EOQ Model for Exponentially Deteriorating Items with Planned Backorders without Differential Calculus

Abstract

We study the Economic Order Quantity (EOQ) model for deteriorating items with planned backorders. In the exponentially deteriorating items model, the inventory deterioration rate is proportional to the inventory level, which leads to an exponentially decreasing inventory level over time, obtained by solving an ordinary differential equation. Due to polynomial and exponential terms in the total cost function, an exact closed form solution is not possible. Therefore, an approximation of the total cost function has to be used. In this paper, we propose a concise and intuitive method to determine the inventory level function without using differential equations, and a method to determine the optimal solution without derivatives, based on an accurate approximation of the total cost function. Our approximation is novel and intuitive and numerical experiments demonstrate the accuracy of the closed form solution based on our approximation.