Technical note: The EOQ and EPQ models with shortages derived without derivatives

Grubbstrom, and Erdem (Int. J. Prod. Econom. 59 (1999) 529) 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 the knowledge of calculus. However, their algebraic procedure is too sophisticated to be absorbed by ordinary readers. Recently, Cardenas-Barron (Int. J. Prod. Econom. 70 (2001) 289) extended the algebraic method to solve the EPQ model with shortages and complete backlogging. We will point out that his method has the same problem as Grubbstrom 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. (C) 2003 Elsevier B.V. All rights reserved.