A Comparison of Order Quantities Computed Using the Average Annual Cost and the Discounted Cost

This note compares the optimal order quantities determined by minimizing the average annual cost and by minimizing the discounted cost over all future time for the simplest imaginable type of inventory model in which the demand rate is assumed to be deterministic and no stockouts are allowed. By specific numerical results it is shown that for all values of the parameters that might reasonably be encountered in an inventory problem there is only a negligible if any difference in the order quantities. It is shown, however, that in extreme cases significant differences may be obtained.