摘要： Complex multi-cluster tools have been extensively used in semiconductor manufacturing. It is crucial to increase their productivity by their effective operation. With structural complexity, multiple robots, and the interaction among individual tools, it is very challenging to schedule a tree-like multi-cluster tool. This paper investigates the scheduling problem of such a tool whose bottleneck individual tool is process-bound. The system is modeled by well-known discrete-event models, i.e., resource-oriented Petri nets. Based on the models, for the ?rst time, this work develops necessary and suf?cient conditions under which a one-unit (wafer) periodic schedule exists and shows that an optimal one-unit periodic schedule can always be found. Algorithms with polynomial complexity are presented to ?nd the optimal cycle time and the one-unit periodic schedule. Industrial examples are used to illustrate the proposed method, and they show that a signi?cant reduction in cycle time can be obtained in comparison with the existing method.