On the Economic Order Quantity Model with Compounding

Abstract

The classical Economic Order Quantity (EOQ) model assumes simple interest to represent the opportunity cost of capital tied up in the inventory. Recently, the classical model has been extended to incorporate compounding, and an intuitive closed-form solution has been proposed. The compounding based model is more realistic than the original EOQ model because compound interest is the standard practice in finance and banking. The resulting closed-form solution proposed for this recent model is based on an approximation of the annual compound interest-based opportunity cost. However, the derivation of the approximation model is rather long and complicated, involving the use of the L’Hôpital’s rule several times. Here, we show an easier way to approximate the annual compound interest-based opportunity cost. Our derivation is shorter and it does not require the use of the L’Hôpital’s rule. We also demonstrate that the approximation is remarkably close to the exact model, and it results in the same intuitive closed-form solution as the earlier one.

KEYWORDS AND PHRASES:

• Compounding
• compound interest
• economic order quantity
• EOQ
• inventory
• net present value
• NPV