A note about ‘on replenishment schedule for deteriorating items with time-proportional demand’

Abstract

In the Economic Order Quantity (EOQ) model for exponentially deteriorating items, the inventory deterioration rate is proportional to the inventory level, which leads to an exponentially decreasing inventory level over time. Due to polynomial and exponential terms in the total cost function, an exact closed form solution is not possible. Previously, an approximation for the total cost function and a closed form optimal solution for the order interval have been proposed for this problem. However, the proposed closed form formula is complicated and it is not intuitive. It is also assumed without justification that the average inventory level is equal to half of the order quantity. We justify this assumption and show that the same approximation yields a much more intuitive formula when it is used to determine the optimal order quantity instead of the order interval. Our intuitive optimal order quantity formula is more likely to be adopted in practice.