Scheduling a cluster tool with wafer residency time constraints is challenging and important in wafer manufacturing. With a backward strategy, the scheduling problem of such single-robot-arm cluster tools is well-studied in the literature. It is much more challenging to schedule a more general case whose optimal scheduling strategy is not limited to the backward one. This work uses a timed Petri net (PN) to model the dynamic behavior of the system and presents a method to determine the optimal scheduling strategy for the system. Based on its PN model and the obtained strategy, it reveals that the key issue to schedule such a tool is to determine when and how long the robot should wait for. Based on this finding, this work establishes for the first time the necessary and sufficient conditions regarding the existence of an optimal and feasible one-wafer cyclic schedule for single-robot-arm cluster tools. It then formulates a computationally efficient linear program to find it if existing, and finally gives industrial examples to show the application and power of the proposed method.

中文翻译：

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通过 Petri 网和线性规划对时间受限的单机械臂集群工具进行建模和优化循环调度

调度具有晶圆驻留时间限制的集群工具在晶圆制造中具有挑战性和重要意义。使用后向策略，此类单机械臂集群工具的调度问题在文献中得到了很好的研究。调度更一般的情况更具挑战性，其最优调度策略不限于后向调度。这项工作使用定时 Petri 网 (PN) 对系统的动态行为进行建模，并提出了一种确定系统最佳调度策略的方法。基于其 PN 模型和获得的策略，它揭示了调度此类工具的关键问题是确定机器人应等待的时间和时间。基于这一发现，这项工作第一次建立了关于单机械臂集群工具存在最优和可行的单晶片循环调度的必要和充分条件。然后它制定了一个计算效率高的线性程序来查找它是否存在，最后给出了工业示例来展示所提出方法的应用和强大。