Job batching and scheduling for parallel non-identical machines via MILP and Petri nets

This paper presents two modeling approaches for batching and scheduling jobs on parallel non-identical machines. For scheduling of jobs the due dates as a hard restriction and machine dependent processing times are considered. Between each of the jobs a setup may be necessary or not, depending on the predecessor. The setup of the machines is done by a single worker who needs to be scheduled as well, since only he can serve one machine at a time. The objective is to maximize the overall workload of the machines meeting the constraint of the due dates. While the first approach uses mixed integer linear programming to calculate an optimal schedule, the second one uses a simulation, based on colored Petri nets. Both methods are tested and evaluated using illustrative simulation examples.