Publication Type

Journal Article

Version

acceptedVersion

Publication Date

7-2026

Abstract

In this paper, we study the assortment optimization problem under the mixed-logit customer choice model. While assortment optimization has been a central topic in revenue management for decades, the mixed-logit model is widely regarded as one of the most general and flexible frameworks for modeling and predicting customer purchasing behavior. The assortment optimization problem is known to be NP-hard to be approximated to any constant factor, even in the unconstrained case. To address this challenge, we first explore the submodularity properties of a simplified version of the objective function to derive novel semi-constant factor approximation solutions for assortment problems under various constraint settings, including unconstrained, cardinality-constrained, (multi-)knapsack-constrained, and matroid-constrained scenarios. Our approximation schemes are applicable to both finite-mixture and infinite-mixture settings. Furthermore, to solve the assortment optimization problem optimally in practice, we propose a novel approach that leverages outer approximation techniques to approximate certain convex and supermodular components of the objective function. This results in novel cutting-plane and branch-and-cut procedures that efficiently solve the problem. Extensive experiments demonstrate that our approaches consistently outperform existing methods in terms of both solution quality and computational efficiency.

Keywords

Capacitated assortment optimization, Mixed logit model, Approximation scheme, Outer-approximation, Cutting plane, Branch-and-Cut

Discipline

Numerical Analysis and Scientific Computing | Operations Research, Systems Engineering and Industrial Engineering

Research Areas

Intelligent Systems and Optimization

Publication

European Journal of Operational Research

Volume

332

Issue

1

First Page

257

Last Page

275

ISSN

0377-2217

Identifier

10.1016/j.ejor.2025.11.004

Publisher

Elsevier

Embargo Period

3-27-2026

Additional URL

https://doi.org/10.1016/j.ejor.2025.11.004

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