A note on “A modified method to compute economic order quantities without derivatives by cost-difference comparisons”

Abstract

There has been growing interest in the last several decades for deriving the optimal solutions to the Economic Order Quantity (EOQ) and the Economic Production Quantity (EPQ) problems and their extensions without using differential calculus; mainly for pedagogical reasons. To this end, numerous algebraic derivation approaches have been proposed over the years. Recently, one such approach has been proposed in Wee, Hui-Ming,Wan-TsuWang, and Chun-Jen Chung. 2009. “A modified method to compute economic order quantities without derivatives by cost-difference comparisons.” European Journal of Operational Research 194 (1): 336 – 338. We show that their approach is equivalent to using the first order conditions; therefore they are implicitly using derivatives. Furthermore, they are neglecting to check the second order conditions to prove optimality; therefore their approach is incomplete. In the case of the EOQ with backorders, their total cost function is not convex, therefore there is no way to prove optimality without derivatives. We propose a different total cost function that results in the same optimal solution and can be proven convex without using derivatives.

Subject Classification:

• 90B05
• 90B06
• 90B50
• 90C56

Keywords:

• Inventory
• EOQ
• EPQ
• Economic order quantity
• Economic production quantity
• Algebraic methods
• Cost comparisons
• Derivative-free methods