Abstract
With wafer residency time constraint of cluster tools in semiconductor manufacturing, activity time variation can make an originally feasible schedule infeasible. Thus, it is difficult to schedule them and schedulability is a vitally important issue. With bounded activity time variation considered, this paper addresses their real-time scheduling issues and conducts their schedulability analysis. A Petri net (PN) model and a control policy are presented. Based on them, this paper derives closed-form schedulability conditions. If schedulable, an algorithm is developed to obtain an offline periodic schedule. This schedule together with the control policy forms a real-time schedule. It is optimal in terms of cycle time and can be analytically computed, which represents significant advance in this area.
Note to Practitioners-This paper addresses the scheduling problem of dual-arm cluster tools with wafer residency time constraint and activity time variation. Based on a PN model, schedulability conditions are presented and can be checked analytically. Then, a closed-form solution is proposed to obtain 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. Thus, it is applicable to the scheduling and real-time control of cluster tools in semiconductor plants. The presented concepts and methods can be extended to other robotic systems such as medical testing facility.