In the area of inventory theory there is a substantial amount of literature based on the Economic Order Quantity (EOQ) model. However all the EOQ-based models have implicitly assumed a perfect production process. On the other hand, researchers in quality control assume that production lot size is predetermined in the optimization of inspection plan and quality level. It is assumed that quality can be achieved only by efficient detection of defective items, not by avoidance of defective production.; A better and more realistic approach brings these two branches of research together and considers the joint optimization of production quantity and quality. We propose a model of a multi-stage production system with imperfect processes. We consider a process that may fail and produce defective items. In our models, process inventory is transported in sub-batches to reduce work-in-process inventory holding cost. The process is inspected before the production of each sub-batch and restored whenever a process failure is detected. Two different item inspection schemes are followed--a finished goods inspection and a work-in-process inspection--and the quality level of the final product is controlled by the inspection schedule. The objective is to determine the production cycle time and number of sub-batches that minimize the total cost.; Comparisons are made between the various models proposed. We have proved that the finished goods inspection model dominates the EOQ model. However, no conclusion can be drawn on the optimal total cost of the finished goods inspection model and work-in-process inspection model. The superiority of one inspection scheme over the other depends on the system parameters. We have derived conditions under which the finished goods inspection model sub-batch time exceeds the work-in-process inspection model sub-batch time, and vice versa.
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