The Economic Order Quantity Model under Compound Interest with Planned Backorders

Abstract

In the classical EOQ model, the annual inventory holding cost per unit is defined as a fixed percentage of the unit price of the item. A portion of the inventory holding cost is the opportunity cost of capital tied up in the inventory, which is based on the best interest rate or the rate of return for the best alternative investment, and assumed as simple interest. In finance and banking, compound interest is the standard and simple interest is very rare; so it is not realistic to use an opportunity cost based on simple interest. To overcome this problem, a number of net present value (NPV)-based approaches have been proposed in the literature but they all recommend the standard EOQ formula as an approximate optimal solution. In this research, we propose an extension of the basic model that uses compound interest for the opportunity cost and allows planned backorders. A closed-form optimal solution is not possible for this model due to the exponential terms in the total cost function. We develop a reasonable approximate model and derive the optimal solution that is intuitive and different from the standard EOQ solution. We show that our solution is very close to the solution of the exact model.