Scheduling analysis of FMS: An unfolding timed Petri nets approach

We are interested in Flexible Manufacturing Systems (FMS) scheduling problem. Different methods have been explored to solve this problem and mainly to master its combinatorial complexity: NP-hard in the general case. This paper presents an analysis of the cyclic scheduling for the determination of the optimal cycle time and the minimization of the Work In Process (WIP). Especially, the product ratio-driven FMS cyclic scheduling problem using timed Petri nets (TPN) unfolding is described. In addition, it has been proved that the Basic Unit of Concurrency (BUC) is a set of the executed control flows based on the behavioral properties of the net. Using our method, one could divide original system into some subnets based on machine's operations using BUC and analyze the feasibility time in each schedule. Herein, our results showed the usefulness of transitive matrix to slice off some subnets from the original net, and explained in an example.