Scheduling analysis with resources share using the transitive matrix based on P-invariant

In this paper, we study the scheduling problem with resource constraints using the Petri nets based on the transitive matrix P-invariant. This work focuses on the analysis of a cyclic schedule for the determination of the optimal cycle time and minimization of work-in-process. Especially, this paper deals with product FMS cyclic scheduling problem with each other products using the transitive matrix. The time Petri net slice is applied to analyze this FMS model. We can divide the original system into subsystems using the transitive matrix and permutate these sub-nets for analyzing the optimal scheduling.