Robust Assortment Optimization Under the Markov Chain Choice Model

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.

Funding: V. Goyal is supported by NSF Grants CMMI 1351838 and 1636046. B. Jiang was supported by the National Natural Science Foundation of China [Grants 11831002, 72150001, and 72171141] and the Program for Innovative Research Team of Shanghai University of Finance and Economics.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2420.