Online Learning for Constrained Assortment Optimization under Markov Chain Choice Model

43 Pages Posted: 20 Apr 2022

See all articles by Shukai Li

Shukai Li

Northwestern University - Department of Industrial Engineering and Management Sciences

Qi Luo

Clemson University, Department of Industrial Engineering

Zhiyuan Huang

Tongji University - School of Economics and Management

Cong Shi

University of Michigan at Ann Arbor - Department of Industrial and Operations Engineering

Date Written: April 9, 2022

Abstract

We study a dynamic assortment selection problem where arriving customers make purchase decisions among offered products from a universe of $N$ products under a Markov-chain-based choice (MCBC) model. The retailer observes only the assortment and the customer's single choice per period. Given limited display capacity, resource constraints, and no a priori knowledge of problem parameters, the retailer's objective is to sequentially learn the choice model and optimize cumulative revenues over a selling horizon of length $T$. We develop an explore-then-exploit learning algorithm that balances the trade-off between exploration and exploitation. The algorithm can simultaneously estimate the arrival and transition probabilities in the MCBC model by solving linear equations and determining the near-optimal assortment based on these estimates. Furthermore, compared to existing heuristic estimation methods that suffer from inconsistency and a large computational burden, our consistent estimators enjoy superior computational times.

Keywords: online learning, assortment planning, Markov chain choice model, capacity, regret analysis

Suggested Citation

Li, Shukai and Luo, Qi and Huang, Zhiyuan and Shi, Cong, Online Learning for Constrained Assortment Optimization under Markov Chain Choice Model (April 9, 2022). Available at SSRN: https://ssrn.com/abstract=4079753 or http://dx.doi.org/10.2139/ssrn.4079753

Shukai Li

Northwestern University - Department of Industrial Engineering and Management Sciences ( email )

2145 Sheridan Road
Room C210
Evanston, IL 60208
United States

Qi Luo

Clemson University, Department of Industrial Engineering ( email )

227B Freeman Hall
Clemson, SC 29634
United States

Zhiyuan Huang

Tongji University - School of Economics and Management ( email )

Siping Road 1500
Shanghai, Shanghai 200092
China

Cong Shi (Contact Author)

University of Michigan at Ann Arbor - Department of Industrial and Operations Engineering ( email )

1205 Beal Avenue
Ann Arbor, MI 48109
United States

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