A note on the economic lot size of the integrated vendor–buyer inventory system derived without derivatives

Numerous researches on the integrated production inventory models use differential calculus to solve the multi-variable problems. This study simplifies the solution procedure using a simple algebraic method to solve the multi-variable problems. As a result, students who are unfamiliar with calculus may be able to understand the solution procedure with ease. This paper refers to the approach by Grubbström and Erdem [R.W. Grubbström, A. Erdem, The EOQ with backlogging derived without derivatives, International Journal of Production Economics 59 (1999) 529–530] and extends the model by Yang and Wee [P.C. Yang, H.M. Wee, The economic lot size of the integrated vendor–buyer system derived without derivatives. Optimal Control Applications and Methods 23 (2002) 163–169] to derive an algebraic method to solve the three decision variables of the proposed model.