Modeling and schedulability analysis of single-arm multi-cluster tools with residency time constraints via Petri nets

This work investigates the challenging problem of scheduling single-arm multi-cluster tools with wafer residency time constraints. They have linear topology and their bottleneck tool is process-bound. This work aims to find an optimal one-wafer cyclic schedule. With a prior developed Petri net model and the minimal cycle time for a multi-cluster tool without wafer residency time constraints, it derives the necessary and sufficient schedulability conditions. Then, it gives an algorithm to find an optimal one-wafer cyclic schedule if schedulable. Such a schedule is found by simply setting the robots' waiting time for each tool. Thus, it is very efficient and can be used to solve practical problems. Examples are presented to illustrate the applications of the proposed methods.