On the Optimality of One-Unit Cycle Scheduling of Multi-Cluster Tools with Single-Blade Robots

In semiconductor manufacturing, finding an efficient way for scheduling a multi-cluster tool is crucial for productivity improvement and cost reduction. In this paper, we analyze optimal scheduling of multi-cluster tools under a general configuration with non-zero constant transfer robot traveling time. A resource-based method is developed to analyze optimal scheduling of single-cluster tools. Optimality conditions for obtaining minimum one-unit cycle time for multi-cluster tools are established. Under these conditions, it is shown that the optimal one-unit cycle can be achieved by first optimally scheduling each single-cluster tool separately and then combining the schedules to form the optimal schedule for the multi-cluster tool. A polynomial-time algorithm is presented to find the optimal one-unit cycle time and its corresponding schedules for a multi-cluster tool.