Scheduling transient periods of single-armed cluster tools

Semiconductor manufacturing fabs recently tend to reduce the lot size, that is, the number of identical wafers in a lot, because of small lot orders and increased die throughput per wafer due to wafer size increase. Therefore, cluster tools for wafer processing, which mostly repeat identical work cycles, are subject to frequent lot changes. We therefore examine scheduling problems for transient periods of single-armed cluster tools that are scheduled to repeat identical work cycles for a number of identical wafers. We first develop a Petri net model for the tool´s operational behavior including the initial transient periods as well as the steady cycles. We then develop a mixed integer programming model for finding an optimal schedule. We also examine how to adapt the simple backward sequence, which is mostly used for scheduling steady work cycles of single-armed cluster tools, for a transient period. We identify a deadlock-free condition and also propose two efficient heuristic algorithms by modifying the backward sequence. Finally, through computational experiments, we analyze the efficiency of the proposed algorithms.