Optimal Supply Chain Contracts

Abstract

This paper characterizes the optimal supply-chain contract from the perspective of contract theory. While most of the supply-chain literature takes the contractual form as given and investigates its implications and uses in various contexts, our approach does not impose any functional form restriction in the contract space. We show that when the retailer faces limited liability and privately observes demand, very generally, the optimal arrangement can be implemented by the familiar buy-back contract. Under this contract, the retailer makes a fixed payment and sells unsold inventory back to the supplier at a price equal to the retailer's salvage value. Even though the returns can be inefficient from the supply chain perspective, they serve as a screening tool that differentiates different types of retailers ex post. When the demand is observable to both parties, the optimal contract resembles the classical consignment arrangement with revenue sharing. On the other hand, in the absence of limited liability, the optimal contract features the franchise fee contract, according to which the retailer pays a fixed transfer regardless of the actual units sold. Our analysis therefore provides a holistic justification of several practical contracts in supply chains.