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dc.contributor.authorAissi, Hassene
dc.contributor.authorAloulou, Mohamed Ali
dc.contributor.authorKovalyov, Mikhail Y.
dc.date.accessioned2010-06-30T13:38:05Z
dc.date.available2010-06-30T13:38:05Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/4508
dc.language.isoenen
dc.subjectSchedulingen
dc.subjectAssignmenten
dc.subjectRobustnessen
dc.subjectMin-max approachen
dc.subjectScenariosen
dc.subjectUncertaintyen
dc.subjectSingle machineen
dc.subject.ddc003en
dc.titleMinimizing the number of late jobs on a single machine under due date uncertaintyen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study the problem of minimizing the number of late jobs on a single machine where job processing times are known precisely and due dates are uncertain. The uncertainty is captured through a set of scenarios. In this environment, an appropriate criterion to select a schedule is to find one with the best worst-case performance, which minimizes the maximum number of late jobs over all scenarios. For a variable number of scenarios and two distinct due dates over all scenarios, the problem is proved NP-hard in the strong sense and non-approximable in pseudo-polynomial time with approximation ratio less than 2. It is polynomially solvable if the number s of scenarios and the number v of distinct due dates over all scenarios are given constants. An O(nlog n) time s-approximation algorithm is suggested for the general case, where n is the number of jobs, and a polynomial 3-approximation algorithm is suggested for the case of unit-time jobs and a constant number of scenarios. Furthermore, an O(n s+v−2/(v−1) v−2) time dynamic programming algorithm is presented for the case of unit-time jobs. The problem with unit-time jobs and the number of late jobs not exceeding a given constant value is solvable in polynomial time by an enumeration algorithm. The obtained results are related to a min-max assignment problem, an exact assignment problem and a multi-agent scheduling problem.en
dc.relation.isversionofjnlnameJournal of Scheduling
dc.relation.isversionofjnlvol14
dc.relation.isversionofjnlissue4
dc.relation.isversionofjnldate2011
dc.relation.isversionofjnlpages351-360
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s10951-010-0183-zen
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelRecherche opérationnelleen


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