Deriving the Optimal Production-Shipment Policy with Imperfect Quality and an Amending Delivery Plan using Algebraic Method

This paper derives the optimal production-shipment policy for a vendor-buyer integrated system with imperfect quality and an amending product delivery plan using an algebraic method. It is assumed that the system may randomly produce certain portion of nonconforming products during each production run. Quality assurance in terms of inspection and rework has been given effect to the defective items during and after the production run. A (n+1) finished goods distribution policy is used in the proposed vendor-buyer integrated system, such a delivery plan aims at reducing inventory holding costs for both producer and buyer. Unlike the conventional approach using the differential calculus on the long-run average production-inventory-delivery cost function with the need to prove optimality before solving the optimal replenishment-delivery problem, this paper adopts a simplified solution procedure using algebraic derivations to deal with the production-shipment decision makings. The result demonstrates that the optimal replenishment lot-size and optimal number of deliveries can be derived without derivatives. Such an alternative approach enables practitioners who with little knowledge of calculus to understand the real world vendor-buyer integrated systems with ease. Key-Words: Replenishment lot size, Multi-deliveries, Supply chain optimization, Vendor-buyer integration, Rework, Scrap