Cyclic Scheduling of Multi-Cluster Tools Based on Mixed Integer Programming

Multi-cluster tools are automated equipment which is increasingly used in semiconductor manufacturing. The scheduling of multi-cluster tools is much more challenging than single-cluster tools due to multi-robot coordination and increasing chambers. In this paper, we develop a mixed integer programming (MIP) model which manages to formulate the multi-robot coordination for cyclic scheduling of multi-cluster tools. Three reformulations of the model are implemented: 1) linearization; 2) eliminating integer variables; and 3) tightening constraints. The first reformulation is designed to make the MIP model solvable by commercial solvers while the other two are intended for promoting computational efficiency which is critical when chambers increase. The proposed model can meet various practical scheduling requirements such as dual-armed robots, wafer residency time constraints, parallel and reentrant processes in multi-cluster tools. Experimental results demonstrate the efficiency of the proposed method.