Data-integrated Supply Chain Contracts: Learning To Price Under Uncertainty

Xuejun Zhao, Purdue University

Abstract

This study examines data-driven contract design in the small data regime and large data regime respectively, and the implications from contract pricing in the pharmaceutical supply chain. We provide below a brief description of the results obtained for the specific problems considered in this study. In the first problem discussed in Chapter 2, we study supply chain contract design under uncertainty. In this problem, the retailer has full information about the demand distribution, while the supplier only has partial information drawn from past demand realizations and contract terms. The supplier wants to optimize the contract terms, but she only has limited data on the true demand distribution. We apply a distributionally robust optimization approach. We show that the classical approach for optimizing the contract terms is fragile in the small data-driven regime by identifying several cases where it incurs a large loss. We propose a robust model for contract design where the uncertainty set requires little prior knowledge from the supplier, and effectively combines the supplier’s information from past demand realizations and past interactions with the retailer. We show how to optimize the supplier’s worst-case profit based on this uncertainty set. In single product case, the worstcase order quantity can be found through bisection search. In the multi-product case, we give a cutting plane algorithm for finding the worst-case order quantity and the worst-case distribution. We also demonstrate the asymptotic optimality of our uncertainty set. Our model offers a versatile framework for combining different sources of information into a single distributionally robust optimization problem. We demonstrate the advantage of our robust model by comparing it against the classical data-driven approaches. This comparison sheds light on the value of information from interactions between agents in a game-theoretic setting, and suggest that such information should not be neglected in data-driven decision-making. In the second problem discussed in Chapter 3, we investigate the supply chain contract design problem faced by a data-driven supplier who needs to respond to the inventory decisions of the downstream retailer. Both the supplier and the retailer are uncertain about the market demand and need to learn about it sequentially. The goal for the supplier is to develop data-driven pricing policies with sublinear regret bound under a wide range of retailer’s inventory learning policies for a fixed time horizon. To capture the dynamics induced by the retailer’s learning strategy, we first make a connection to nonstationary online learning by following the notion of variation budget. The variation budget quantifies the impact of the retailer’s learning strategy on the supplier’s decision-making environments. We then propose dynamic pricing policies for the supplier for both discrete and continuous demand. We also note that our proposed pricing policy only requires access to the support of demand distribution, but critically, does not require the supplier to have any prior knowledge about the retailer’s inventory policy or the demand realizations. We examine several well known data-driven policies for the retailer, including sample average approximation, distributionally robust optimization, and parametric approaches, and show that our pricing policies lead to sublinear regret bounds under these retailer policies.

Degree

Ph.D.

Advisors

Haskell, Purdue University.

Subject Area

Operations research

COinS