Robust Assortment Optimization Under the Markov Chain Choice Model

• 成果类型: Article
• 署名作者: Desir, Antoine; Goyal, Vineet; Jiang, Bo; Xie, Tian; Zhang, Jiawei
• 署名单位: INSEAD Business School; Columbia University; Shanghai University of Finance & Economics; New York University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.2420
• 发表日期: 2024
• 页码: 1595-1614
• 关键词: assortment optimization; Markov chain choice model; robust optimization

摘要

Assortment optimization arises widely in many practical applications, such as retailing and online advertising. In this problem, the goal is to select a subset from a universe of substitutable products to offer customers in order to maximize the expected revenue. We study a robust assortment optimization problem under the Markov chain choice model. In this formulation, the parameters of the choice model are assumed to be uncertain, and the goal is to maximize the worst case expected revenue over all parameter values in an uncertainty set. Our main contribution is to prove a min-max duality result when the uncertainty set is row-wise. The result is surprising as the objective function does not satisfy the properties usually needed for known min-max results. Inspired by the duality result, we develop an efficient iterative algorithm for computing the optimal robust assortment under the Markov chain choice model. Moreover, our results yield operational insights into the effect of changing the uncertainty set on the optimal robust assortment. In particular, consistent with previous literature, we find that bigger uncertainty sets always lead to bigger assortments, and a firm should offer larger assortments to hedge against uncertainty.