Petri-Net-Based Scheduling of Flexible Manufacturing Systems Using an Estimate Function

In this paper, a novel admissible estimate function is proposed to schedule flexible manufacturing systems (FMSs) by using heuristic search. The FMSs to be scheduled are modeled by P-timed Petri nets. The problem is to make the system evolve from the initial marking to a given final marking by firing a sequence of transitions. The structure of jobs in an FMS is always symmetrical to utilize the shared resources, but the processing time of each job is asymmetrical to reduce the global process time. By utilizing the structural symmetry of a Petri net model of an FMS, a partial reachability graph is generated such that the notorious state explosion problem is mitigated. For each generated marking, the proposed estimate function is used to provide an estimated cost for firing the transition sequence. Then, we can select the marking with the smallest cost from the generated markings and compute its successors. This process is continued until the system reaches the final marking. With the proposed method, the performance is evaluated in terms of the cost of the obtained transition firing sequence and the number of the expanded markings. The cost provided by the proposed estimate function is closer to the optimal cost than the previous work, i.e., the proposed method can find a transition firing sequence with less expanded markings and minimal process time from a marking to the final marking. Experimental results are used to demonstrate and evaluate the proposed approach.