The Average Annual Cost and Discounted Cost Mathematical Modeling Methods in the Inflationary Inventory Systems - A Comparison Analysis

Abstract

The purpose of the inventory models is to minimize the total system costs. This paper considers the inventory systems with time value of money and inflation and compares two methods for calculating the optimal total cost. These methods are Average annual cost (a simpler method) and discounted cost methods (the theoretically more accurate). The inventory and shortages behavior have been analyzed with using the differential equations. A constant fraction of the on-hand inventory deteriorates when the item was received into inventory. The model was expressed in terms of inflation. The theoretical results have been tested and illustrated via the numerical examples. A sensitivity analysis on the model parameters has been performed and the results show the little difference between two methods in a wide range of parameters. For two parameters, , the constant deterioration rate and c, the per unit purchase cost, we saw that discounted cost method is more accurate than average annual cost method.