A Comparison of Average and Discounted Cost Models for the Dynamic Lot Size Inventory Problem

Abstract

It is a common practice in the inventory literature to use average cost models as approximations to the theoretically correct discounted cost models. An average cost model minimizes the average undiscounted cost per period, while a discounted cost model minimizes the total discounted cost over the problem horizon. This paper attempts to answer an important question: How good are the results (the total discounted costs) for the average cost models compared to those for the discounted cost models? This question has been conclusively answered for the simplest inventory model where the demand rate and other parameters are assumed to remain constant in time. This paper addresses this issue for the first time for the case where demand rates are allowed to be nonstationary in time. A discounted cost model has been developed in the paper to carry out this comparison. It is shown that a simple dynamic programming algorithm can be used to find optimal order policies for the discounted cost model. The effect of the varying interest rates and other parameters on the relative performance of the average cost model has been studied by developing an insightful analysis and also by doing a computational study. The results show that, while the average cost model can cost as much as about 26% more than the discounted cost model in extreme cases, this increase is not significant for the parameter values in the range of the common interest.