The single-item lot-sizing polytope with continuous start-up costs and uniform production capacity

Autores
Escalante, Mariana Silvina; Marenco, Javier; Varaldo, Maria del Carmen
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this work we consider the uniform capacitated single-item single-machine lot-sizing problem with continuous start-up costs. A continuous start-up cost is generated in a period whenever there is a nonzero production in the period and the production capacity in the previous period is not saturated. This concept of start-up does not correspond to the standard (discrete) start-up considered in previous models, thus motivating a polyhedral study of this problem. In this work we explore a natural integer programming formulation for this problem. We consider the polytope obtained as convex hull of the feasible points in this problem. We state some general properties, study whether the model constraints define facets, and present an exponentially-sized family of valid inequalities for it. We analyze the structure of the extreme points of this convex hull, their adjacency and bounds for the polytope diameter. Finally, we study the particular case when the demands are high enough in order to require production in all the periods. We provide a complete description of the convex hull of feasible solutions in this case and show that all the inequalities in this description are separable in polynomial time, thus proving its polynomial time solvability.
Fil: Escalante, Mariana Silvina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Cientifico Tecnológico Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Cs.exactas Ingenieria y Agrimensura. Escuela de Cs.exactas y Naturales. Departamento de Matematica; Argentina
Fil: Marenco, Javier. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Varaldo, Maria del Carmen. Universidad Nacional de Rosario. Facultad de Cs.exactas Ingenieria y Agrimensura. Escuela de Cs.exactas y Naturales. Departamento de Matematica; Argentina
Materia
Lot-Sizing
Continuous Start-Up
Polyhedral Combinatorics
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/13341
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The single-item lot-sizing polytope with continuous start-up costs and uniform production capacityEscalante, Mariana SilvinaMarenco, JavierVaraldo, Maria del CarmenLot-SizingContinuous Start-UpPolyhedral Combinatoricshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this work we consider the uniform capacitated single-item single-machine lot-sizing problem with continuous start-up costs. A continuous start-up cost is generated in a period whenever there is a nonzero production in the period and the production capacity in the previous period is not saturated. This concept of start-up does not correspond to the standard (discrete) start-up considered in previous models, thus motivating a polyhedral study of this problem. In this work we explore a natural integer programming formulation for this problem. We consider the polytope obtained as convex hull of the feasible points in this problem. We state some general properties, study whether the model constraints define facets, and present an exponentially-sized family of valid inequalities for it. We analyze the structure of the extreme points of this convex hull, their adjacency and bounds for the polytope diameter. Finally, we study the particular case when the demands are high enough in order to require production in all the periods. We provide a complete description of the convex hull of feasible solutions in this case and show that all the inequalities in this description are separable in polynomial time, thus proving its polynomial time solvability.Fil: Escalante, Mariana Silvina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Cientifico Tecnológico Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Cs.exactas Ingenieria y Agrimensura. Escuela de Cs.exactas y Naturales. Departamento de Matematica; ArgentinaFil: Marenco, Javier. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Varaldo, Maria del Carmen. Universidad Nacional de Rosario. Facultad de Cs.exactas Ingenieria y Agrimensura. Escuela de Cs.exactas y Naturales. Departamento de Matematica; ArgentinaSpringer2015-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/13341Escalante, Mariana Silvina; Marenco, Javier; Varaldo, Maria del Carmen; The single-item lot-sizing polytope with continuous start-up costs and uniform production capacity; Springer; Annals Of Operations Research; 235; 1; 12-2015; 233–2580254-53301572-9338enginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10479-015-1915-4info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs10479-015-1915-4info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:07:13Zoai:ri.conicet.gov.ar:11336/13341instacron: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:34982025-09-03 10:07:13.562CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The single-item lot-sizing polytope with continuous start-up costs and uniform production capacity
title The single-item lot-sizing polytope with continuous start-up costs and uniform production capacity
spellingShingle The single-item lot-sizing polytope with continuous start-up costs and uniform production capacity
Escalante, Mariana Silvina
Lot-Sizing
Continuous Start-Up
Polyhedral Combinatorics
title_short The single-item lot-sizing polytope with continuous start-up costs and uniform production capacity
title_full The single-item lot-sizing polytope with continuous start-up costs and uniform production capacity
title_fullStr The single-item lot-sizing polytope with continuous start-up costs and uniform production capacity
title_full_unstemmed The single-item lot-sizing polytope with continuous start-up costs and uniform production capacity
title_sort The single-item lot-sizing polytope with continuous start-up costs and uniform production capacity
dc.creator.none.fl_str_mv Escalante, Mariana Silvina
Marenco, Javier
Varaldo, Maria del Carmen
author Escalante, Mariana Silvina
author_facet Escalante, Mariana Silvina
Marenco, Javier
Varaldo, Maria del Carmen
author_role author
author2 Marenco, Javier
Varaldo, Maria del Carmen
author2_role author
author
dc.subject.none.fl_str_mv Lot-Sizing
Continuous Start-Up
Polyhedral Combinatorics
topic Lot-Sizing
Continuous Start-Up
Polyhedral Combinatorics
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this work we consider the uniform capacitated single-item single-machine lot-sizing problem with continuous start-up costs. A continuous start-up cost is generated in a period whenever there is a nonzero production in the period and the production capacity in the previous period is not saturated. This concept of start-up does not correspond to the standard (discrete) start-up considered in previous models, thus motivating a polyhedral study of this problem. In this work we explore a natural integer programming formulation for this problem. We consider the polytope obtained as convex hull of the feasible points in this problem. We state some general properties, study whether the model constraints define facets, and present an exponentially-sized family of valid inequalities for it. We analyze the structure of the extreme points of this convex hull, their adjacency and bounds for the polytope diameter. Finally, we study the particular case when the demands are high enough in order to require production in all the periods. We provide a complete description of the convex hull of feasible solutions in this case and show that all the inequalities in this description are separable in polynomial time, thus proving its polynomial time solvability.
Fil: Escalante, Mariana Silvina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Cientifico Tecnológico Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Cs.exactas Ingenieria y Agrimensura. Escuela de Cs.exactas y Naturales. Departamento de Matematica; Argentina
Fil: Marenco, Javier. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Varaldo, Maria del Carmen. Universidad Nacional de Rosario. Facultad de Cs.exactas Ingenieria y Agrimensura. Escuela de Cs.exactas y Naturales. Departamento de Matematica; Argentina
description In this work we consider the uniform capacitated single-item single-machine lot-sizing problem with continuous start-up costs. A continuous start-up cost is generated in a period whenever there is a nonzero production in the period and the production capacity in the previous period is not saturated. This concept of start-up does not correspond to the standard (discrete) start-up considered in previous models, thus motivating a polyhedral study of this problem. In this work we explore a natural integer programming formulation for this problem. We consider the polytope obtained as convex hull of the feasible points in this problem. We state some general properties, study whether the model constraints define facets, and present an exponentially-sized family of valid inequalities for it. We analyze the structure of the extreme points of this convex hull, their adjacency and bounds for the polytope diameter. Finally, we study the particular case when the demands are high enough in order to require production in all the periods. We provide a complete description of the convex hull of feasible solutions in this case and show that all the inequalities in this description are separable in polynomial time, thus proving its polynomial time solvability.
publishDate 2015
dc.date.none.fl_str_mv 2015-12
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/11336/13341
Escalante, Mariana Silvina; Marenco, Javier; Varaldo, Maria del Carmen; The single-item lot-sizing polytope with continuous start-up costs and uniform production capacity; Springer; Annals Of Operations Research; 235; 1; 12-2015; 233–258
0254-5330
1572-9338
url http://hdl.handle.net/11336/13341
identifier_str_mv Escalante, Mariana Silvina; Marenco, Javier; Varaldo, Maria del Carmen; The single-item lot-sizing polytope with continuous start-up costs and uniform production capacity; Springer; Annals Of Operations Research; 235; 1; 12-2015; 233–258
0254-5330
1572-9338
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s10479-015-1915-4
info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs10479-015-1915-4
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
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: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 13.13397

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