COMPLEXITY REDUCTION FOR OPTIMIZATION OF DETERMINISTIC TIMED PETRI-NET SCHEDULING BY TRUNCATION

Abstract

Methods of applying Petri nets to model and analyze scheduling problems, with constraints such as precedence relationships and multiple resource allocation, have been available in the literature. Searching for an optimum schedule can be implemented by combining the branch-and-bound technique with the execution of the timed Petri net. The resulting complexity problem in a large Petri net is handled by a truncation technique such that the original large Petri net is divided into several smaller subnets. The complexity involved in the analysis of each subnet individually is greatly reduced. However, as illustrated in this paper, the schedules for the subnets obtained by treating them separately may not lead to an optimal overall schedule for the original Petri net. To circumvent this problem, algorithms are developed that can be used to search for a proper schedule for each subnet such that the combination of these schedules yields an overall optimum schedule for the original timed Petri net. These algorithms are based on the idea of Petri net execution and branch-and-bound with modification. Finally, the practical application of the timed Petri net truncation technique to scheduling problems in manufacturing systems is illustrated by an example of multirobot task scheduling.