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.
Applied Mathematics and Computation 217(12), pp.5972-5977