K-Wafer Cyclic Sequence for Scheduling of Dual-Armed Cluster Tool with Purge Operation

Efficient scheduling of semiconductor manufacturing equipment, known as cluster tools, is essential for achieving high productivity. Cluster tools process semiconductor wafers using multiple chambers arranged around a central robot. To ensure wafer quality, chambers must be periodically cleaned, interrupting production and complicating the scheduling process. Previous scheduling methods typically process one wafer per robot sequence cycle, 1-wafer cyclic schedule, leading to inefficiencies when multiple chambers operate in parallel. To overcome this limitation, we propose swap(A, z), an advanced scheduling approach extending swap(a, z), which flexibly combines swap and push-and-wait operations within a K-wafer cyclic framework, allowing varied robot task sequences for each wafer cycle over a total of K wafer cycles. We formally prove that swap(A, z) achieves optimality in regions where traditional 1-wafer cyclic methods exhibit inefficiencies in two-parallel-chamber configurations. Experiments based on realistic industry scenarios demonstrate that our method substantially reduces these inefficiencies and consistently delivers near-optimal performance.