Robust Assortment Optimization Under the Markov Chain Choice Model

Abstract

Robust Assortment Optimization Under the Markov Chain Choice Model Assortment optimization arises widely in many practical applications. In this problem, the goal is to select 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 which 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.