A simple derivation of the optimal solution for the EOQ model for deteriorating items with planned backorders

Abstract

We consider the Economic Order Quantity (EOQ) model for exponentially deteriorating items in which the items deteriorate at a rate proportional to the inventory level per unit time, which leads to an exponentially decreasing inventory level function over time. The coexistence of the exponential and polynomial terms in the total cost function makes closed-form exact solutions impossible, so approximations are used. Methods that optimize management science models without derivatives have recently been used to provide insights to managers who may not have a background in calculus. We propose such an approach for the deteriorating items inventory model with and without planned backorders and compare it with an existing one. Our derivation is much simpler and succinct; our closed-form solution is more intuitive than the existing one. We conduct numerical experiments to analyze the accuracy of the closed-form solution.