Economic order and production quantity models with shortages derived without derivatives

Grubbström and Erdem derived the EOQ model with shortages and complete backlogging without derivatives, and they predicted that their method could be introduced to younger students in school without knowledge of calculus. However, their algebraic procedure is too sophisticated to be absorbed by ordinary readers. Recently, Cárdenas-Barrón extended the algebraic method to solve the EOQ model with shortages and complete backlogging. We will point out that his method has the same problem as Grubbström and Erdem's. In this note, our method applies basic algebraic skill to derive the optimal solution for EOQ and EPQ models with shortages and complete backlogging.