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Nouvelles méthodes pour les problèmes d'ordonnancement cyclique

Touria Ben Rahhou 1
1 LAAS-ROC - Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : Research on scheduling has been mobilizing a large number of researchers, this is mainly due to the broad range of application of scheduling problems, among them, there is the problem of tracking multiple workshops, commonly called "JobShop". JobShop problems can often be simplified by considering them as cyclic problems. The tasks scheduling becomes cyclic and its purpose is to organize the production activities by repeating a basic cycle that has been optimized. Many parameters are involved in the optimization of the basic cycle such as the period of the cycle chosen, the order of operations to perform basic work, the duration of these operations, the number of outputs per cycle, etc. Several approaches have been used to solve this problem, among which the approach by Petri nets, especially in timed event graphs, graph approach, linear programming approach and heap of pieces approach. The graph approach allows a graphical representation of the problem as a graph where the nodes represent the different operations and where the arcs illustrate constraints. A cyclic scheduling problem has a feasible solution if and only if it is consistent. This consistency property of a cyclic scheduling problem and its associated graph allows to prune the search tree of the branch-bound procedure proposed for this approach. In the heap of pieces approach, the sub-problem of evaluating a solution can be easily solved. Indeed, by translating the problem into an appropriate mathematical structure, finding the cycle time is equivalent to the calculation of an eigenvalue of a product of matrices where each matrix represents an elementary operation. This property is particularly significant in the case of successive sets of evaluation of many schedules. In addition, the theory allows an intuitive representation of scheduling, since it is illustrated as a stack of several blocks. Several cycles will be symbolized by the stack of piles.
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Touria Ben Rahhou. Nouvelles méthodes pour les problèmes d'ordonnancement cyclique. Automatique / Robotique. Université Paul Sabatier - Toulouse III, 2013. Français. ⟨tel-00926977⟩

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