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

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.