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Assortment Optimization Under the Multinomial Logit Model with Sequential Offerings

Author

Listed:
  • Nan Liu

    (Carroll School of Management, Boston College, Chestnut Hill, Massachusetts 02467)

  • Yuhang Ma

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

  • Huseyin Topaloglu

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

Abstract

We consider assortment optimization problems, where the choice process of a customer takes place in multiple stages. There is a finite number of stages. In each stage, we offer an assortment of products that does not overlap with the assortments offered in the earlier stages. If the customer makes a purchase within the offered assortment, then the customer leaves the system with the purchase. Otherwise, the customer proceeds to the next stage, where we offer another assortment. If the customer reaches the end of the last stage without a purchase, then the customer leaves the system without a purchase. The choice of the customer in each stage is governed by a multinomial logit model. The goal is to find an assortment to offer in each stage to maximize the expected revenue obtained from a customer. For this assortment optimization problem, it turns out that the union of the optimal assortments to offer in each stage is nested by revenue in the sense that this union includes a certain number of products with the largest revenues. However, it is still difficult to figure out the stage in which a certain product should be offered. In particular, the problem of finding an assortment to offer in each stage to maximize the expected revenue obtained from a customer is NP hard. We give a fully polynomial time approximation scheme for the problem when the number of stages is fixed.

Suggested Citation

  • Nan Liu & Yuhang Ma & Huseyin Topaloglu, 2020. "Assortment Optimization Under the Multinomial Logit Model with Sequential Offerings," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 835-853, July.
    • Handle: RePEc:inm:orijoc:v:32:y:3:i:2020:p:835-853
    DOI: 10.1287/ijoc.2019.0910
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    References listed on IDEAS

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    7. Dipankar Das, 2023. "A Model of Competitive Assortment Planning Algorithm," Papers 2307.09479, arXiv.org.
    8. Zhen-Yu Chen & Zhi-Ping Fan & Minghe Sun, 2023. "Machine Learning Methods for Data-Driven Demand Estimation and Assortment Planning Considering Cross-Selling and Substitutions," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 158-177, January.
    9. Xiangyu Gao & Stefanus Jasin & Sajjad Najafi & Huanan Zhang, 2022. "Joint Learning and Optimization for Multi-Product Pricing (and Ranking) Under a General Cascade Click Model," Management Science, INFORMS, vol. 68(10), pages 7362-7382, October.
    10. Canhong Wen & Zhenduo Li & Ruipeng Dong & Yijin Ni & Wenliang Pan, 2023. "Simultaneous Dimension Reduction and Variable Selection for Multinomial Logistic Regression," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1044-1060, September.
    11. Markus Leitner & Andrea Lodi & Roberto Roberti & Claudio Sole, 2024. "An Exact Method for (Constrained) Assortment Optimization Problems with Product Costs," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 479-494, March.
    12. Julia Heger & Robert Klein, 2024. "Assortment optimization: a systematic literature review," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(4), pages 1099-1161, December.

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