The mixed general routing polyhedron

[EN] In Arc Routing Problems, ARPs, the aim is to find on a graph a minimum cost traversal satisfying some conditions related to the links of the graph. Due to restrictions to traverse some streets in a specified way, most applications of ARPs must be modeled with a mixed graph. Although several exa...

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Autores: Corberán, Angel, Romero Rozalén, Antonio, Sanchís Llopis, José María|||0000-0002-0039-8122
Formato: artículo
Fecha de publicación:2003
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/100415
Acesso em linha:https://riunet.upv.es/handle/10251/100415
Access Level:acceso abierto
Palavra-chave:Polyhedral combinatorics
Facets
routing
Arc Routing
Rural Postman Problem
General Routing Problem
Mixed Chinese Postman Problem
MATEMATICA APLICADA
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spelling The mixed general routing polyhedronCorberán, AngelRomero Rozalén, AntonioSanchís Llopis, José María|||0000-0002-0039-8122Polyhedral combinatoricsFacetsroutingArc RoutingRural Postman ProblemGeneral Routing ProblemMixed Chinese Postman ProblemMATEMATICA APLICADA[EN] In Arc Routing Problems, ARPs, the aim is to find on a graph a minimum cost traversal satisfying some conditions related to the links of the graph. Due to restrictions to traverse some streets in a specified way, most applications of ARPs must be modeled with a mixed graph. Although several exact algorithms have been proposed, no polyhedral investigations have been done for ARPs on a mixed graph. In this paper we deal with the Mixed General Routing Problem which consists of finding a minimum cost traversal of a given link subset and a given vertex subset of a mixed graph. A formulation is given that uses only one variable for each link (edge or arc) of the graph. Some properties of the associated polyhedron and some large families of facet-inducing inequalities are described. A preliminary cutting-plane algorithm has produced very good lower bounds over a set of 100 randomly generated instances of the Mixed Rural Postman Problem. Finally, applications of this study to other known routing problems are described.The authors wish to thank the Ministerio de Innovación y Ciencia/FEDER of Spain (projects MTM2009-14039-C06-02, MTM2010-19576-C02-02 and DE2009-0057) and Junta de Andalucía/FEDER (grant number FQM-5849) for its support. They also thank two anonymous referees for their careful reading of the manuscript and for their many suggestions and comments that have helped to improve the contents and readability of the paper.Springer-VerlagDepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería IndustrialMinisterio de Ciencia e InnovaciónEuropean Regional Development FundJunta de AndalucíaRepositorio Institucional de la Universitat Politècnica de València Riunet20032003-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/100415reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2009-14039-C06-02 Modelos Y Metodos De Programacion Matematica Y Sus Aplicaciones (Optimos2)Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2010-19576-C02-02 DISEÑO OPTIMO EN REDES LOGISTICASMinisterio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 DE2009-0057 DE2009-0057Juanta de Andalucía Juanta de Andalucía FQM-5849open accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1004152026-06-13T07:49:27Z
dc.title.none.fl_str_mv The mixed general routing polyhedron
title The mixed general routing polyhedron
spellingShingle The mixed general routing polyhedron
Corberán, Angel
Polyhedral combinatorics
Facets
routing
Arc Routing
Rural Postman Problem
General Routing Problem
Mixed Chinese Postman Problem
MATEMATICA APLICADA
title_short The mixed general routing polyhedron
title_full The mixed general routing polyhedron
title_fullStr The mixed general routing polyhedron
title_full_unstemmed The mixed general routing polyhedron
title_sort The mixed general routing polyhedron
dc.creator.none.fl_str_mv Corberán, Angel
Romero Rozalén, Antonio
Sanchís Llopis, José María|||0000-0002-0039-8122
author Corberán, Angel
author_facet Corberán, Angel
Romero Rozalén, Antonio
Sanchís Llopis, José María|||0000-0002-0039-8122
author_role author
author2 Romero Rozalén, Antonio
Sanchís Llopis, José María|||0000-0002-0039-8122
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería Industrial
Ministerio de Ciencia e Innovación
European Regional Development Fund
Junta de Andalucía
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Polyhedral combinatorics
Facets
routing
Arc Routing
Rural Postman Problem
General Routing Problem
Mixed Chinese Postman Problem
MATEMATICA APLICADA
topic Polyhedral combinatorics
Facets
routing
Arc Routing
Rural Postman Problem
General Routing Problem
Mixed Chinese Postman Problem
MATEMATICA APLICADA
description [EN] In Arc Routing Problems, ARPs, the aim is to find on a graph a minimum cost traversal satisfying some conditions related to the links of the graph. Due to restrictions to traverse some streets in a specified way, most applications of ARPs must be modeled with a mixed graph. Although several exact algorithms have been proposed, no polyhedral investigations have been done for ARPs on a mixed graph. In this paper we deal with the Mixed General Routing Problem which consists of finding a minimum cost traversal of a given link subset and a given vertex subset of a mixed graph. A formulation is given that uses only one variable for each link (edge or arc) of the graph. Some properties of the associated polyhedron and some large families of facet-inducing inequalities are described. A preliminary cutting-plane algorithm has produced very good lower bounds over a set of 100 randomly generated instances of the Mixed Rural Postman Problem. Finally, applications of this study to other known routing problems are described.
publishDate 2003
dc.date.none.fl_str_mv 2003
2003-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/100415
url https://riunet.upv.es/handle/10251/100415
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2009-14039-C06-02 Modelos Y Metodos De Programacion Matematica Y Sus Aplicaciones (Optimos2)
Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2010-19576-C02-02 DISEÑO OPTIMO EN REDES LOGISTICAS
Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 DE2009-0057 DE2009-0057
Juanta de Andalucía Juanta de Andalucía FQM-5849
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer-Verlag
publisher.none.fl_str_mv Springer-Verlag
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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