The role of an ordering policy as an inventory and cost controller

We investigate the relationships between an ordering policy, the variance of the inventory levels it maintains and forecasting scheme it exploits. These factors play a major role in the bullwhip effect, an important problem in the field of supply chain management. We start by showing that the order-up-to (OUT) policy is identical to the ordering policy of Vassian (1955). This policy minimizes the variance of the inventory levels subject to the assumptions of a periodic order interval, a constant lead-time and backlogging of excess demand for a particular forecasting policy. These ordering policies are able to match the variance of inventory levels to the variance of the error of the forecasted demand over the lead-time. We compare the performance of the OUT policy with a minimum mean square error (MMSE) forecasting mechanism to that of the moving average (MA) and the exponentially weighted moving average (EWMA) forecasting mechanisms. We also present the myopic inventory policy (e.g. Heyman and Sobel, 1984). This policy minimizes the sum of linear inventory holding and shortage costs. We show that the myopic inventory policy is also equivalent to the OUT policy. Finally, we investigate the relationship between the variance of orders and inventory levels for the three forecasting methods