Petri nets for the formulation of aperiodic scheduling problems in FMSs

This paper presents two classes of timed-place Petri net models, symmetrical and asymmetrical nets, for the formulation of aperiodic scheduling problems in flexible manufacturing systems. An asymmetrical net is defined as a net where some part types have alternative operation sequences, while a symmetrical net is defined as a net where each part type has exactly one operation sequence. It is shown that under either of two conditions, these two classes of nets reveal well-behaved properties of boundedness and proper termination. Boundedness implies that the system has no capacity or resource overflow problems. Proper termination means that the system can always reach the goal state from the initial state. In terms of scheduling, this denotes that no matter what the scheduling decisions are made, the system will successfully complete parts of all types.