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An Exact Method for (Constrained) Assortment Optimization Problems with Product Costs

Author

Listed:
  • Markus Leitner

    (Department of Operations Analytics, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands)

  • Andrea Lodi

    (Jacobs Technion-Cornell Institute, Cornell Tech and Technion - IIT, New York, New York 10044)

  • Roberto Roberti

    (Department of Information Engineering, University of Padua, 35131 Padua, Italy)

  • Claudio Sole

    (Canada Excellence Research Chair in Data-Science for Real-time Decision-Making, Polytechnique Montréal, Montreal, Quebec H3T 1J4, Canada)

Abstract

We study the problem of optimizing assortment decisions in the presence of product-specific costs when customers choose according to a multinomial logit model. This problem is NP-hard, and approximate solutions methods have been proposed in the literature to obtain both lower and upper bounds in a tractable manner. We propose the first exact solution method for this problem and show that provably optimal assortments of instances with up to 1,000 products can be found, on average, in about 2/10 of a second. In particular, we propose a bounding procedure to enhance an approximation method originally proposed by Feldman and Topaloglu and provide tight lower and upper bounds at a fraction of a second. We show how these bounds can be used to effectively identify an optimal assortment. We also describe how to adapt our approach to handle cardinality or space/resource capacity constraints on the assortment as well as assortment optimization under a mixed-multinomial logit model. In both cases, our solution method provides significant computational boosts compared with exact methods from the literature.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:orijoc:v:36:y:2024:i:2:p:479-494
    DOI: 10.1287/ijoc.2022.0262
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    References listed on IDEAS

    as
    1. Sumit Kunnumkal & Victor Martínez-de-Albéniz, 2019. "Tractable Approximations for Assortment Planning with Product Costs," Operations Research, INFORMS, vol. 67(2), pages 436-452, March.
    2. Dorothee Honhon & Sreelata Jonnalagedda & Xiajun Amy Pan, 2012. "Optimal Algorithms for Assortment Selection Under Ranking-Based Consumer Choice Models," Manufacturing & Service Operations Management, INFORMS, vol. 14(2), pages 279-289, April.
    3. Jacob Feldman & Alice Paul & Huseyin Topaloglu, 2019. "Technical Note—Assortment Optimization with Small Consideration Sets," Operations Research, INFORMS, vol. 67(5), pages 1283-1299, September.
    4. Juan José Miranda Bront & Isabel Méndez-Díaz & Gustavo Vulcano, 2009. "A Column Generation Algorithm for Choice-Based Network Revenue Management," Operations Research, INFORMS, vol. 57(3), pages 769-784, June.
    5. Guillermo Gallego & Huseyin Topaloglu, 2014. "Constrained Assortment Optimization for the Nested Logit Model," Management Science, INFORMS, vol. 60(10), pages 2583-2601, October.
    6. Silvano Martello & Paolo Toth, 2003. "An Exact Algorithm for the Two-Constraint 0--1 Knapsack Problem," Operations Research, INFORMS, vol. 51(5), pages 826-835, October.
    7. Paat Rusmevichientong & David Shmoys & Chaoxu Tong & Huseyin Topaloglu, 2014. "Assortment Optimization under the Multinomial Logit Model with Random Choice Parameters," Production and Operations Management, Production and Operations Management Society, vol. 23(11), pages 2023-2039, November.
    8. Kalyan Talluri & Garrett van Ryzin, 2004. "Revenue Management Under a General Discrete Choice Model of Consumer Behavior," Management Science, INFORMS, vol. 50(1), pages 15-33, January.
    9. Strauss, Arne K. & Klein, Robert & Steinhardt, Claudius, 2018. "A review of choice-based revenue management: Theory and methods," European Journal of Operational Research, Elsevier, vol. 271(2), pages 375-387.
    10. 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.
    11. Sumit Kunnumkal & Huseyin Topaloglu, 2008. "A refined deterministic linear program for the network revenue management problem with customer choice behavior," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(6), pages 563-580, September.
    12. Silvano Martello & Paolo Toth, 1997. "Upper Bounds and Algorithms for Hard 0-1 Knapsack Problems," Operations Research, INFORMS, vol. 45(5), pages 768-778, October.
    13. 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.
    14. Heng Zhang & Paat Rusmevichientong & Huseyin Topaloglu, 2020. "Assortment Optimization Under the Paired Combinatorial Logit Model," Operations Research, INFORMS, vol. 68(3), pages 741-761, May.
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