Supply Chain Contracts in the Small Data Regime

Problem definition: We study supply chain contract design under uncertainty. In this problem, the retailer has full information about the demand distribution, whereas the supplier only has partial information drawn from historical demand realizations and contract terms. The supplier wants to optimize the contract terms, but she only has limited data on the true demand distribution. Methodology/results: We show that the classical approach for contract design is fragile in the small data regime by identifying cases where it incurs a large loss. We then show how to combine the historical demand and retailer data to improve the supplier's contract design. On top of this, we propose a robust contract design model where the uncertainty set requires little prior knowledge from the supplier. We show how to optimize the supplier's worst-case profit based on this uncertainty set. In the single-product case, the worst-case profit can be found with bisection search. In the multiproduct case, the worst-case profit can be found with a cutting plane algorithm. Managerial implications: Our framework demonstrates the importance of combining the demand and retailer information into the supplier's contract design problem. We also demonstrate the advantage of our robust model by comparing it against classical data-driven approaches. This comparison sheds light on the value of information from interactions between agents in a game-theoretic setting and suggests that such information should be utilized in data-driven decision making.