Noncyclic Scheduling of Multi-Cluster Tools with Residency Constraints Based on Pareto Optimization

Multi-cluster tools are widely used in semiconductor manufacturing. When the lot size of wafers tends to be quite small, a cyclic scheduling strategy is not suitable. However, the noncyclic scheduling of multi-cluster tools is much more challenging due to multi-robot coordination and the increasing number of chambers. This paper focuses on the noncyclic scheduling problem of multi-cluster tools with residency constraints. We construct a universal model to describe such problem to fit both single-armed and dual-armed robots, where serial flow, parallel flow and reentrant flow are all considered. Correspondingly, an improved dynamic programming algorithm is proposed. Specifically, a sequential constraint is first added to deal with the chronological conflicts brought by multi-robot coordination together with a normalization rule to improve searching efficiency. Meanwhile, considering the residency constraints, a path deleting method is also introduced to remove the infeasible solutions. Besides, the theoretical analysis of computation efficiency is also discussed. Numerical experiments demonstrate that the proposed algorithm can meet various practical scheduling requirements, while achieving distinctive improvements in efficiency.