An Algorithm for Seeking the Minimal Cost Maximal Flow Based on Petri Net

Abstract

In this paper, Petri net is adopted for seeking the minimal cost maximal flow of a network. The cost Petri net is proposed and the enabled rules of transitions are given. In addition, an algorithm for obtaining the minimal cost maximal flow based on cost Petri net is developed. The proposed algorithm, which is different from the others, is to find the firing sequence of transitions by labeling places and increase flows in this sequence. Finally, an example is given to demonstrate the application of the algorithm. The results show that the given method can find the minimal cost maximal flow of a network efficiently.