Optimal scheduling of dual-armed cluster tools without swap restriction

In a dual-armed cluster tool, the swap operation method that exchanges a wafer on a robot arm with another wafer at a chamber has been mostly used. It is known to minimize the tool cycle time although it restricts the robot task sequence. Recent cluster tools have new scheduling requirements such as reentrant wafer flows for atomic layer deposition processes, constraints on the wafer delay times within chambers after processing, and concurrent processing of different wafer types. The restricted swap operation method may neither minimize the tool cycle time nor satisfy the wafer delay constraints, and even cause a deadlock. We examine new robot task sequences for dual-armed cluster tools that use the two robot arms more flexibly without the swap restriction. We first propose a Petri net modeling method without the swap restriction. From the model, we identify necessary conditions for which deadlocks are prevented. We then systematically develop a mixed integer programming model that determines an optimal robot task sequence. From experiments, we show that deadlock prevention constraints, not required for the model, together with the initial branching rule for a branch and bound procedure reduce the solution space significantly.