CONTROL OF BATCH PROCESSING SYSTEMS IN SEMICONDUCTOR WAFER FABRICATION FACILITIES

This paper describes 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 structure of process flows and the predominance of batch processing systems in a semiconductor wafer fabrication facility. We 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. We assume a control limit policy for loading the batch machine, i.e., load if the queue length greater-than-or-equal-to Q, else wait until the number of jobs in queue is at least Q. The basic tradeoffs considered are delay (if we wait too long) vs. capacity utilization (if we load early with very few jobs). We do an average cost analysis and optimize to compute the critical number Q. In the extension to the basic model, we analyze the effect of due dates on the critical number. Comparison with simulation results is very encouraging.