Optimal one-wafer cyclic scheduling analysis of hybrid multi-cluster tools with one-space buffering module

A multi-cluster tool with both single and dual-arm individual cluster tools is called a hybrid multi-cluster tool. To operate it, one needs to coordinate different types of robots for accessing the shared buffering modules. Aiming at finding a one-wafer periodic schedule such that the lower bound of cycle time can be reached, this work studies its scheduling when its bottleneck individual tool is process-bound. With a timed Petri net model, the scheduling problem is reduced to determine the waiting time of robots. Then, the conditions are presented, under which a one-wafer periodic schedule exists such that the lower bound of cycle time can be reached. Based on them, an efficient algorithm is given to check whether such a one-wafer periodic schedule exists. If so, it is found via simple calculation. An example is given to show its effectiveness.