Processing networks with planned inventories: Tandem queues with feedback

This note continues the investigation, initiated by Lee and Zipkin, of tandem queues with planned inventories. Such models are designed to represent make-to-stock production processes, where intermediate and finished goods can be produced and stored in advance of demand. Otherwise, the setup is much like that of the classic Jackson network model. We suppose each production stage occasionally produces a defective unit, which must then repeat processing, return to an earlier stage, or be discarded. We propose and test a tractable approximation scheme. The approximation appears to be reasonably accurate. This implies that poor quality degrades performance mainly by wasting production capacity.