Abstract
This paper presents a simple algebraic approach for deriving the optimal lot size for economic production quantity (EPQ) model with rework process. Conventional methods for solving lot size problems are by using differential calculus on the long-run average production-inventory cost function with the need to prove optimality first. A few recent articles proposed the algebraic approach to the solution of classic economic order quantity (EOQ) and EPQ model without reference to the use of derivatives. This paper extends it to an EPQ model with reworking of defective items. We demonstrate that optimal lot size and optimal production-inventory cost for such an imperfect EPQ model can be derived without derivatives. As a result, it may enable the practitioners or students who with little knowledge of calculus to understand or handle with ease the realistic production systems.
Highlights
The mathematical modeling and analysis was employed by the economic order quantity (EOQ) model several decades ago [1] to balance the setup and holding costs and to derive the optimal order quantity that minimizes overall inventory costs
Effect of random defective rate and the reworking of defective items on economic production quantity (EPQ) model were studied by Chiu and Chiu [15] using conventional methodology
Conventional methods for solving lot size problems are by using differential calculus on the long-run average production-inventory cost function with the need to prove optimality first
Summary
The mathematical modeling and analysis was employed by the EOQ model several decades ago [1] to balance the setup and holding costs and to derive the optimal order quantity that minimizes overall inventory costs. Effect of random defective rate and the reworking of defective items on EPQ model were studied by Chiu and Chiu [15] using conventional methodology They employed the differential calculus on the long-run average production-inventory cost function with the need to prove optimality first. A few recent articles for example, Grubbström AND Erdem [16] and Cárdenas-Barrón [17] presented algebraic approaches for solving classic EOQ and EPQ model without reference to the use of derivatives (neither applying the first-order nor second-order differentiations) This paper extends it to a prior research [15] which takes the reworking of random defective items into consideration
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