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Mixing MIR Inequalities with Two Divisible Coefficients

hal.structure.identifierCentro de Investigação Operacional - Departamento de Estatística e Investigação Operacional [CIO - DEIO]
dc.contributor.authorCONSTANTINO, Miguel
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierReformulations based algorithms for Combinatorial Optimization [Realopt]
dc.contributor.authorMILLER, Andrew
hal.structure.identifierN-Side S.A.
dc.contributor.authorVAN VYVE, Mathieu
dc.date.accessioned2024-04-04T02:38:17Z
dc.date.available2024-04-04T02:38:17Z
dc.date.issued2010
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190862
dc.description.abstractEnThis paper is a polyhedral study of a generalization of the mixing set where two different, divisible coefficients are allowed for the integral variables. Our results generalize earlier work on mixed integer rounding, mixing, and extensions. They also directly apply to applications such as production planning problems involving lower bounds or start-ups on production, when these are modeled as mixed-integer linear programs. We define a new class of valid inequalities and give two proofs that they suffice to describe the convex hull of this mixed-integer set. We give a characterization of each of the maximal faces of the convex hull, as well as a closed form description of its extreme points and rays, and show how to separate over this set in O(n log n). Finally, we give several extended formulations of polynomial size, and study conditions under which adding certain simple constraints on the integer variables preserves our main result.
dc.language.isoen
dc.publisherSpringer
dc.title.enMixing MIR Inequalities with Two Divisible Coefficients
dc.typeArticle de revue
dc.identifier.doi10.1007/s10107-009-0266-9
dc.subject.halInformatique [cs]/Recherche opérationnelle [cs.RO]
bordeaux.journalMathematical Programming, Series A
bordeaux.page451-483
bordeaux.volume123
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00387098
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00387098v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematical%20Programming,%20Series%20A&rft.date=2010&rft.volume=123&rft.spage=451-483&rft.epage=451-483&rft.au=CONSTANTINO,%20Miguel&MILLER,%20Andrew&VAN%20VYVE,%20Mathieu&rft.genre=article


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