The economic lot size of the integrated vendor-buyer inventory system derived without derivatives: A simple derivation

In this paper, we first complement an inappropriate mathematical error on the total cost in two previous published research papers in inventory field. Then an arithmetic-geometric inequality method is proposed not only to simplify the algebraic method of completing prefect squares, but also to complement their shortcomings. In addition, we also provide a closed-form optimal solution to the integrated vendor-buyer inventory system without using complex derivatives. Finally, the proposed method seems to be easy-to-understand and simple-to-apply by individuals who are not familiar with differential calculus.