Replenishment Lot Size and Number of Shipments for Epq Model Derived without Derivatives

This paper investigates optimal replenishment lot size and optimal number of shipments for economic production quantity (EPQ) model with rework process using an algebraic approach. The classic EPQ model assumes a perfect quality production for all items produced and a continuous issuing policy for satisfying customer‟s demand. However, in a real life vendor-buyer integrated-production-inventory system, a multidelivery policy is commonly used in lieu of a continuous issuing policy and generation of defective items during a production run seems to be inevitable. A recent published work examined such an identical problem using mathematical modeling and differential calculus to derive the optimal replenishment lot size and optimal number of deliveries that minimizes overall production-inventory-shipment costs. This paper proposes a straightforward algebraic approach to replace the use of calculus on the cost function for determining optimal production-shipment policies. It also presents a simpler form for calculating the long-run average cost for such an imperfect EPQ problem. Keywords–Replenishment lot size; Multiple shipments; Algebraic approach; Random defective rate; EPQ model; Rework