The time varying cyclic job shop problem

Abstract : 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.
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Laurent Houssin, Idir Hamaz, Sonia Cafieri. The time varying cyclic job shop problem. International Conference on Project Management and Scheduling (PMS), Apr 2016, Valencia, Spain. 4p. ⟨hal-01335143⟩

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