Optimal scheduling of transient cycles for single-armed cluster tools

Cluster tools, widely used for wafer fabrication processes, have complex scheduling problems because a tool consists of several single-wafer processing chambers and a robot, and has a number of scheduling constraints. Most scheduling studies on cluster tools have focused on steady cyclic cycles where identical work cycles are repeated. However, as the lot size tends to be smaller, a tool has longer noncyclic operation cycles such as the start-up and the close-down. Therefore, we examine a way of scheduling for noncyclic cycles of single-armed cluster tools so as to minimize the makespan. To do this, we first analyse fundamental properties of tool behaviours including noncyclic transient cycles. Using the properties, we identify the workload of processing a lot with a number of wafers. Then, we develop the condition for which the conventional backward sequence, which is known to be optimal for cyclic work cycles, has the optimal makespan. Finally, we develop a linear programming model to find the minimum makespan of the backward sequence.