A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems

Autores
Rossit, Daniel Alejandro; Vásquez, Óscar C.; Tohmé, Fernando Abel; Frutos, Mariano; Safe, Martin Dario
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we introduce a novel approach to the combinatorial analysis of flow shop scheduling problems for the case of two jobs, assuming that processing times are unknown. The goal is to determine the dominance properties between permutation flow shop (PFS) and non-permutation flow shop (NPFS) schedules. In order to address this issue we develop a graph-theoretical approach to describe the sets of operations that define the makespan of feasible PFS and NPFS schedules (critical paths). The cardinality of these sets is related to the number of switching machines at which the sequence of the previous operations of the two jobs becomes reversed. This, in turn, allows us to uncover structural and dominance properties between the PFS and NPFS versions of the scheduling problem. We also study the case in which the ratio between the shortest and longest processing times, denoted ρ, is the only information known about those processing times. A combinatorial argument based on ρ leads to the identification of the NPFS schedules that are dominated by PFS ones, restricting the space of feasible solutions to the NPFS problem. We also extend our analysis to the comparison of NPFS schedules (with different number of switching machines). Again, based on the value of ρ, we are able to identify NPFS schedules dominated by other NPFS schedules.
Fil: Rossit, Daniel Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Vásquez, Óscar C.. Universidad de Santiago de Chile; Chile
Fil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Frutos, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentina
Fil: Safe, Martin Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Materia
CRITICAL PATH
MAKESPAN
NON-PERMUTATION FLOW SHOP SCHEDULING PROBLEM
STRUCTURAL AND DOMINANCE PROPERTIES
UNKNOWN PROCESSING TIMES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/93276
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/93276
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A combinatorial analysis of the permutation and non-permutation flow shop scheduling problemsRossit, Daniel AlejandroVásquez, Óscar C.Tohmé, Fernando AbelFrutos, MarianoSafe, Martin DarioCRITICAL PATHMAKESPANNON-PERMUTATION FLOW SHOP SCHEDULING PROBLEMSTRUCTURAL AND DOMINANCE PROPERTIESUNKNOWN PROCESSING TIMEShttps://purl.org/becyt/ford/2.11https://purl.org/becyt/ford/2In this paper we introduce a novel approach to the combinatorial analysis of flow shop scheduling problems for the case of two jobs, assuming that processing times are unknown. The goal is to determine the dominance properties between permutation flow shop (PFS) and non-permutation flow shop (NPFS) schedules. In order to address this issue we develop a graph-theoretical approach to describe the sets of operations that define the makespan of feasible PFS and NPFS schedules (critical paths). The cardinality of these sets is related to the number of switching machines at which the sequence of the previous operations of the two jobs becomes reversed. This, in turn, allows us to uncover structural and dominance properties between the PFS and NPFS versions of the scheduling problem. We also study the case in which the ratio between the shortest and longest processing times, denoted ρ, is the only information known about those processing times. A combinatorial argument based on ρ leads to the identification of the NPFS schedules that are dominated by PFS ones, restricting the space of feasible solutions to the NPFS problem. We also extend our analysis to the comparison of NPFS schedules (with different number of switching machines). Again, based on the value of ρ, we are able to identify NPFS schedules dominated by other NPFS schedules.Fil: Rossit, Daniel Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Vásquez, Óscar C.. Universidad de Santiago de Chile; ChileFil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Frutos, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; ArgentinaFil: Safe, Martin Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaElsevier Science2021-03-30info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/93276Rossit, Daniel Alejandro; Vásquez, Óscar C.; Tohmé, Fernando Abel; Frutos, Mariano; Safe, Martin Dario; A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems; Elsevier Science; European Journal of Operational Research; 289; 3; 30-3-2021; 841-8540377-2217CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0377221719306344info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ejor.2019.07.055info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:07:10Zoai:ri.conicet.gov.ar:11336/93276instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 12:07:10.748CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems
title A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems
spellingShingle A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems
Rossit, Daniel Alejandro
CRITICAL PATH
MAKESPAN
NON-PERMUTATION FLOW SHOP SCHEDULING PROBLEM
STRUCTURAL AND DOMINANCE PROPERTIES
UNKNOWN PROCESSING TIMES
title_short A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems
title_full A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems
title_fullStr A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems
title_full_unstemmed A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems
title_sort A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems
dc.creator.none.fl_str_mv Rossit, Daniel Alejandro
Vásquez, Óscar C.
Tohmé, Fernando Abel
Frutos, Mariano
Safe, Martin Dario
author Rossit, Daniel Alejandro
author_facet Rossit, Daniel Alejandro
Vásquez, Óscar C.
Tohmé, Fernando Abel
Frutos, Mariano
Safe, Martin Dario
author_role author
author2 Vásquez, Óscar C.
Tohmé, Fernando Abel
Frutos, Mariano
Safe, Martin Dario
author2_role author
author
author
author
dc.subject.none.fl_str_mv CRITICAL PATH
MAKESPAN
NON-PERMUTATION FLOW SHOP SCHEDULING PROBLEM
STRUCTURAL AND DOMINANCE PROPERTIES
UNKNOWN PROCESSING TIMES
topic CRITICAL PATH
MAKESPAN
NON-PERMUTATION FLOW SHOP SCHEDULING PROBLEM
STRUCTURAL AND DOMINANCE PROPERTIES
UNKNOWN PROCESSING TIMES
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.11
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv In this paper we introduce a novel approach to the combinatorial analysis of flow shop scheduling problems for the case of two jobs, assuming that processing times are unknown. The goal is to determine the dominance properties between permutation flow shop (PFS) and non-permutation flow shop (NPFS) schedules. In order to address this issue we develop a graph-theoretical approach to describe the sets of operations that define the makespan of feasible PFS and NPFS schedules (critical paths). The cardinality of these sets is related to the number of switching machines at which the sequence of the previous operations of the two jobs becomes reversed. This, in turn, allows us to uncover structural and dominance properties between the PFS and NPFS versions of the scheduling problem. We also study the case in which the ratio between the shortest and longest processing times, denoted ρ, is the only information known about those processing times. A combinatorial argument based on ρ leads to the identification of the NPFS schedules that are dominated by PFS ones, restricting the space of feasible solutions to the NPFS problem. We also extend our analysis to the comparison of NPFS schedules (with different number of switching machines). Again, based on the value of ρ, we are able to identify NPFS schedules dominated by other NPFS schedules.
Fil: Rossit, Daniel Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Vásquez, Óscar C.. Universidad de Santiago de Chile; Chile
Fil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Frutos, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentina
Fil: Safe, Martin Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
description In this paper we introduce a novel approach to the combinatorial analysis of flow shop scheduling problems for the case of two jobs, assuming that processing times are unknown. The goal is to determine the dominance properties between permutation flow shop (PFS) and non-permutation flow shop (NPFS) schedules. In order to address this issue we develop a graph-theoretical approach to describe the sets of operations that define the makespan of feasible PFS and NPFS schedules (critical paths). The cardinality of these sets is related to the number of switching machines at which the sequence of the previous operations of the two jobs becomes reversed. This, in turn, allows us to uncover structural and dominance properties between the PFS and NPFS versions of the scheduling problem. We also study the case in which the ratio between the shortest and longest processing times, denoted ρ, is the only information known about those processing times. A combinatorial argument based on ρ leads to the identification of the NPFS schedules that are dominated by PFS ones, restricting the space of feasible solutions to the NPFS problem. We also extend our analysis to the comparison of NPFS schedules (with different number of switching machines). Again, based on the value of ρ, we are able to identify NPFS schedules dominated by other NPFS schedules.
publishDate 2021
dc.date.none.fl_str_mv 2021-03-30
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/93276
Rossit, Daniel Alejandro; Vásquez, Óscar C.; Tohmé, Fernando Abel; Frutos, Mariano; Safe, Martin Dario; A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems; Elsevier Science; European Journal of Operational Research; 289; 3; 30-3-2021; 841-854
0377-2217
CONICET Digital
CONICET
url http://hdl.handle.net/11336/93276
identifier_str_mv Rossit, Daniel Alejandro; Vásquez, Óscar C.; Tohmé, Fernando Abel; Frutos, Mariano; Safe, Martin Dario; A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems; Elsevier Science; European Journal of Operational Research; 289; 3; 30-3-2021; 841-854
0377-2217
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0377221719306344
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ejor.2019.07.055
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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