Branch and bound approach for marking optimization problem of weighted marked graphs

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 (WMG) 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, we present a "branch and bound" approach to solve the marking optimization problem of a WMG.