Optimization of consuming resource problem based on reachability graph of petri nets

The problem of resource optimization is one of the most important issues in discrete event systems (DES). Assuming that the firing of transition consumes the resource of DES but the place does not, an improved consuming Petri net (ICPN) is proposed to deal with this problem by associating a consuming function with each transition. In order to describe this process and obtain the minimal consuming function, transitions are divided into two subsets T_P (with a positive real number) and T_Z (with a zero number). Based on the reachability graph (RG), an optimal algorithm is presented to compute the optimal resources and the corresponding firing count vector, and an example is also provided to illustrate the validity and efficiency.