Deadlock-free scheduling in flexible manufacturing systems using Petri nets

This paper addresses the deadlock-free scheduling problem in Flexible Manufacturing Systems. An efficient deadlock-free scheduling algorithm was developed, using timed Petri nets, for a class of FMSs called Systems of Sequential Systems with Shared Resources (S⁴R). The algorithm generates a partial reachability graph to find the optimal or near-optimal deadlock-free schedule in terms of the firing sequence of the transitions of the Petri net model. The objective is to minimize the mean flow time (MFT). An efficient truncation technique, based on the siphon concept, has been developed and used to generate the minimum necessary portion of the reachability graph to be searched. It has been shown experimentally that the developed siphon truncation technique enhances the ability to develop deadlock-free schedules of systems with a high number of deadlocks, which cannot be achieved using standard Petri net scheduling approaches. It may be necessary, in some cases, to relax the optimality condition for large FMSs in order to make the search effort reasonable. Hence, a User Control Factor (UCF) was defined and used in the scheduling algorithm. The objective of using the UCF is to achieve an acceptable trade-off between the solution quality and the search effort. Its effect on the MFT and the CPU time has been investigated. Randomly generated examples are used for illustration and comparison. Although the UCF did not affect the mean flow time, it was shown that increasing it reduces the search effort (CPU time) significantly.