Using timed Petri nets for the scheduling of job-shop systems

In this paper, the authors study the job-shop problem with repetitive demands in steady state. The control is given by the sequencing of the jobs on the machines. Petri nets are used to model and evaluate the system. The authors prove that it is possible to utilize fully the bottleneck machine(s) whatever the sequencing of the jobs on the machines may be. The number of transportation resources used to reach the maximal production depends on the sequencing of the jobs on the machines. The authors suggest an algorithm to give the optimal set of sequences, i.e. the set which provides the maximal productivity with the minimal number of transportation resources.