Scheduling of single-arm multi-cluster tools to achieve the minimum cycle time

It is very challenging to schedule a multi-cluster tool to maximize its throughput. This work studies its one-wafer optimal periodic schedule. It is found that the key to schedule it is to determine its robots waiting times. A resource-oriented Petri net model is developed for it such that the robot waiting times are well modeled. Based on the model, optimality conditions are derived and the scheduling problem is reduced to the determination of robot waiting times. By the derived conditions, an optimal one-wafer optimal periodic schedule for a multi-cluster tool can be obtained by scheduling its individual cluster tools one by one. Then, a highly efficient algorithm is proposed to compute it for an entire multi-cluster tool.