A note on cost comparisons method for the EOQ and EPQ problems

Abstract

In the last two decades, a number of papers have appeared in the literature regarding solving the Economic Order Quantity (EOQ) and the Economic Production Quantity (EPQ) problems with and without backorders, as well as their numerous variants, without using derivatives. The motivation behind these approaches is presumed pedagogical benefits and making these models easier to understand for people without a background in differential calculus. One such method is called cost comparisons, which is essentially a specialised version of marginal analysis. In this note, we show that this method is the same as using the first order conditions. In addition, it is not checking the second order conditions; making the method incomplete. We prove the second order conditions without using derivatives and complete the method.

Subject Classification:

• 90B05
• 90B06
• 90B50
• 90C56

Keywords:

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