Controlling job arrivals with processing time windows into Batch Processor Buffer

front of the batch processor, where they wait to be processed. The batch processor has a finite capacity Q, and the processing time is independent of the number of jobs loaded into the batch processor. In certain manufacturing systems (including semiconductor wafer fabrication), a processing time window exists from the time the job exits the feeder processor till the time it enters the batch processor. If the batch processor has not started processing a job within the job's processing time window, the job cannot proceed without undergoing rework or validation by process engineers. We generalize this scenario by assigning a reward R for each successfully processed job by the feeder processor, and a cost C for each job that exceeds its processing time window without being processed by the batch processor. We examine a problem where the feeder processor has a deterministic processing time and the batch processor has stochastic processing time, and determine that the optimal control policy at the feeder processor is insensitive to whether the batch processor is under no-idling or full-batch policy.