Publication Type

Journal Article

Version

submittedVersion

Publication Date

8-2022

Abstract

We study the maximum capture problem in facility location under random utility models, i.e., the problem of seeking to locate new facilities in a competitive market such that the captured user demand is maximized, assuming that each customer chooses among all available facilities according to a random utility maximization model. We employ the generalized extreme value (GEV) family of discrete choice models and show that the objective function in this context is monotonic and submodular. This finding implies that a simple greedy heuristic can always guarantee a (1−1/e) approximation solution. We further develop a new algorithm combining a greedy heuristic, a gradient-based local search, and an exchanging procedure to efficiently solve the problem. We conduct experiments using instances of different sizes and under different discrete choice models, and we show that our approach significantly outperforms prior approaches in terms of both returned objective value and CPU time. Our algorithm and theoretical findings can be applied to the maximum capture problems under various random utility models in the literature, including the popular multinomial logit, nested logit, cross nested logit, and mixed logit models.

Keywords

Facilities planning and design, Maximum capture, Random utility maximization, Generalized extreme value, Greedy heuristic

Discipline

Operations Research, Systems Engineering and Industrial Engineering | Theory and Algorithms

Research Areas

Intelligent Systems and Optimization

Publication

European Journal of Operational Research

Volume

300

Issue

3

First Page

953

Last Page

965

ISSN

0377-2217

Identifier

10.1016/j.ejor.2021.09.006

Publisher

Elsevier

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1016/j.ejor.2021.09.006

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