Ordering and Inventory Policies for Step Changes in the Unit Item Cost: A Discounted Cash Flow Approach

This paper considers the problem of determining the optimal ordering quantities of a purchased item where there are step changes in price, either up or down. Other costs incurred include ordering costs associated with each replenishment and holding costs related to capital tied up in inventory and physical stock holding. The net present value (NPV) principle is applied. Explicit expressions for the development of the optimal order quantities over time are presented. It is shown that three cases may be distinguished: (i) when the price change is very small, (ii) when an essential price increase occurs, and (iii) when there is an essential price decrease. Although the optimal last-order quantity before a price increase is similar in magnitude to what has been presented in other articles applying average cost approaches, in certain respects, this paper offers novel results contradictory to those suggested by other authors. Analysis shows that the average-cost model solutions are first-order approximations in the discount rate. Numerical evaluations of a range of price increases and times to the price increase suggest that, with certain important caveats, the average-cost formulae are likely to be acceptable for most practical situations for the infinite horizon situation.