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Assortment Optimization Under Variants of the Nested Logit Model

Author

Listed:
  • James M. Davis

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

  • Guillermo Gallego

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Huseyin Topaloglu

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

Abstract

We study a class of assortment optimization problems where customers choose among the offered products according to the nested logit model. There is a fixed revenue associated with each product. The objective is to find an assortment of products to offer so as to maximize the expected revenue per customer. We show that the problem is polynomially solvable when the nest dissimilarity parameters of the choice model are less than one and the customers always make a purchase within the selected nest. Relaxing either of these assumptions renders the problem NP-hard. To deal with the NP-hard cases, we develop parsimonious collections of candidate assortments with worst-case performance guarantees. We also formulate a convex program whose optimal objective value is an upper bound on the optimal expected revenue. Thus, we can compare the expected revenue provided by an assortment with the upper bound on the optimal expected revenue to get a feel for the optimality gap of the assortment. By using this approach, our computational experiments test the performance of the parsimonious collections of candidate assortments that we develop.

Suggested Citation

  • James M. Davis & Guillermo Gallego & Huseyin Topaloglu, 2014. "Assortment Optimization Under Variants of the Nested Logit Model," Operations Research, INFORMS, vol. 62(2), pages 250-273, April.
    • Handle: RePEc:inm:oropre:v:62:y:2014:i:2:p:250-273
    DOI: 10.1287/opre.2014.1256
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    References listed on IDEAS

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