Disaggregation and consolidation of imperfect quality shipments in an extended EPQ model

We consider a standard economic production quantity (EPQ) model. Due to manufacturing variability, a fraction P of the produced inventory will have imperfect quality, where P is a random variable with a known distribution. We consider a 100% inspection policy and further assume that the inspection rate is larger than that of production. Thus, all imperfect quality items will be detected by the end of the production cycle. For such an augmented EPQ model, we first derive the new optimal production quantity assuming that the imperfect quality items are salvaged once at the end of every production cycle. Then, we extend this base model to allow for disaggregating the shipments of imperfect quality items during a single production run. Finally, we consider aggregating (or consolidating) the shipments of imperfect items over multiple production runs. Under both scenarios we derive closed-form expressions for both the economic production quantity and the batching policy, and show that our desegregation/consolidation schemes can lead to significant cost savings over the base model.