Optimal scheduling of time-constrained single-arm cluster tools with wafer revisiting

It is very difficult to schedule a single-arm cluster tool with wafer revisiting such that wafer residency time constraints are satisfied. This paper conducts a study on this challenging problem for a single-arm cluster tool with atomic layer deposition (ALD) process. With a so called p-backward strategy being applied, a Petri net model is developed to describe the dynamic behavior of the system. Based on the model, existence of a feasible schedule is analyzed, schedulability conditions are derived, and a scheduling algorithm is presented if there is a schedule. A schedule is obtained by simply setting the robot waiting time and it is very computationally efficient. The obtained schedule is shown to be optimal. Illustrative examples are given to demonstrate the proposed approach.