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dc.contributor.authorGabrel, Virginieen_US
dc.contributor.authorMurat, Cécileen_US
dc.date.accessioned2009-12-15T09:19:11Z
dc.date.available2009-12-15T09:19:11Z
dc.date.issued2010en_US
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/2699
dc.descriptionLa version attachée est une version française (Note de recherche du LAMSADE n° 41)
dc.language.isoenen_US
dc.subjectprogrammation linéaire
dc.subjectsecond membre incertain
dc.subjectrobustesse
dc.subjectcritère du pire cas
dc.subjectcritère du regret maximum
dc.subject.ddc003
dc.titleRobustness and duality in linear programmingen_US
dc.typeArticle accepté pour publication ou publiéen_US
dc.description.abstractenIn this paper, we consider a linear program in which the right hand sides of the constraints are uncertain and inaccurate. This uncertainty is represented by intervals, that is to say that each right hand side can take any value in its interval regardless of other constraints. The problem is then to determine a robust solution, which is satisfactory for all possible coefficient values. Classical criteria, such as the worst case and the maximum regret, are applied to define different robust versions of the initial linear program. More recently, Bertsimas and Sim have proposed a new model that generalizes the worst case criterion. The subject of this paper is to establish the relationships between linear programs with uncertain right hand sides and linear programs with uncertain objective function coefficients using the classical duality theory. We show that the transfer of the uncertainty from the right hand sides to the objective function coefficients is possible by establishing new duality relations. When the right hand sides are approximated by intervals, we also propose an extension of the Bertsimas and Sim's model and we show that the maximum regret criterion is equivalent to the worst case criterion.
dc.relation.isversionofjnlnameThe Journal of the Operational Research Society
dc.relation.isversionofjnlvol61
dc.relation.isversionofjnldate2010-08en_US
dc.relation.isversionofjnlpages1288-1296
dc.relation.isversionofdoihttp://dx.doi.org/10.1057/jors.2009.81
dc.relation.isversionofjnlpublisherPalgrave Macmillan
dc.subject.ddclabelRecherche opérationnelle


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