Economic lot sizing with imperfect rework derived without derivatives

摘要

This paper presents an algebraic method for solving economic production quantity (EPQ) model with imperfect rework. Conventional method for deriving optimal lot size is by using differential calculus on the cost function with the need to prove optimality first. Recent articles proposed algebraic approach to the solution of classic economic order quantity (EOQ) and EPQ model without reference to the use of derivatives. This note extends them to an EPQ model taking into consideration an imperfect rework of defective items. We demonstrate that the optimal lot size and the expected production-inventory cost for such a realistic EPQ model can be derived without derivatives.