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Joint Pricing-Production Decisions in Supply Chains of Complementary Products with Uncertain Demand

School of Management, University of Texas at Dallas, Richardson, Texas 75083
yunzeng.wang{at}utdallas.edu

Consider n manufacturers, each producing a different product and selling it to a market, either directly or through a common retailer. The n products are perfectly complementary in the sense that they are always sold and consumed jointly or in sets of one unit of each. Demand for the products during a selling season is both price sensitive and uncertain. Each of the n manufacturers faces the problem of choosing a production quantity and a selling price for his product. Two settings are considered, regarding the decision sequence of the n manufacturers: They are either simultaneous or sequential. The retailer, when present, employs a consignment-sales contract with revenue sharing to bind her relationship with the manufacturers and to extract profit for herself. Using a multiplicative demand model in this paper, we fully characterize individual firms’ decisions in equilibria, under each of the two game settings, and derive closed-form performance measures, both for the channel and for individual channel members. These closed-form solutions allow us to explore the effects of channel structure and parameters on firms’ decisions and performance that lead to conclusions of managerial interest.

Subject classifications: games/group decisions: noncooperative; inventory/production: uncertainty.
History: Received January 2004; revision received August 2005; accepted August 2005.

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