Robust Assortment Optimization Under the Markov Chain Model

40 Pages Posted: 29 Oct 2021

See all articles by Antoine Désir

Antoine Désir

INSEAD

Vineet Goyal

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Bo Jiang

Shanghai University of Finance and Economics - School of Information Management and Engineering

Tian Xie

Shanghai University of Finance and Economics - School of Information Management and Engineering

Jiawei Zhang

New York University (NYU) - Department of Information, Operations, and Management Sciences

Date Written: October 8, 2021

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.

Suggested Citation

Désir, Antoine and Goyal, Vineet and Jiang, Bo and Xie, Tian and Zhang, Jiawei, Robust Assortment Optimization Under the Markov Chain Model (October 8, 2021). Available at SSRN: https://ssrn.com/abstract=3938924 or http://dx.doi.org/10.2139/ssrn.3938924

Antoine Désir (Contact Author)

INSEAD ( email )

Boulevard de Constance
77305 Fontainebleau Cedex
France

Vineet Goyal

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

Bo Jiang

Shanghai University of Finance and Economics - School of Information Management and Engineering ( email )

No. 100 Wudong Road
Shanghai, Shanghai 200433
China

Tian Xie

Shanghai University of Finance and Economics - School of Information Management and Engineering ( email )

No. 100 Wudong Road
Shanghai, Shanghai 200433
China

Jiawei Zhang

New York University (NYU) - Department of Information, Operations, and Management Sciences ( email )

44 West Fourth Street
New York, NY 10012
United States

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