The Single Period Coverage Facility Location Problem: Lagrangean heuristic and column generation approaches

In this paper we introduce the Single Period Coverage Facility Location Problem. It is a multi-period discrete location problem in which each customer is serviced in exactly one period of the planning horizon. The locational decisions are made independently for each period, so that the facilities th...

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Authors: Albareda Sambola, María, Fernández Aréizaga, Elena, Hinojosa Bergillos, Yolanda, Puerto Albandoz, Justo
Format: article
Status:Published version
Publication Date:2010
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/83316
Online Access:https://hdl.handle.net/11441/83316
Access Level:Open access
Keyword:Discrete facility location
Multi-period location
Lagrangean heuristic
Column generation
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spelling The Single Period Coverage Facility Location Problem: Lagrangean heuristic and column generation approachesAlbareda Sambola, MaríaFernández Aréizaga, ElenaHinojosa Bergillos, YolandaPuerto Albandoz, JustoDiscrete facility locationMulti-period locationLagrangean heuristicColumn generationIn this paper we introduce the Single Period Coverage Facility Location Problem. It is a multi-period discrete location problem in which each customer is serviced in exactly one period of the planning horizon. The locational decisions are made independently for each period, so that the facilities that are open need not be the same in different time periods. It is also assumed that at each period there is a minimum number of customers that can be assigned to the facilities that are open. The decisions to be made include not only the facilities to open at each time period and the time period in which each customer will be served, but also the allocation of customers to open facilities in their service period. We propose two alternative formulations that use different sets of decision variables. We prove that in the first formulation the coefficient matrix of the allocation subproblem that results when fixing the facilities to open at each time period is totally unimodular. On the other hand, we also show that the pricing problem of the second model can be solved by inspection. We prove that a Lagrangean relaxation of the first one yields the same lower bound as the LP relaxation of the second one. While the Lagrangean dual can be solved with a classical subgradient optimization algorithm, the LP relaxation requires the use of column generation, given the large number of variables of the second model. We compare the computational burden for obtaining this lower bound through both models.Sociedad Española de Estadística e Investigación OperativaEconomía Aplicada I2010info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/83316reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)Inglésinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/833162026-06-17T12:51:07Z
dc.title.none.fl_str_mv The Single Period Coverage Facility Location Problem: Lagrangean heuristic and column generation approaches
title The Single Period Coverage Facility Location Problem: Lagrangean heuristic and column generation approaches
spellingShingle The Single Period Coverage Facility Location Problem: Lagrangean heuristic and column generation approaches
Albareda Sambola, María
Discrete facility location
Multi-period location
Lagrangean heuristic
Column generation
title_short The Single Period Coverage Facility Location Problem: Lagrangean heuristic and column generation approaches
title_full The Single Period Coverage Facility Location Problem: Lagrangean heuristic and column generation approaches
title_fullStr The Single Period Coverage Facility Location Problem: Lagrangean heuristic and column generation approaches
title_full_unstemmed The Single Period Coverage Facility Location Problem: Lagrangean heuristic and column generation approaches
title_sort The Single Period Coverage Facility Location Problem: Lagrangean heuristic and column generation approaches
dc.creator.none.fl_str_mv Albareda Sambola, María
Fernández Aréizaga, Elena
Hinojosa Bergillos, Yolanda
Puerto Albandoz, Justo
author Albareda Sambola, María
author_facet Albareda Sambola, María
Fernández Aréizaga, Elena
Hinojosa Bergillos, Yolanda
Puerto Albandoz, Justo
author_role author
author2 Fernández Aréizaga, Elena
Hinojosa Bergillos, Yolanda
Puerto Albandoz, Justo
author2_role author
author
author
dc.contributor.none.fl_str_mv Economía Aplicada I
dc.subject.none.fl_str_mv Discrete facility location
Multi-period location
Lagrangean heuristic
Column generation
topic Discrete facility location
Multi-period location
Lagrangean heuristic
Column generation
description In this paper we introduce the Single Period Coverage Facility Location Problem. It is a multi-period discrete location problem in which each customer is serviced in exactly one period of the planning horizon. The locational decisions are made independently for each period, so that the facilities that are open need not be the same in different time periods. It is also assumed that at each period there is a minimum number of customers that can be assigned to the facilities that are open. The decisions to be made include not only the facilities to open at each time period and the time period in which each customer will be served, but also the allocation of customers to open facilities in their service period. We propose two alternative formulations that use different sets of decision variables. We prove that in the first formulation the coefficient matrix of the allocation subproblem that results when fixing the facilities to open at each time period is totally unimodular. On the other hand, we also show that the pricing problem of the second model can be solved by inspection. We prove that a Lagrangean relaxation of the first one yields the same lower bound as the LP relaxation of the second one. While the Lagrangean dual can be solved with a classical subgradient optimization algorithm, the LP relaxation requires the use of column generation, given the large number of variables of the second model. We compare the computational burden for obtaining this lower bound through both models.
publishDate 2010
dc.date.none.fl_str_mv 2010
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/83316
url https://hdl.handle.net/11441/83316
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Sociedad Española de Estadística e Investigación Operativa
publisher.none.fl_str_mv Sociedad Española de Estadística e Investigación Operativa
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
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score 15,301629

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