Petri Net Modeling and Decomposition Method for Solving Production Scheduling Problems

Abstract

Considering the need to develop general scheduling problem solver, the recent integration of Petri Nets as modeling tools into effective optimization methods for scheduling problems is very promising. The paper addresses a Petri Net modeling and decomposition method for solving a wide variety of scheduling problems. The scheduling problems are represented as the optimal transition firing sequence problems for timed Petri Nets. The Petri Net is decomposed into several subnets in which each subproblem can be easily solved by Dijkstra' algorithm. The approach is applied to a flowshop scheduling problem. The performance of the proposed algorithm is compared with that of a simulated annealing method.

Petri Net decomposition approach for the simultaneous optimization of task assignment and routing with automated guided vehicles

“…The set of transition can be decomposed into N l + N m subnets consisting of the set of transitions T ui and the set of places P ui satisfying (6)- (8).…”

“…The solution of each subnet is coordinated by the algorithmic procedure. The Petri Net decomposition approach is successfully applied to solve AGVs route planning problems [7], production scheduling problems [8].…”

Decomposition of timed automata for solving scheduling problems

“…The primary difficulty associate with the scheduling of Petri Nets is state explosion. To resolve the problem, several decomposition approach have been studied [5] [6]. Although the Petri Net decomposition approach is useful to reduce state explosion, it is still difficult to create effective Petri Net model for large-scaled systems.…”