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A Unified Framework to Impose Market Share Constraints for Selected Product Classes: Randomized and Deterministic Assortments Under the Multinomial Logit Model

Author

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  • Wenchang Zhu

    (School of Operations Research and Information Engineering, Cornell Tech, New York, New York 10044)

  • Paat Rusmevichientong

    (Marshall School of Business, University of Southern California, Los Angeles, California 90089)

  • Huseyin Topaloglu

    (School of Operations Research and Information Engineering, Cornell Tech, New York, New York 10044)

Abstract

Problem definition : We study assortment optimization problems with market share constraints. The products are partitioned into product classes, each with a market share threshold. If a product class is represented in the offered assortment, then the total purchase probability of the products offered in the class should be above the market share threshold of the product class. Customers choose among offered products according to the multinomial logit model. The goal is to maximize the expected revenue while satisfying the market share constraints. Our work is motivated by the fact that focusing only on maximizing the expected revenue often results in offering many products with small demand quantities, causing operational burden. Retailers are interested in ensuring that the products represented in their assortments command reasonably large demand quantities. Methodology/results : Imposing the market share constraints only for product classes represented in the offered assortment brings unique unexplored dynamics. In the randomized variant, we randomize the offered assortments. In the deterministic variant, we offer a single assortment. The randomized variant is NP-hard, whereas the deterministic variant is NP-hard to approximate within a factor of 1 2 . Our main contributions are a fully polynomial-time approximation scheme for the randomized variant, an approximation scheme for the deterministic variant that yields a ( 1 − ϵ ) -approximate solution while violating market share constraints with a ( 1 − ϵ ) -factor in running time that is polynomial in 1 ϵ , and a 1 2 -approximation algorithm for the deterministic variant that yields a solution satisfying market share constraints exactly in running time that is pseudopolynomial in the input size. We develop a unified approximation framework that applies to both variants and leverage this approximation framework. Managerial implications : We are motivated by a practical need for assortments where the offered products command reasonably large demand quantities. Imposing market share constraints for the selected product classes is a natural way to satisfy this need.

Suggested Citation

  • Wenchang Zhu & Paat Rusmevichientong & Huseyin Topaloglu, 2026. "A Unified Framework to Impose Market Share Constraints for Selected Product Classes: Randomized and Deterministic Assortments Under the Multinomial Logit Model," Manufacturing & Service Operations Management, INFORMS, vol. 28(1), pages 172-192, January.
    • Handle: RePEc:inm:ormsom:v:28:y:2026:i:1:p:172-192
    DOI: 10.1287/msom.2024.1396
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    References listed on IDEAS

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    1. Yufeng Cao & Paat Rusmevichientong & Huseyin Topaloglu, 2023. "Revenue Management Under a Mixture of Independent Demand and Multinomial Logit Models," Operations Research, INFORMS, vol. 71(2), pages 603-625, March.
    2. Pin Gao & Yuhang Ma & Ningyuan Chen & Guillermo Gallego & Anran Li & Paat Rusmevichientong & Huseyin Topaloglu, 2021. "Assortment Optimization and Pricing Under the Multinomial Logit Model with Impatient Customers: Sequential Recommendation and Selection," Operations Research, INFORMS, vol. 69(5), pages 1509-1532, September.
    3. Mika Sumida & Guillermo Gallego & Paat Rusmevichientong & Huseyin Topaloglu & James Davis, 2021. "Revenue-Utility Tradeoff in Assortment Optimization Under the Multinomial Logit Model with Totally Unimodular Constraints," Management Science, INFORMS, vol. 67(5), pages 2845-2869, May.
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