Publication Type

Journal Article

Version

submittedVersion

Publication Date

11-2023

Abstract

We study a robust version of the maximum capture facility location problem in a competitive market, assuming that each customer chooses among all available facilities according to a random utility maximization (RUM) model. We employ the generalized extreme value (GEV) family of models and assume that the parameters of the RUM model are not given exactly but lie in convex uncertainty sets. The problem is to locate new facilities to maximize the worst-case captured user demand. We show that, interestingly, our robust model preserves the monotonicity and submodularity from its deterministic counterpart, implying that a simple greedy heuristic can guarantee a (1−1/�) approximation solution. We further show the concavity of the objective function under the classical multinomial logit (MNL) model, suggesting that an outer-approximation algorithm can be used to solve the robust model under MNL to optimality. We conduct experiments comparing our robust method to other deterministic and sampling approaches, using instances from different discrete choice models. Our results clearly demonstrate the advantages of our robust model in protecting the decision-maker from worst-case scenarios.

Keywords

Facilities planning and design, Local search, Maximum capture, Random utility maximization, Robust optimization, Uuter-approximation

Discipline

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

Research Areas

Intelligent Systems and Optimization

Publication

European Journal of Operational Research

Volume

310

Issue

3

First Page

1128

Last Page

1150

ISSN

0377-2217

Identifier

10.1016/j.ejor.2023.04.024

Publisher

Elsevier

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1016/j.ejor.2023.04.024

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