Recognizing Finite Repetitive Scheduling Patterns in Manufacturing Systems

Optimization of timing behaviour of manufacturing systems can be regarded as a scheduling problem in which tasks model the various production processes. Typical for many manufacturing systems is that tasks or collections of tasks can be associated with manufacturing entities, which can be structured hierarchically. Execution of production processes for several instances of these entities results in nested finite repetitions, which blows up the size of the task graph that is needed for the specification of the scheduling problem, and, in an even worse way, the number of possible schedules. We present a subclass of UML activity diagrams which is generic for the number of repetitions, and therefore suitable for the compact specification of task graphs for these manufacturing systems. The approach to reduce the complexity of the scheduling problem exploits the repetitive patterns extracted from the activity diagrams. It reduces the original problem to a problem containing some minimal number of identical repetitions, and after scheduling of this much smaller problem the schedule is expanded to the original size. We demonstrate our technique on a real-life example from the semiconductor industry.