Abstract
This paper studies the challenging problem of scheduling single-arm multi-cluster tools with wafer residency time constraints. They have a linear topology and their bottleneck tool is process-bound. This work aims to find an optimal one-wafer cyclic schedule. With the Petri net model developed in our previous work and the minimal cycle time for a multi-cluster tool without wafer residency time constraints, it derives the necessary and sufficient schedulability conditions for multi-cluster tools with wafer residency time constraints for the first time. Then, it gives an algorithm to find an optimal one-wafer cyclic schedule if schedulable. This is done by simply setting the robots' waiting time for each tool. Thus, it is very computationally efficient and applicable to practical problems. An example is presented to illustrate the proposed method.