Control of batch processing systems in semiconductor wafer fabrication facilities

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, are described. The motivation for the study is the structure of process flows and the predominance of batch processing systems in a semiconductor wafer fabrication facility. A two stage serial-batch system with the serial stage (e.g. photolithography) feeding the batch (e.g. furnace) is considered. Machines in the serial stage process one job at a time; further, these machines are subject to failure. A control limit policy for loading the batch machine is assumed, i.e. load if the queue length >or=Q, else wait until the number of jobs in queue is at least Q. The basic tradeoffs considered are delay (waiting too long) vs. capacity utilization (loading early with very few jobs). An average cost analysis is done and optimized to compute the critical number Q. In an extension to the basic model, the effect of due dates on the critical number is analyzed. Comparison with simulation results is very encouraging. >