketing interface. In: Aronson JE, Zionts S (eds) Operations research: methods, models, and applications. Quorum Books, Westport
He X, Prasad A, Sethi SP, Gutierrez GJ (2007) A survey of Stackelberg differential game models in supply and marketing channels. J Syst Sci Syst Eng 16:385–413
Jeuland AP, Shugan SM (1983) Managing channel profits. Mark Sci 2:239–272
Jørgensen S (1986) Optimal production, purchasing, and pricing: a differential games approach. Eur J Oper Res 24:64–76
Jørgensen S, Kort PM (2002) Optimal pricing and inventory policies: centralized and decentralized decision making. Eur J Oper Res 138:578–600
Jørgensen S, Kort PM, Zaccour G (1999) Production, inventory, and pricing under cost and demand learning effects. Eur J Oper Res 117:382–395
Krishnan H, Winter RA (2010) Inventory dynamics and supply chain coordination. Manag Sci 56:141–147
Lariviere MA (1999) Supply chain contracting and coordination with stochastic demand. In: Tayur S, Ganeshan R, Magazine M (eds) Quantitative methods for supply chain management. Kluwer, Boston
McGuire TW, Staelin R (1986) Channel efficiency, incentive compatibility, transfer pricing, and market structure. Res Mark 8:181–223
Moorthy KS (1987) Managing channel profits: comment. Mark Sci 6:375–379
Pekelman D (1974) Simultaneous price-production decision. Oper Res 22:788–794
Van Gorder RA, Caputo MR (2010) Envelope theorems for locally differentiable open-loop Stackelberg equilibria of finite horizon differential games. J Econ Dyn Control 34:1123–1139
Zaccour G (2008) On the coordination of dynamic marketing channels and two-part tariffs. Automatica 44:1233–1239
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Jørgensen, S. Intertemporal Contracting in a Supply Chain. Dyn Games Appl 1, 280–300 (2011). https://doi.org/10.1007/s13235-011-0016-5
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DOI: https://doi.org/10.1007/s13235-011-0016-5