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.