On gradient estimation of scheduling for multi-cluster tools with general robot moving times

This paper introduces three methods to deriving gradient estimators of system performance of multi-cluster tools. A multi-cluster tool is composed of multiple single cluster tools connected non-cyclically through intermediate buffer modules. Each single cluster has a separate robot for transporting wafers within the cluster and in and out of the cluster. The coordination among these robots poses a challenge in system-performance analysis and optimal scheduling. This paper focuses on two-cluster tools and develops three approaches (formula-based, linear programming-based, and regression-based) for estimating the gradient of the throughput or any activity times with respect to all timing parameters.