Asymptotic optimal state of a generalized time event graph: application to an assembly problem. (Régime asymptotique optimal d’un graphe d’événements temporisé généralisé: application à un problème d’assemblage.) (French) Zbl 0801.90056

Summary: The aim of this paper is to study the optimal behavior of a generalized timed event graph and to apply these results to an assembly system. As there are no conflicts between the firings of the transitions for a generalized timed event graph, their frequencies are maximum for the earliest operational mode. We prove that the resulting schedule is \(K\)- periodic and we propose an algorithm to compute these frequencies. This algorithm is based on a particular decomposition of the set of transitions and on the expansion of its components. We construct a valued graph by contracting these components and we show that the longest paths of that graph provide the maximum values of the frequencies.


90B30 Production models
90B35 Deterministic scheduling theory in operations research