Replenishment lot sizing with an improved issuing policy and imperfect rework derived without derivatives

Abstract

This study uses an alternative approach to reexamine a replenishment lot size problem with discontinuous issuing policy and imperfect rework. A straightforward approach in terms of algebraic derivation is proposed instead of conventional method with the need of applying first-order and second-order differentiations to system cost function for proof of convexity before derivation of the optimal lot size. The research result obtained in this study is identical to that in Lee et al. (2011), where they adopted conventional method to solve the problem. The proposed algebraic approach is helpful for practitioners who may have insufficient knowledge of differential calculus to understand with ease such a real life vendor-buyer integrated problem.