A derivation of the optimal solution for exponentially deteriorating items without derivatives

摘要

We study the Economic Order Quantity (EOQ) model for exponentially deteriorating items in which the inventory deterioration rate is proportional to the inventory level, which leads to an exponentially decreasing inventory level function. Because of the coexistence of exponential and polynomial terms, an exact closed form solution is not possible. An approximate model and a heuristic solution approach has previously been proposed for this problem. We derive the exact optimal solution for this model without using derivatives and propose a more accurate way to model the inventory holding cost. We show that the difference in total cost is significant between the improved and the original model. We also compare our model with another one based on a different approximation and show that our approach is far superior than the former.