Scheduling of Petri nets as a multi-objective shortest path problem

Petri nets are widely used for modeling and analysis of discrete event dynamic systems such as complex automated manufacturing systems or cluster tools for semiconductor manufacturing. We define a data structure for noncyclic Petri net scheduling problems and then transform the scheduling problem into an equivalent multi-objective shortest path (MSP) problem in the state transition graph. Solving the MSP problem will find a path which minimizes the completion time for tokens at each subsequence step, and hence when the corresponding resource becomes available or ready for the next task. This will ultimately minimize the firing epoch of the final destination transition, corresponding to the makespan. We extend a label correction algorithm for existing multi-objective shortest path problems to handle the path dependent edge lengths in the graph and dynamic objectives. We then apply the Petri net-based scheduling method to noncyclic cluster tool scheduling problems. We demonstrate the efficiency of the scheduling method as compared to a branch and bound method.