Petri Net-Based Efficient Determination of Optimal Schedules for Transport-Dominant Single-Arm Multi-Cluster Tools

It is a great challenge to find an optimal one-wafer cyclic schedule for a single-arm multicluster tool that is widely adopted in semiconductor fabrication. Aiming to tackle this significant problem, an optimal scheduling strategy is determined first for each individual tool under the condition that the bottleneck individual tool is transport-bound. Then, by developing a Petri net model with robot waiting being explicitly described to reveal the properties of the entire system, this paper shows that to schedule such a tool optimally is to allocate the robot waiting time properly. Then, this paper presents the necessary and sufficient conditions for the existence of an optimal one-wafer cyclic schedule. Thereafter, an efficient algorithm is developed to check the given conditions and find such a schedule efficiently if existing. Finally, two industrial examples are used to verify that the proposed method is applicable and effective.