Robust Assortment Optimization Under the Markov Chain Choice Model

Antoine Désir (), Vineet Goyal (), Bo Jiang (), Tian Xie () and Jiawei Zhang ()
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Antoine Désir: Technology and Operations Management Area, INSEAD, 77300 Fontainebleau, France
Vineet Goyal: Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
Bo Jiang: Research Institute for Interdisciplinary Sciences, School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, China
Tian Xie: Research Institute for Interdisciplinary Sciences, School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, China
Jiawei Zhang: Stern School of Business, New York University, New York, New York 10012

Operations Research, 2024, vol. 72, issue 4, 1595-1614

Abstract: 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.

Keywords: Optimization; assortment optimization; Markov chain choice model; robust optimization (search for similar items in EconPapers)
Date: 2024
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