Virtual Cell-Based Scheduling Approach to Single-Robotic-Arm Cluster Tools Subject to Wafer Residency Time Constraints

Scheduling single-robotic-arm cluster tools subject to wafer residency time constraints has received much attention. Compared to some scheduling strategies that use all processing modules (PMs) to process wafers, it is much more challenging to schedule a more general case whose optimal scheduling strategy is not limited to the case of using all PMs. The strategy of only adjusting the robot's waiting time may fail to produce a desired schedule. When a tool using all PMs is not schedulable, it may become schedulable if only some PMs of a type are used. Therefore, it is very important to select an appropriate number of PMs to process wafers. This work studies the cyclic scheduling problem of wafer-residency-time-constrained single-robotic-arm cluster tools by simultaneously adjusting the number of PMs and robot waiting time. We build a virtual cell that includes an appropriate number of PMs to process wafers with the maximal productivity. We establish sufficient and necessary conditions under which the system is schedulable. The schedulability conditions are less conservative than the state-of-the-art one. A polynomial algorithm is developed to find the optimal cyclic schedule, a virtual cell's configuration, and robot waiting time. We illustrate the practicability of the proposed algorithm via several examples, and its superiority over the existing one. Note to Practitioners-This paper addresses the optimal cyclic scheduling problem of wafer-residency-time-constrained single-robotic-arm cluster tools that are used in every wafer fabrication factory. This work for the first time simultaneously adjusts the number of PMs and the robot waiting time given such a cluster tool such that it can be scheduled with the highest productivity. It presents the optimal scheduling method with polynomial complexity. We confirm that the proposed approach can improve schedulability of single-robotic-arm cluster tools over existing methods by using multiple examples. It can thus be readily applied to industrial wafer fabrication.