Competitive contract design in a retail supply chain under demand uncertainty

Abstract

This article studies the design of contracts involving a single retailer and multiple competing manufacturers who supply substitutable products. We consider a retail context in which contracts with manufacturers are negotiated relatively infrequently and signed before the demand environment is known, and the retail prices are determined when the demand is known. We develop a 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 contract with nonlinear prices so that total payments are the total production cost plus a fixed additional cost. 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. In an extension it is found that our equilibrium continues to hold when the retailer's reservation profit is below a threshold, but the competition dynamics may change when the reservation profit is above the threshold. 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.