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Online Learning for Constrained Assortment Optimization Under Markov Chain Choice Model

Author

Listed:
  • 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)

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.

Suggested Citation

  • Shukai Li & Qi Luo & Zhiyuan Huang & Cong Shi, 2025. "Online Learning for Constrained Assortment Optimization Under Markov Chain Choice Model," Operations Research, INFORMS, vol. 73(1), pages 109-138, January.
    • Handle: RePEc:inm:oropre:v:73:y:2025:i:1:p:109-138
    DOI: 10.1287/opre.2022.0693
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