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Multicommodity flows and benders decomposition for restricted continuous location problems

Multicommodity flows and benders decomposition for restricted continuous location problems
Multicommodity flows and benders decomposition for restricted continuous location problems
The restricted continuous facility location problem arises when there is a need to locate a number of facilities to serve a discrete set of demand points, and where the location of a facility can be anywhere on the plane except for in restricted regions. The problem finds applications in urban planning, disaster management, and healthcare logistics. The restricted regions can occur randomly or are known in advance. The paper describes a new model for the problem that is based on multicommodity flows with unknown destinations and defined on a discretization of the plane. The model and discretization are applied to both the deterministic and the stochastic continuous restricted location problem, where the latter is converted into a deterministic equivalent problem by minimizing the expected value of the objective function weighted by the probabilities of scenarios. The paper also describes a Benders decomposition algorithm to optimally solve the model. Extensive computational results are presented on both benchmark instances from the literature and new instances, on both the deterministic and stochastic variant of the problem. The results indicate that the proposed algorithm is superior to an off-the-shelf solver in terms of computational time. To the best of the authors’ knowledge, the exact algorithm described here is the first to address both the deterministic and the stochastic variants of continuous restricted location problems with any number of facilities.
0377-2217
851-863
Oguz, Murat
0be6ef56-cf3d-4d4c-9933-61d96a0952c1
Bektas, Tolga
0db10084-e51c-41e5-a3c6-417e0d08dac9
Bennell, Julia A.
38d924bc-c870-4641-9448-1ac8dd663a30
Oguz, Murat
0be6ef56-cf3d-4d4c-9933-61d96a0952c1
Bektas, Tolga
0db10084-e51c-41e5-a3c6-417e0d08dac9
Bennell, Julia A.
38d924bc-c870-4641-9448-1ac8dd663a30

Oguz, Murat, Bektas, Tolga and Bennell, Julia A. (2018) Multicommodity flows and benders decomposition for restricted continuous location problems European Journal of Operational Research, 266, (3), pp. 851-863. (doi:10.1016/j.ejor.2017.11.033).

Record type: Article

Abstract

The restricted continuous facility location problem arises when there is a need to locate a number of facilities to serve a discrete set of demand points, and where the location of a facility can be anywhere on the plane except for in restricted regions. The problem finds applications in urban planning, disaster management, and healthcare logistics. The restricted regions can occur randomly or are known in advance. The paper describes a new model for the problem that is based on multicommodity flows with unknown destinations and defined on a discretization of the plane. The model and discretization are applied to both the deterministic and the stochastic continuous restricted location problem, where the latter is converted into a deterministic equivalent problem by minimizing the expected value of the objective function weighted by the probabilities of scenarios. The paper also describes a Benders decomposition algorithm to optimally solve the model. Extensive computational results are presented on both benchmark instances from the literature and new instances, on both the deterministic and stochastic variant of the problem. The results indicate that the proposed algorithm is superior to an off-the-shelf solver in terms of computational time. To the best of the authors’ knowledge, the exact algorithm described here is the first to address both the deterministic and the stochastic variants of continuous restricted location problems with any number of facilities.

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More information

Accepted/In Press date: 15 November 2017
e-pub ahead of print date: 23 November 2017
Published date: 1 May 2018

Identifiers

Local EPrints ID: 415728
URI: https://eprints.soton.ac.uk/id/eprint/415728
ISSN: 0377-2217
PURE UUID: ea3ad739-0fb3-46b6-89f0-3a0a8479b43a
ORCID for Tolga Bektas: ORCID iD orcid.org/0000-0003-0634-144X

Catalogue record

Date deposited: 21 Nov 2017 17:30
Last modified: 30 Jan 2018 17:32

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