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Dynamic Assortment Optimization with a Multinomial Logit Choice Model and Capacity Constraint

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  • Paat Rusmevichientong

    (School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853)

  • Zuo-Jun Max Shen

    (Department of Industrial Engineering and Operations Research, University of California--Berkeley, Berkeley, California 94720)

  • David B. Shmoys

    (School of Operations Research and Information Engineering, and Department of Computer Science, Cornell University, Ithaca, New York 14853)

Abstract

We consider an assortment optimization problem where a retailer chooses an assortment of products that maximizes the profit subject to a capacity constraint. The demand is represented by a multinomial logit choice model. We consider both the static and dynamic optimization problems. In the static problem, we assume that the parameters of the logit model are known in advance; we then develop a simple algorithm for computing a profit-maximizing assortment based on the geometry of lines in the plane and derive structural properties of the optimal assortment. For the dynamic problem, the parameters of the logit model are unknown and must be estimated from data. By exploiting the structural properties found for the static problem, we develop an adaptive policy that learns the unknown parameters from past data and at the same time optimizes the profit. Numerical experiments based on sales data from an online retailer indicate that our policy performs well.

Suggested Citation

  • Paat Rusmevichientong & Zuo-Jun Max Shen & David B. Shmoys, 2010. "Dynamic Assortment Optimization with a Multinomial Logit Choice Model and Capacity Constraint," Operations Research, INFORMS, vol. 58(6), pages 1666-1680, December.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:6:p:1666-1680
    DOI: 10.1287/opre.1100.0866
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    References listed on IDEAS

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