A Conic Integer Programming Approach to Constrained Assortment Optimization under the Mixed Multinomial Logit Model

2017/05/25 by Alper Sen, Alper Şen, Alper Atamtürk +5
Business, Management and Accounting · Engineering · Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Mathematical Programming #Supply Chain and Inventory Management #Vehicle Routing Optimization Methods #math.OC

paper · pdf · doi:10.48550/arxiv.1705.09040

openalex publication_date 2017/05/25 · arxiv created 2017/08/12 · arxiv updated 2017/08/15 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We consider the constrained assortment optimization problem under the mixed multinomial logit model. Even moderately sized instances of this problem are challenging to solve directly using standard mixed-integer linear optimization formulations. This has motivated recent research exploring customized optimization strategies and approximation techniques. In contrast, we develop a novel conic quadratic mixed-integer formulation. This new formulation, together with McCormick inequalities exploiting the capacity constraints, enables the solution of large instances using commercial optimization software.

Citations

• Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems
• Mixed MNL models for discrete response

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