Solving nonconvex planar location problems by nite dominating sets

It is well-known that some of the classical location problems with polyhedral gauges can be solved in polynomial time by nding a fi nite dominating set, i.e. a finite set of candidates guaranteed to contain at least one optimal location. In this paper it is fi rst established that this result holds...

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Detalhes bibliográficos
Autores: Carrizosa Priego, Emilio José, Hamacher, Horst W., Klein, Rolf, Nickel, Stefan
Formato: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2000
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/49901
Acesso em linha:http://hdl.handle.net/11441/49901
https://doi.org/10.1023/A:1008395305189
Access Level:acceso abierto
Palavra-chave:Continuous location
Polyhedral gauges
Finite dominating sets
Approximation
Sandwich algorithm
Greedy algorithm
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spelling Solving nonconvex planar location problems by nite dominating setsCarrizosa Priego, Emilio JoséHamacher, Horst W.Klein, RolfNickel, StefanContinuous locationPolyhedral gaugesFinite dominating setsApproximationSandwich algorithmGreedy algorithmIt is well-known that some of the classical location problems with polyhedral gauges can be solved in polynomial time by nding a fi nite dominating set, i.e. a finite set of candidates guaranteed to contain at least one optimal location. In this paper it is fi rst established that this result holds for a much larger class of problems than currently considered in the literature. The model for which this result can be proven includes, for instance, location problems with attraction and repulsion, and location-allocation problems. Next, it is shown that the approximation of general gauges by polyhedral ones in the objective function of our general model can be analyzed with regard to the subsequent error in the optimal ob jective value. For the approximation problem two di erent approaches are described, the sandwich procedure and the greedy algorithm. Both of these approaches lead - for fixed e - to polynomial approximation algorithms with accuracy for solving the general model considered in this paper.Dirección General de Enseñanza SuperiorSpringerEstadística e Investigación OperativaFQM329: OptimizaciónDirección General de Enseñanza Superior. España2000info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/49901https://doi.org/10.1023/A:1008395305189reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Global Optimization, 18 (2), 195-210.PB96-1416-C02-02http://download.springer.com/static/pdf/497/art%253A10.1023%252FA%253A1008395305189.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1023%2FA%3A1008395305189&token2=exp=1481282172~acl=%2Fstatic%2Fpdf%2F497%2Fart%25253A10.1023%25252FA%25253A1008395305189.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Farticle%252F10.1023%252FA%253A1008395305189*~hmac=5960aa94077c042ff8b01592890497aa48adad45c2d598493fb02bcb562c8eb6info:eu-repo/semantics/openAccessoai:idus.us.es:11441/499012026-06-17T12:51:07Z
dc.title.none.fl_str_mv Solving nonconvex planar location problems by nite dominating sets
title Solving nonconvex planar location problems by nite dominating sets
spellingShingle Solving nonconvex planar location problems by nite dominating sets
Carrizosa Priego, Emilio José
Continuous location
Polyhedral gauges
Finite dominating sets
Approximation
Sandwich algorithm
Greedy algorithm
title_short Solving nonconvex planar location problems by nite dominating sets
title_full Solving nonconvex planar location problems by nite dominating sets
title_fullStr Solving nonconvex planar location problems by nite dominating sets
title_full_unstemmed Solving nonconvex planar location problems by nite dominating sets
title_sort Solving nonconvex planar location problems by nite dominating sets
dc.creator.none.fl_str_mv Carrizosa Priego, Emilio José
Hamacher, Horst W.
Klein, Rolf
Nickel, Stefan
author Carrizosa Priego, Emilio José
author_facet Carrizosa Priego, Emilio José
Hamacher, Horst W.
Klein, Rolf
Nickel, Stefan
author_role author
author2 Hamacher, Horst W.
Klein, Rolf
Nickel, Stefan
author2_role author
author
author
dc.contributor.none.fl_str_mv Estadística e Investigación Operativa
FQM329: Optimización
Dirección General de Enseñanza Superior. España
dc.subject.none.fl_str_mv Continuous location
Polyhedral gauges
Finite dominating sets
Approximation
Sandwich algorithm
Greedy algorithm
topic Continuous location
Polyhedral gauges
Finite dominating sets
Approximation
Sandwich algorithm
Greedy algorithm
description It is well-known that some of the classical location problems with polyhedral gauges can be solved in polynomial time by nding a fi nite dominating set, i.e. a finite set of candidates guaranteed to contain at least one optimal location. In this paper it is fi rst established that this result holds for a much larger class of problems than currently considered in the literature. The model for which this result can be proven includes, for instance, location problems with attraction and repulsion, and location-allocation problems. Next, it is shown that the approximation of general gauges by polyhedral ones in the objective function of our general model can be analyzed with regard to the subsequent error in the optimal ob jective value. For the approximation problem two di erent approaches are described, the sandwich procedure and the greedy algorithm. Both of these approaches lead - for fixed e - to polynomial approximation algorithms with accuracy for solving the general model considered in this paper.
publishDate 2000
dc.date.none.fl_str_mv 2000
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/49901
https://doi.org/10.1023/A:1008395305189
url http://hdl.handle.net/11441/49901
https://doi.org/10.1023/A:1008395305189
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Global Optimization, 18 (2), 195-210.
PB96-1416-C02-02
http://download.springer.com/static/pdf/497/art%253A10.1023%252FA%253A1008395305189.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1023%2FA%3A1008395305189&token2=exp=1481282172~acl=%2Fstatic%2Fpdf%2F497%2Fart%25253A10.1023%25252FA%25253A1008395305189.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Farticle%252F10.1023%252FA%253A1008395305189*~hmac=5960aa94077c042ff8b01592890497aa48adad45c2d598493fb02bcb562c8eb6
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 Springer
publisher.none.fl_str_mv Springer
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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