Online Learning for Constrained Assortment Optimization under Markov Chain Choice Model

52 Pages Posted: 20 Apr 2022 Last revised: 5 Apr 2023

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

Management Science, Herbert Business School, University of Miami

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 choice (MCC) model. The retailer only observes the assortment and the customer's single choice per period. Given limited display capacity, resource constraints, and no \emph{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 MCC model by solving linear equations and determining the near-optimal assortment based on these estimates. Furthermore, our consistent estimators enjoy superior computational times compared to existing heuristic estimation methods that suffer from inconsistency or a large computational burden.

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 )

Zhiyuan Huang

Tongji University - School of Economics and Management ( email )

Siping Road 1500
Shanghai, Shanghai 200092
China

Cong Shi (Contact Author)

Management Science, Herbert Business School, University of Miami ( email )

5250 University Dr
Coral Gables, FL 33146
United States

HOME PAGE: http://https://congshi-research.github.io/

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