Efficient scheduling method based on an assignment model for robotized cluster tools

A cluster tool consists of several wafer processing modules and material handling robot(s). Cluster tools are being prevalently used for semiconductor manufacturing. The scheduling problem is complicated due to no intermediate buffer and diverse wafer flow patterns. We examine the scheduling problem when operations are repetitively performed in a cyclic order. We propose a way of modeling a Petri net for cluster tool operation. By examining the Petri net model, we develop a mixed integer programming model as a version of well-known assignment problem for determining a deadlock-free optimal schedule that maximizes the throughput rate. By using well-known efficient algorithms for assignment problems, we efficiently compute an optimal schedule for dual-armed or single-armed cluster tools, cluster tools with reentrant wafer flows and cyclic cleaning operations.