Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines

Detalhes bibliográficos
Autor(a) principal: Kramer, Arthur Harry Frederico Ribeiro
Data de Publicação: 2019
Outros Autores: Dell’Amico, Mauro, Iori, Manuel
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRN
Texto Completo: https://repositorio.ufrn.br/handle/123456789/31052
Resumo: We consider the problem of scheduling a set of jobs on a set of identical parallel machines, with the aim of minimizing the total weighted completion time. The problem has been solved in the literature with a number of mathematical formulations, some of which require the implementation of tailored branch-and-price methods. In our work, we solve the problem instead by means of new arc-flow formulations, by first representing it on a capacitated network and then invoking a mixed integer linear model with a pseudo-polynomial number of variables and constraints. According to our computational tests, existing formulations from the literature can solve to proven optimality benchmark instances with up to 100 jobs, whereas our most performing arc-flow formulation solves all instances with up to 400 jobs and provides very low gap for larger instances with up to 1000 jobs
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spelling Kramer, Arthur Harry Frederico RibeiroDell’Amico, MauroIori, Manuel2020-12-17T21:29:48Z2020-12-17T21:29:48Z2019-05-16KRAMER, Arthur; DELL'AMICO, Mauro; IORI, Manuel. Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines. European Journal of Operational Research, v. 275, p. 67-79, 2019. Disponível em: https://www.sciencedirect.com/science/article/pii/S0377221718309809?via%3Dihub Acesso em 10 dez 2020. https://doi.org/10.1016/j.ejor.2018.11.039.0377-2217https://repositorio.ufrn.br/handle/123456789/3105210.1016/j.ejor.2018.11.039ElsevierSchedulingArc-flow formulationsParallel machinesWeighted completion timeEnhanced arc-flow formulations to minimize weighted completion time on identical parallel machinesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleWe consider the problem of scheduling a set of jobs on a set of identical parallel machines, with the aim of minimizing the total weighted completion time. The problem has been solved in the literature with a number of mathematical formulations, some of which require the implementation of tailored branch-and-price methods. In our work, we solve the problem instead by means of new arc-flow formulations, by first representing it on a capacitated network and then invoking a mixed integer linear model with a pseudo-polynomial number of variables and constraints. According to our computational tests, existing formulations from the literature can solve to proven optimality benchmark instances with up to 100 jobs, whereas our most performing arc-flow formulation solves all instances with up to 400 jobs and provides very low gap for larger instances with up to 1000 jobsengreponame:Repositório Institucional da UFRNinstname:Universidade Federal do Rio Grande do Norte (UFRN)instacron:UFRNinfo:eu-repo/semantics/openAccessCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8914https://repositorio.ufrn.br/bitstream/123456789/31052/2/license_rdf4d2950bda3d176f570a9f8b328dfbbefMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81484https://repositorio.ufrn.br/bitstream/123456789/31052/3/license.txte9597aa2854d128fd968be5edc8a28d9MD53TEXTEnhancedArc-flowFormulations_Kramer_2019.pdf.txtEnhancedArc-flowFormulations_Kramer_2019.pdf.txtExtracted texttext/plain72634https://repositorio.ufrn.br/bitstream/123456789/31052/4/EnhancedArc-flowFormulations_Kramer_2019.pdf.txt1fee67325ed34ef03c27cd70cb4fb784MD54THUMBNAILEnhancedArc-flowFormulations_Kramer_2019.pdf.jpgEnhancedArc-flowFormulations_Kramer_2019.pdf.jpgGenerated Thumbnailimage/jpeg1744https://repositorio.ufrn.br/bitstream/123456789/31052/5/EnhancedArc-flowFormulations_Kramer_2019.pdf.jpg25932f9a405aad43ff7b547ff82fce3cMD55123456789/310522023-02-03 19:08:23.531oai:https://repositorio.ufrn.br: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Repositório de PublicaçõesPUBhttp://repositorio.ufrn.br/oai/opendoar:2023-02-03T22:08:23Repositório Institucional da UFRN - Universidade Federal do Rio Grande do Norte (UFRN)false
dc.title.pt_BR.fl_str_mv Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines
title Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines
spellingShingle Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines
Kramer, Arthur Harry Frederico Ribeiro
Scheduling
Arc-flow formulations
Parallel machines
Weighted completion time
title_short Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines
title_full Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines
title_fullStr Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines
title_full_unstemmed Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines
title_sort Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines
author Kramer, Arthur Harry Frederico Ribeiro
author_facet Kramer, Arthur Harry Frederico Ribeiro
Dell’Amico, Mauro
Iori, Manuel
author_role author
author2 Dell’Amico, Mauro
Iori, Manuel
author2_role author
author
dc.contributor.author.fl_str_mv Kramer, Arthur Harry Frederico Ribeiro
Dell’Amico, Mauro
Iori, Manuel
dc.subject.por.fl_str_mv Scheduling
Arc-flow formulations
Parallel machines
Weighted completion time
topic Scheduling
Arc-flow formulations
Parallel machines
Weighted completion time
description We consider the problem of scheduling a set of jobs on a set of identical parallel machines, with the aim of minimizing the total weighted completion time. The problem has been solved in the literature with a number of mathematical formulations, some of which require the implementation of tailored branch-and-price methods. In our work, we solve the problem instead by means of new arc-flow formulations, by first representing it on a capacitated network and then invoking a mixed integer linear model with a pseudo-polynomial number of variables and constraints. According to our computational tests, existing formulations from the literature can solve to proven optimality benchmark instances with up to 100 jobs, whereas our most performing arc-flow formulation solves all instances with up to 400 jobs and provides very low gap for larger instances with up to 1000 jobs
publishDate 2019
dc.date.issued.fl_str_mv 2019-05-16
dc.date.accessioned.fl_str_mv 2020-12-17T21:29:48Z
dc.date.available.fl_str_mv 2020-12-17T21:29:48Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.citation.fl_str_mv KRAMER, Arthur; DELL'AMICO, Mauro; IORI, Manuel. Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines. European Journal of Operational Research, v. 275, p. 67-79, 2019. Disponível em: https://www.sciencedirect.com/science/article/pii/S0377221718309809?via%3Dihub Acesso em 10 dez 2020. https://doi.org/10.1016/j.ejor.2018.11.039.
dc.identifier.uri.fl_str_mv https://repositorio.ufrn.br/handle/123456789/31052
dc.identifier.issn.none.fl_str_mv 0377-2217
dc.identifier.doi.none.fl_str_mv 10.1016/j.ejor.2018.11.039
identifier_str_mv KRAMER, Arthur; DELL'AMICO, Mauro; IORI, Manuel. Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines. European Journal of Operational Research, v. 275, p. 67-79, 2019. Disponível em: https://www.sciencedirect.com/science/article/pii/S0377221718309809?via%3Dihub Acesso em 10 dez 2020. https://doi.org/10.1016/j.ejor.2018.11.039.
0377-2217
10.1016/j.ejor.2018.11.039
url https://repositorio.ufrn.br/handle/123456789/31052
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFRN
instname:Universidade Federal do Rio Grande do Norte (UFRN)
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