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Display optimization under the multinomial logit choice model: Balancing revenue and customer satisfaction

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  • Jacob Feldman
  • Puping Jiang

Abstract

In this paper, we consider an assortment optimization problem in which a platform must choose pairwise disjoint sets of assortments to offer across a series of T stages. Arriving customers begin their search process in the first stage, and progress sequentially through the stages until their patience expires, at which point they make a multinomial logit–based purchasing decision from among all products they have viewed throughout their search process. The goal is to choose the sequential displays of product offerings to maximize expected revenue. Additionally, we impose stage‐specific constraints that ensure that as each customer progresses farther and farther through the T stages, there is a minimum level of “desirability” met by the collections of displayed products. We consider two related measures of desirability: purchase likelihood and expected utility derived from the offered assortments. In this way, the offered sequence of assortments must be both high earning and well liked, which breaks from the traditional assortment setting, where customer‐centric considerations are generally not explicitly accounted for. We show that our assortment problem of interest is strongly NP‐Hard, thus ruling out the existence of a fully polynomial‐time approximation scheme (FPTAS). From an algorithmic standpoint, as a warm‐up, we develop a simple constant factor approximation scheme in which we carefully stitch together myopically selected assortments for each stage. Our main algorithmic result consists of a polynomial‐time approximation scheme (PTAS), which combines a handful of structural results related to the make‐up of the optimal assortment sequence within an approximate dynamic programming framework. We also provide an additional approximation scheme, which, under mild assumptions, can handle a cardinality constraint that enforces that an exact number of new products are introduced at each stage. Using an extensive set of numerical experiments, we demonstrate that both algorithms exhibit excellent practical performance, producing sequences of assortments that are, on average, always within 2% of optimal.

Suggested Citation

  • Jacob Feldman & Puping Jiang, 2023. "Display optimization under the multinomial logit choice model: Balancing revenue and customer satisfaction," Production and Operations Management, Production and Operations Management Society, vol. 32(11), pages 3374-3393, November.
  • Handle: RePEc:bla:popmgt:v:32:y:2023:i:11:p:3374-3393
    DOI: 10.1111/poms.14040
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    References listed on IDEAS

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    1. Flores, Alvaro & Berbeglia, Gerardo & Van Hentenryck, Pascal, 2019. "Assortment optimization under the Sequential Multinomial Logit Model," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1052-1064.
    2. Guillermo Gallego & Huseyin Topaloglu, 2019. "Revenue Management and Pricing Analytics," International Series in Operations Research and Management Science, Springer, number 978-1-4939-9606-3, April.
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    4. Mahsa Derakhshan & Negin Golrezaei & Vahideh Manshadi & Vahab Mirrokni, 2022. "Product Ranking on Online Platforms," Management Science, INFORMS, vol. 68(6), pages 4024-4041, June.
    5. 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.
    6. 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.
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    8. 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.
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