Schedulability and Scheduling of Dual-Arm Cluster Tools with Residency Time Constraints Based on Petri Net

Because of residency time constraints for cluster tools, it is very difficult to schedule them. This paper addresses their scheduling issues and conducts their schedulability analysis. A Petri net (PN) model, called resource-oriented PN (ROPN) is developed to model them. Based on it, for the first time, necessary and sufficient conditions under which the system is schedulable are presented. Meanwhile, an algorithm is developed for the scheduling of dual-armed cluster tool. The algorithm finds an optimal periodic schedule analytically if it is schedulable. A method is also presented for the implementation of the obtained cyclic schedule by appropriately controlling the initial transient process. Examples are presented to show the application and power of the theory and algorithm