Online Learning for Constrained Assortment Optimization Under Markov Chain Choice Model

Shukai Li (), Qi Luo (), Zhiyuan Huang () and Cong Shi ()
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Shukai Li: Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208
Qi Luo: Department of Business Analytics, University of Iowa, Iowa City, Iowa 52242
Zhiyuan Huang: Department of Management Science and Engineering, Tongji University, Shanghai 200092, China
Cong Shi: Management Science, Miami Herbert Business School, University of Miami, Coral Gables, Florida 33146

Operations Research, 2025, vol. 73, issue 1, 109-138

Abstract: We study a dynamic assortment selection problem where arriving customers make purchase decisions among offered products from a universe of 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 a priori knowledge of problem parameters, the retailer’s objective is to sequentially learn the choice model and optimize cumulative revenues over a finite selling horizon. We develop a fast linear system based explore-then-commit (FastLinETC for short) learning algorithm that balances the tradeoff between exploration and exploitation. The algorithm can simultaneously estimate the arrival and transition probabilities in the MCC model by solving a linear system of equations and determining the near-optimal assortment based on these estimates. Furthermore, our consistent estimators offer superior computational times compared with existing heuristic estimation methods, which often suffer from inconsistency or a significant computational burden.

Keywords: Market Analytics and Revenue Management; online learning; assortment planning; Markov chain choice model; capacity; regret analysis (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:73:y:2025:i:1:p:109-138

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