Scheduling of a dual-armed cluster tool with two independent robot arms

Most research on cluster tools focuses on dual armed cluster tools with arms fixed in opposite directions and single armed cluster tools. Little research has been done on how novel cluster tool architectures may improve cluster tool performance. In this paper, a design for two independently moving wafer handling robot arms inside a radial configuration cluster tool is proposed. For this architecture, we develop a Petri net model which describes the tool behavior. It is shown that the well-known swap sequence is not unconditionally the optimal sequence. Instead, we identify three dominant types of sequences. The workload concept for cluster tools is extended. With this, conditions for optimality are introduced and optimality is proven. Moreover, we develop a mixed integer programming formulation to determine optimal sequences amongst 1-cyclic schedules for the cases where the conditions for optimality are not satisfied. The MIP formulation can additionally be used to minimize the cycle time with consideration of wafer delay constraints.