Joint Determination of the Production Lot Size and Number of Shipments for Epq Model with Rework

This paper is concerned with joint determination of the optimal lot size and optimal number of shipments for an economic production quantity (EPQ) model with the reworking of random defective items produced. The classic EPQ model assumes a continuous issuing policy for satisfying product demand and perfect quality production for all items produced. However, in a real life vendor-buyer integrated-productioninventory system, a multi-delivery policy is used practically in lieu of the continuous issuing policy, and it is inevitable to generate defective items during a production run. In this study, all nonconforming items produced are considered to be repairable and are reworked in each cycle after the end of a production run. The fixed-quantity multiple installments of the finished batch can only be delivered to customers if the whole lot is quality assured at the end of the rework. Mathematical modeling is used and the longrun average integrated cost per unit time is derived. Convexity of the cost function is proved by the use of the Hessian matrix equations. A closed-form optimal productionshipment policy to the problem is obtained. A special case to the model is discussed. Finally, a numerical example is provided to demonstrate the model’s practical usage. Key Words–Multiple shipments; EPQ model; Rework; Lot sizing; Random defective rate; Manufacturing