Control of batch processing systems

The authors describe loading policies for a batch processing machine, i.e., a machine that can process more than one job at a time, when the arrival times of jobs to the machine are uncertain. The study is motivated by the structure of process flows and the predominance of batch processing systems in a semiconductor wafer fabrication facility. The authors consider a two-stage serial-batch system with the serial stage (e.g., photolithography) feeding the batch (e.g., furnace). Machines in the serial stage process one job at a time; further, these machines are subject to failure. The following control limit policy for loading the batch machine is assumed: load if the queue length ≥ Q, else wait until the number of jobs in queue is at least Q. The basic tradeoff considered is delay vs. capacity utilization. The authors do an average cost analysis and optimize to compute the critical number Q.