Minimizing Place Capacities of Weighted Event Graphs for Enforcing Liveness
Discrete Event Dynamic Systems
Complexity results for Weighted Timed Event Graphs
Discrete Optimization
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Cyclic manufacturing systems can be modeled by marked graphs, which are an elementary class of Petri nets. To model systems with bulk services and arrivals and to reduce the size of the model, weighted marked graphs can be used. An important step when designing these systems is the definition of the number of manufacturing resources to be used in order to reach a given productivity. In terms of timed Petri nets, this is known as the marking optimization problem and consists of reaching a given average cycle time while minimizing a linear combination of markings. In this paper, a necessary and sufficient condition to obtain a feasible solution of the marking optimization problem of weighted marked graphs with deterministic times is established. A fast heuristic solution, based on an iterative process and using simulation, is given. An example and an application to manufacturing systems are presented.