A heuristic approach based on the state equations of Petri nets for FMS scheduling

The paper proposes a heuristic method based on the state equations of Petri nets for flexible manufacturing systems (FMSs) scheduling. We formulate the FMS scheduling problem as a transition firing sequence of a timed Petri net, and then generate a partial reachability graph of the net. The net is searched for the goal state, using the solutions, which are firing count vectors, of the state equation to predict the total cost from the initial state through the current state to the goal. The solutions may contain spurious solutions because a firing count loses sequence information. However the optimal solution which is the smallest makespan is always contained in them. If we eliminate the effect of spurious solutions as much as possible, this method can obtain a good near-optimal schedule. Since this heuristic approach exploits the linear characterization of the state equations, we can not only efficiently obtain a good near-optimal solution, but also evaluate the performance of the schedules. On the other hand, memory requirement is an important issue for a scheduling algorithm. If a scheduling algorithm needs a lot of memory, and even if we are able to get optimal solutions, the algorithm is still impractical for large problems. Thus, searching less states in the scheduling procedure corresponds to improving the scheduling efficiency. Therefore, the scheduling algorithm proposed in the paper contains an step to reduce the search space.