Optimal Scheduling of Multicluster Tools With Constant Robot Moving Times, Part II: Tree-Like Topology Configurations

In this paper, we analyze optimal scheduling of a tree-like multicluster tool with single-blade robots and constant robot moving times. We present a recursive minimal cycle time algorithm to reveal a multi-unit resource cycle for multicluster tools under a given robot schedule. For a serial-cluster tool, we provide a closed-form formulation for the minimal cycle time. The formulation explicitly provides the interaction relationship among clusters. We further present decomposition conditions under which the optimal scheduling of multicluster becomes much easier and straightforward. Optimality conditions for the widely used robot pull schedule are also provided. An example from industry production is used to illustrate the analytical results. The decomposition and optimality conditions for the robot pull schedule are also illustrated by Monte Carlo simulation for the industrial example.