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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.

2011) Solving production lot size problem with an improved delivery policy and failure in rework by a simplifi ed solution procedureAbstract A simplifi ed solution procedure is proposed in this paper to solve a specifi c production lot size problem with an improved delivery policy and failure in rework. Unlike the conventional method using diff erential calculus with the need for proving optimality of the longrun average cost function, this paper demonstrates that the optimal lot size and its related costs for the aforementioned production model can be derived without derivatives. Such an approach may enable practitioners who with little knowledge of calculus to understand with ease the realistic production-shipment integrated systems.