Cluster tools that integrate several single wafer processing modules with a wafer handling robot have been increasingly used for semiconductor manufacturing. Scheduling steady state operation of a cluster tool has been widely studied. We examine the scheduling problems for transient periods of cluster tool operation, start-up and close-down. The transient periods and wafer residency times within processing chambers should be minimized. We prove that for a given steady state schedule, the earliest starting policy that starts each operation as soon as the preceding operations complete is optimal for the close-down period. We also show that by a kind of duality relationship, the lastest starting policy is optimal for the start-up period. We also suggest a way of improving the steady state schedule so that the total makespan is minimized.
