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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

A branch-and-bound algorithm for the maximum capture problem with random utilities

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Author(s):
Freire, Alexandre S. [1] ; Moreno, Eduardo [2] ; Yushimito, Wilfredo F. [2]
Total Authors: 3
Affiliation:
[1] Univ Sao Paulo, Escola Artes Ciencias & Humanidades, Sao Paulo - Brazil
[2] Univ Adolfo Ibanez, Fac Sci & Engn, Santiago - Chile
Total Affiliations: 2
Document type: Journal article
Source: European Journal of Operational Research; v. 252, n. 1, p. 204-212, JUL 1 2016.
Web of Science Citations: 1
Abstract

The MAXIMUM CAPTURE PROBLEM WITH RANDOM UTILITIES seeks to locate new facilities in a competitive market such that the captured demand of users is maximized, assuming that each individual chooses among all available facilities according to the well-know a random utility model namely the multinomial logit. The problem is complex mostly due to its integer nonlinear objective function. Currently, the most efficient approaches deal with this complexity by either using a nonlinear programing solver or reformulating the problem into a Mixed-Integer Linear Programing (MILP) model. In this paper, we show how the best MILP reformulation available in the literature can be strengthened by using tighter coefficients in some inequalities. We also introduce a new branch-and-bound algorithm based on a greedy approach for solving a relaxation of the original problem. Extensive computational experiments are presented, bench marking the proposed approach with other linear and non-linear relaxations of the problem. The computational experiments show that our proposed algorithm is competitive with all other methods as there is no method which outperforms the others in all instances. We also show a large-scale real instance of the problem, which comes from an application in park-and-ride facility location, where our proposed branch-and-bound algorithm was the most effective method for solving this type of problem. (C) 2015 Elsevier B.V. All rights reserved. (AU)

FAPESP's process: 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science
Grantee:Carlos Eduardo Ferreira
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 12/17585-9 - Modeling Techniques for Solving Combinatorial Optimization Problems
Grantee:Alexandre da Silva Freire
Support Opportunities: Scholarships in Brazil - Post-Doctoral