A heap of pieces model for the cyclic job shop problem
Résumé
In classical scheduling, a set of tasks is executed once while the determined schedule
optimizes objective functions such as the makespan or earliness-tardiness. In contrast, cyclic
scheduling means performing a set of generic tasks infinitely often while minimizing the
time between two occurrences of the same task. Cyclic scheduling has several applications,
e.g. in robotic industry (see Kats and Levner [1997]), in manufacturing systems (see Pinedo
[2005] and Hillion and Proth [1989]) or multiprocessor computing (see Hanen and Munier
[1995b]). It has been studied from multiple perspectives, since there exist several possible
representations of the problem such as graph theory, mixed integer linear programming,
Petri nets or (max; +) algebra. An overview about cyclic scheduling problems and the
different approaches can be found in Hanen and Munier [1995a].
However, a less known tool is the heaps of pieces approach. A first paper considering
this modelling for cyclic scheduling is Gaubert and Mairesse [1999]. The authors introduce
a method to represent safe Petri nets as particular automata which compute the height of
heaps of pieces. This approach enables to compute efficiently the throughput of a cyclic
schedule. In this paper, we use the heaps of pieces approach for solving cyclic scheduling
problems with resource constraints.
Domaines
Recherche opérationnelle [math.OC]Origine | Fichiers produits par l'(les) auteur(s) |
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