Mathematical modeling for determining the replenishment policy for EMQ model with rework and multiple shipments

This paper uses mathematical modeling to determine optimal inventory replenishment policy for the economic manufacturing quantity (EMQ) with rework and multiple shipments. The classic EMQ model considers a continuous inventory issuing policy for satisfying customer’s demands. It also assumes that all products produced are of perfect quality. However, in a real world vendor-buyer integrated environment, multi-shipment policy is practically used in lieu of the continuous issuing approach and generation of random defective items is inevitable. In this study, we assume the reworking of all defective items takes place when the regular production process ends in each cycle. Failure in repair exists; a portion of reworked items fails during the reworking and becomes scrap. The finished items can only be delivered to customers if the whole lot is quality assured at the end of rework. Fixed quantity multiple installments of the finished batch are delivered to customers at a fixed interval of time. Mathematical modeling and analysis are employed in this study for solving such a realistic EMQ model. The long-run average cost function is derived, its convexity is proved, and a closed-form optimal manufacturing lot size is obtained. Two special cases to the proposed model are examined.