Job shop scheduling with petri nets

In job shop scheduling problem (JSSP), deadlock-free design and scheduling optimization are important issues, which are difficult to tackle in the JSSP having multiple shared resources. To deal with these issues, this chapter introduces a modular-based system design method for modeling and optimizing JSSP. Several operators are presented for handling the combination of JSSP modules and resource sharing. For handling deadlock issues with multi-resources sharing, the conditions on "dead transitions" and "circular waiting" are considered. Based on a transitive matrix, deadlock detection and deadlock recovery algorithms are developed in order to get a deadlock-free system. For each operator, the partial schedule and makespan of each module are obtained. The optimal scheduling of JSSP can be derived from these theoretical results step by step. With the modular- based system design method, one cannot only design a correct system model which is live, bounded, reversible, and deadlock-free and terminate properly but also find the optimal scheduling of JSSP in a formal way. For handling large-scale JSSP, the traditional optimization technologies such as genetic algorithm, branch and bound method, hybrid methods, and rule-based methods can be applied together with the modular-based approach in this chapter. Based on the Petri net model, a genetic algorithm is also introduced here.