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

Markus Leitner (), Andrea Lodi (), Roberto Roberti () and Claudio Sole ()
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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

INFORMS Journal on Computing, 2024, vol. 36, issue 2, 479-494

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.

Keywords: assortment optimization; product costs; multinomial logit; exact methods (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:36:y:2024:i:2:p:479-494

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