Supply Chain Contracts in the Small Data Regime

Xuejun Zhao, William B. Haskell, Guodong Yu
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Abstract

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.Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0325 .
小数据制度下的供应链合同
问题定义:我们研究的是不确定情况下的供应链合同设计。在这个问题中,零售商拥有关于需求分布的全部信息,而供应商只有从历史需求实现和合同条款中获得的部分信息。供应商希望优化合同条款,但她只有关于真实需求分布的有限数据。方法/结果:我们通过确定会造成巨大损失的情况,说明经典的合同设计方法在小数据环境下非常脆弱。然后,我们展示了如何结合历史需求和零售商数据来改进供应商的合同设计。在此基础上,我们提出了一种稳健的合同设计模型,在该模型中,不确定性集对供应商的先验知识要求不高。我们展示了如何基于该不确定性集优化供应商的最坏情况利润。在单产品情况下,最坏情况利润可以通过分段搜索找到。在多产品情况下,最坏情况利润可通过切割面算法求得。管理意义:我们的框架证明了在供应商的合同设计问题中结合需求和零售商信息的重要性。我们还通过与传统的数据驱动方法进行比较,证明了我们的稳健模型的优势。这种比较揭示了博弈论环境中代理之间互动信息的价值,并建议在数据驱动决策中利用这些信息:在线附录见 https://doi.org/10.1287/msom.2022.0325 。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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