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Mathematics > Optimization and Control

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

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 primal and dual 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 one thousand products can be found, on average, in about two tenths of a second. In particular, we propose a bounding procedure based on the approximation method of Feldman and Topaloglu (2015a) to provide tight primal and dual bounds at a fraction of their computing times. We show how these bounds can be used to effectively identify an optimal assortment. We also describe how to adapt our approach for handling cardinality constraints on the size of the assortment or space/resource capacity constraints.
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:2109.03357 [math.OC]
  (or arXiv:2109.03357v1 [math.OC] for this version)

Submission history

From: Claudio Sole [view email]
[v1] Tue, 7 Sep 2021 22:25:14 GMT (53kb)

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