Marking optimization of weighted marked graphs

Addresses the marking optimization problem of a weighted marked graph (WMG) with deterministic times. The goal is to reach a given productivity while minimizing the number of transportation resources. In terms of timed Petri nets, this problem consists of reaching a given average cycle time while minimizing a linear combination of markings. To limit the size of the model, we use strongly connected WMG. We establish a necessary and sufficient condition to obtain a feasible solution of the problem. A fast heuristic solution, based on iterative process and using simulation, is given. An example and an application to manufacturing systems are presented.