The time varying 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, in manufacturing systems or multiprocessor computing. 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] and [Brucker and Kampmeyer, 2008]. However, few
works have tackled the robust version of this problem although the literature for robust
classical scheduling problem is large. In this paper, we consider a subset of tasks that
have variable processing times. Besides, the minimum processing time and the maximum
processing time of these tasks are known. We propose a method that finds the schedule
which minimizes the expected cycle time. We show that the evaluation of a schedule can be
considered as a volume calculus of polyhedron. More precisely, for each schedule we derive a
set of polyhedron and the integral calculus (based on the Vinci library [Bueler et al., 2000])
of their volume leads to an evaluation of the performance of the considered schedule. This
approach enables to derive a branch and bound procedure to choose the best schedule in
the sense of the smallest cycle time with respect to the variability of the processing times.
Domaines
Recherche opérationnelle [math.OC]Origine | Fichiers produits par l'(les) auteur(s) |
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