Non-Cyclic Scheduling of Single-Armed Cluster Tools for Processing Two Wafer Types

Cluster tools are extensively used for processing wafers in semiconductor manufacturing. To enhance the throughput of cluster tools, concurrent processing of multiple types of wafers has become a popular approach. In practice, due to mass customization and the shrinking of chips’ feature sizes, the lot size of wafers tends to become smaller, leading to more frequent transient and non-cyclic periods. Therefore, the scheduling problem of single-armed cluster tools that concurrently process two types of wafers from start-up to close-down period should be urgently addressed. To do so, a mixed integer programming (MIP) model is established to optimize the release sequence of wafer types and robot task sequence so that the total completion time of the two wafer types can be minimized. Since solving the MIP model for large-sized instances is hard, a two-combined backward sequence (2-CBS) is further proposed. Experimental results show that the 2-CBS can save a significant amount of computing time and increase the total completion time by only 1.09% on average. However, by quickly determining the completion time of each wafer lot, the throughput of cluster tools could be enhanced to some extent, as the idle time caused by the arrival delay of overhead hoist transports can be reduced. Note to Practitioners—When considering the concurrent processing of multiple wafer types, almost all existing studies focus on cyclic scheduling and thus fail to address the growing importance of non-cyclic scenarios. To fill this gap, the present work develops an MIP model to optimize the release sequence of wafer types and robot task sequence such that the total completion time of two wafer types can be minimized. Such a model is efficient for small-sized instances. Meanwhile, a 2-CBS strategy is developed for large-sized instances, which can be solved quickly and results in an increase in the total completion time by only 1.09%, demonstrating its effectiveness and applicability.