On the Consequences of Un-Modeled Dynamics to the Optimality of Schedules in Clustered Photolithography Tools

Abstract

Clustered photography tools (CPTs) are very complex and can substantially influence the throughput of wafer fabrication facilities. Therefore, efficient lot scheduling for CPTs can directly improve fab performance. In this paper, we develop mixed integer linear programs for linear, affine, exit recursion, and flow line models of CPTs to optimize schedules with respect to mean cycle time, makespan, and tardiness. We simulate a true CPT using a flow line and solve the MILPs for other above mentioned, reduced models. Schedules from reduced models are then input into the flow line optimization model in order to evaluate the loss. Using numerical experiments, we show that exit recursion models outperform other models. Under time limits, exit recursion models exhibit at least 6% better performance than flow lines for large problems on cycle time.