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Evaluating flexible solutions in single machine scheduling via objective function maximization: the study of a computational complexity

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Date
2007
Indexation documentaire
Recherche opérationnelle
Subject
Scheduling; single machine; maxi- mization problems
Nom de la revue
RAIRO
Volume
41
Numéro
1
Date de publication
2007
Pages article
1-18
Nom de l'éditeur
EDP Sciences
DOI
http://dx.doi.org/10.1051/ro:20070012
URI
https://basepub.dauphine.fr/handle/123456789/2650
Collections
  • LAMSADE : Publications
Métadonnées
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Auteur
Portmann, Marie-Claude
Kovalyov, Mikhail Y.
Aloulou, Mohamed Ali
Type
Article accepté pour publication ou publié
Résumé en anglais
We study a deterministic problem of evaluating the worst case performance of flexible solutions in the single machine scheduling. A flexible solution is a set of schedules following a given structure de- termined by a partial order of jobs and a type of the schedules. In this paper, the schedules of active and non-delay type are considered. A flexible solution can be used on-line to absorb the impact of data disturbances related to, for example, job arrival, tool availability or machine breakdowns. The performance of a flexible solution includes the best case and the worst case performances. The best case perfor- mance is an ideal performance that can be achieved only if the on-line conditions allow to implement the best schedule of the set of schedules characterizing the flexible solution. In contrast, the worst case perfor- mance indicates how poorly the flexible solution may perform when fol- lowing the given structure in the on-line circumstances. The best-case and the worst-case performances are usually evaluated by the minimum and maximum values of the considered objective function, respectively. We present algorithmic and computational complexity results for some maximization scheduling problems. In these problems, the jobs to be scheduled have different release dates and precedence constraints may be given on the set of jobs.

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