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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/93276
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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 Técnicas2025-09-29T10:34:45Zoai: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:34982025-09-29 10:34:45.576CONICET 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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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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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1844614364591554560 |
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13.070432 |