Controlling job arrivals with processing time windows into Batch Processor Buffer

We consider a two-stage manufacturing system composed of a batch processor and its upstream processor. Jobs exit the upstream processor and join a queue in front of the batch processor, where they wait to be processed. The batch processor has a finite capacity Q, and its 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 instance the job exits the upstream processor till the time instance it enters the batch processor. If a job is not processed before reaching the end of its processing time window, job rework or validation is required. We model this drawback by assigning a reward R for each successfully processed job by the upstream processor, and a penalty C for each job that reaches the end of its processing time window without being processed by the batch processor. We initially assume an infinite job source in front of the serial processor and also assume that the batch processor is operated under a threshold policy. We provide a method for controlling the production of the serial processor, considering the processing time window between the upstream processor and the downstream batch processor. We then show how the serial processor control policy can be modified when the serial processor also experiences intermittent job arrival.