Real-Time Scheduling of Single-Arm Cluster Tools Subject to Residency Time Constraints and Bounded Activity Time Variation

It is very challenging to schedule cluster tools subject to wafer residency time constraints and activity time variation. This work develops a Petri net model to describe the system and proposes a two-level real-time scheduling architecture. At the lower level, a real-time control policy is used to offset the activity time variation as much as possible. At the upper level, a periodical off-line schedule is derived under the normal condition. This work presents the schedulability conditions and scheduling algorithms for an off-line schedule. The schedulability conditions can be analytically checked. If they are satisfied, an off-line schedule can be analytically found. The off-line schedule together with a real-time control policy forms the real-time schedule for the system. It is optimal in terms of cycle time minimization. Illustrative examples are given to show the application of the proposed approach. Note to Practitioners-This paper discusses the real-time scheduling problem of single-arm cluster tools with wafer residency time constraints and bounded activity time variation. With a Petri net model, schedulability is analyzed and schedulability conditions are presented by using analytical expressions. Then, an efficient algorithm is proposed to find a periodical schedule if it is schedulable. Such a schedule is optimal in terms of cycle time and can adapt to bounded activity time variation. Therefore, it is applicable to the scheduling and real-time control of cluster tools in semiconductor manufacturing plants.