Abstract
Because of wafer residency time constraints for cluster tools, it is very difficult to schedule them. This paper addresses their scheduling issues and conducts their schedulability and scheduling analysis. A Petri net (PN) model is developed to model them. With this model, to schedule a dual-arm cluster tool with wafer residency time constraints is to determine when and how long the robot should wait for. Based on the model, necessary and sufficient conditions under which the system is schedulable are presented. The conditions can be checked analytically. Meanwhile, an algorithm is developed for the optimal scheduling of dual-arm cluster tools. The algorithm finds an optimal periodic schedule with closed form expressions 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.
Note to Practitioners-Cluster tools are a kind of integrated manufacturing equipment adopted in semiconductor fabrication. With residency time constraints and no intermediate buffer, it is difficult to schedule them. This paper presents a unique Petri net formalism to the problem of scheduling dual-arm cluster tools. Based on this model, schedulability conditions and algorithms for finding an optimal periodic schedule are presented. With the proposed method, schedulability conditions can be checked and the optimal periodic schedule can be found analytically. Thus, it can be applied to solve practical application problems.