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Utilisation d'ordres partiels pour la caractérisation de solution robustes en ordonnancement

Hoang Trung La 1
1 LAAS-MOGISA
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : This work aims at characterizing offline stes of scheduling solutions which aim at providing some flexibility. It belongs to the fields of robust scheduling where one wants to build a schedule which is insensitive, regarding its performances, to unforeseen events which occur during the schedule execution in a disrupted environment. The proposed robust approach is of proactive-reactive type. It is based on the notions of interval structure and of dominant or sufficient conditions regarding the admissibility or optimality of scheduling solutions. This work focuses, in particular, on the proactive phase which aims at anticipating the execution of the schedule by building as soon as possible an organization which is relatively insensitive to disruptions, while possessing some indicators related to the temporal performance. Within this framework, we particularly show the interest of some partial orders, established by using a reduced hypothsis frame. Thses partial orders allow in one hand the determination of the best and the worst performances of the characterized solution set, and in the other hand the calculation of flexibility indicators.
In the first part, the one machine scheduling problem is studied. For this problem, we describe a dominant partial order based on an analysis of particular interval structures. This partial order characterizes a set of solutions having a calculable cardinality. Moreover, the best and the worst performances of this solution set, in term of lateness, can be computed in a polynomial time. Then, two robust scheduling approaches are proposed, which allow either to characterize all optimal sequences contained in the initial dominant set or to find an acceptable flexibility/performance trade-off.
In the second part, we are interested in scheduling problems with several machines. A sufficient partial order is firstly proposed for the two-machine permutation flow shop problem. Then, two algorithms using the results for the one machine problem are presented in order to solve the job shop problem.
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Submitted on : Tuesday, July 12, 2005 - 3:56:25 PM
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Hoang Trung La. Utilisation d'ordres partiels pour la caractérisation de solution robustes en ordonnancement. Automatique / Robotique. INSA de Toulouse, 2005. Français. ⟨tel-00009741⟩

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