Joint determination of rotation cycle time and number of shipments for a multi-item EPQ model with random defective rate

a r t i c l e i n f o JEL classification: C02 M11 C44 C61 Keywords: Multi-item production system Rotation cycle time Multi-delivery Economic production quantity model Scrap Vendor–buyer integrated system This paper addresses the joint determination of a rotation cycle time and number of shipments for a multi-item economic production quantity (EPQ) model with random defective rate. The classic EPQ model considers production planning for a single product with a perfect production process and continuous inventory issuing policy for its finished goods. However, in real vendor–buyer integrated systems, the multi-delivery policy is often used in lieu of the continuous issuing policy, and due to various uncontrollable factors, the generation of defective items is inevitable. Furthermore, in order to maximize machine utilization, management often plans the production of m products in turn on a single machine, rather than a single product on one machine, as assumed by the EPQ model. Therefore, by assuming that all defective items produced are scrap, this study aims to jointly determine the optimal rotation cycle time and number of shipments that minimize the long-run average cost for such an imperfect quality multi-item EPQ model. We employ mathematical modeling with the renewal reward theorem and obtain closed-form optimal operating policies for the proposed model. Further, we demonstrate the practical use of the results by using a numerical example and sensitivity analysis. The economic production quantity (EPQ) model was introduced (Taft, 1918) to assist the manufacturing firms in deciding the optimal batch size that would minimize the expected production–inventory costs. The classic EPQ model considers production planning for single product with perfect production process, and a continuous inventory issuing policy for its finished goods. However, in real vendor–buyer integrated systems: (1) the multi-delivery policy is often used in lieu of the continuous issuing policy, and (2) due to various uncontrollable factors, generation of defective items is inevitable. Studies that related to different aspects of multi-delivery vendor–buyer systems are surveyed as follows. Goyal (1977) studied an integrated single supplier–single customer problem. He presented a method that is typically applicable to the inventory problems where a product is procured by a single customer from a single supplier using examples to demonstrate his proposed model. Schwarz et al. (1985) studied the system fill-rate of a one-warehouse N-identical retailer distribution system as a function of warehouse and retailer safety stock. They employed an approximation model from a prior study …