Competitive Contract Design in a Retail Supply Chain Under Demand Uncertainty

Abstract

This paper studies the design of contracts involving a single retailer and multiple competing manufacturers who supply substitutable products in a retail context. The contracts are signed before the demand environment is known, and the retail prices and orders are determined when more information about demand is available. We develop a two-stage Stackelberg model to study the retailer's product selection and pricing decisions and the manufacturers' contract design decisions. We show that it is optimal for each manufacturer to offer a cost-plus contract. In the case of two manufacturers this result allows us to characterize an equilibrium in which the retailer's choice maximizes the supply chain profit, each manufacturer makes a profit equal to its marginal contribution to the supply chain, and the retailer takes the remaining profit. We also find that while increasing demand correlation always benefits the retailer, it benefits the manufacturers only when the production costs are convex. This suggests that category level advertising is beneficial for all parties only when the manufacturers' costs are convex. Finally, we show that the equilibrium results remain true for the case with more than two manufacturers under a submodularity property, which holds in the case of quadratic costs and linear demand.

Keywords: supply contracts, supply function competition, product selection, retail supply chains, submodularity