A single-producer multi-retailer integrated inventory system with scrap in production

Abstract

This study determines the replenishment-distribution policy for a single-producer multi-retailer integrated inventory system with scrap rate in production. The objective is to find the optimal lot-size and number of shipments that minimizes the total expected costs for such a specific system. It is assumed that an item is manufactured by a producer and then delivered to its n different retailers for sale. Each retailer has its own annual product demand and the demand will be satisfied by synchronized multiple shipments during each production cycle. Unlike the classic Finite Production Rate (FPR) model assuming perfect production and a continuous inventory issuing policies, the proposed system assumes that there is an inevitable random defective rate in production and all nonconforming items are scrap and delivery of product is under a practical multiple shipment policy. Mathematical modeling is employed and the renewal reward theorem is used to cope with the variable cycle length. Then the expected system cost function is derived and the convexity of this function is proved. Finally, a closed-form optimal replenishmentdistribution policy for such a specific single-producer multi-retailer integrated system is obtained. A numerical example is provided to demonstrate the practical usage of the obtained results. © Maxwell Scientific Organization, 2013.