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Robust Assortment Optimization Under the Markov Chain Choice Model

Journal Article
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. The authors 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. The authors' 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, the authors develop an efficient iterative algorithm for computing the optimal robust assortment under the Markov chain choice model. Moreover, the authors' results yield operational insights into the effect of changing the uncertainty set on the optimal robust assortment. In particular, consistent with previous literature, the authors find that bigger uncertainty sets always lead to bigger assortments, and a firm should offer larger assortments to hedge against uncertainty.
Faculty

Associate Professor of Technology and Operations Management