Cyclic scheduling of cluster tools with non-identical chamber access times

Most cluster tool scheduling studies assume identical access times between chambers, or do not discuss impact of the access times although the optimal scheduling rule and the cycle time can depend on the access times or physical configuration of parallel chambers. We examine cyclic scheduling problems for cluster tools that have non-identical access times. We first develop Petri net models of tool behaviors and analyze the cycle time by identifying the workloads of the process steps. We prove that the conventional backward and swap sequencing strategies are still optimal for a single-armed and a dual-armed cluster tools, respectively, when a process step is the bottleneck and the tool repeats a minimal cyclic work cycle. We also present a closed form formula for the cycle time and identify a co-prime condition on the number of parallel chambers for which the cycle time is independent of the order of using parallel chambers.