Scheduling Dual-Arm Multi-Cluster Tools With Residency Time Constraints Beyond Swap-Based Strategies and Module-Bound Regions

Multi-cluster tools are widely utilized in wafer fabrications. It is of great significance to schedule such tools optimally to improve productivity and ensure wafer quality. However, previous research mainly focuses on scheduling dual-arm multi-cluster tools by adopting swap-based strategies, leaving a gap on other alternative schedules. Additionally, process-bound and transport-bound regions are distinguished for analysis. How to connect both regions is open. This study aims to address such gaps by dealing with more general conditions beyond swap-based strategies and module-bound regions in dual-arm multi-cluster tools with residency time constraints. Based on detailed analysis of operations in the system, specifically more practical positions on the two-arm configuration, a mixed integer linear programming model is formulated to tackle the challenging problem. Furthermore, this model can be directly adopted to single-arm tools by assigning all operations to the same arm, enabling it to schedule all types of dual-arm, single-arm, and hybrid cluster tools in general. In addition, the model is extended to minimize total post-processing time in all process modules. To validate the proposed approach, two illustrative examples which were previously considered unschedulable are tested, conducting the model's efficiency and validity. Furthermore, a sensitivity analysis on transport module times conducts a transition shift between process-bound and transport-bound regions for the first time. Results of randomly generated instances conduct that larger transportation module times correlate with increased computing times.