Determining replenishment lot size and shipment policy for an extended EPQ model with delivery and quality assurance issues

Abstract

This paper derives the optimal replenishment lot size and shipment policy for an Economic Production Quantity (EPQ) model with multiple deliveries and rework of random defective items. The classic EPQ model assumes a continuous inventory issuing policy for satisfying demand and perfect quality for all items produced. However, in a real life vendor–buyer integrated system, multi-shipment policy is practically used in lieu of continuous issuing policy and generation of defective items is inevitable. It is assumed that the imperfect quality items fall into two groups: the scrap and the rework-able items. Failure in repair exists, hence additional scrap items generated. The finished items can only be delivered to customers if the whole lot is quality assured at the end of rework. Mathematical modeling is used in this study and the long-run average production–inventory-delivery cost function is derived. Convexity of the cost function is proved by using the Hessian matrix equations. The closed-form optimal replenishment lot size and optimal number of shipments that minimize the long-run average costs for such an EPQ model are derived. Special case is examined, and a numerical example is provided to show its practical usage.