Optimal scheduling of k-unit production of cluster tools with single-blade robots

The main challenge in scheduling multi-cluster tools in semiconductor manufacturing is the interactions among clusters. These interactions create a k-unit optimal production that do not exist in single-cluster tools. This paper analyzes optimal scheduling of k-unit cycle production of multi-cluster tools with single-blade robots. A resource-based method is used to analytically derive closed-form expressions for the minimal cycle time of a multi-cluster tool. Conditions for decoupling multi-cluster tools and optimality conditions for the widely used pull schedule are also presented. An example from industry production is used to illustrate the derived formula and decoupling conditions.