Hosoda, T. and Disney, S.M., 2004, “The role of an ordering policy as an inventory and cost controller”, Logistics Research Network Annual Conference, Dublin, Ireland, September 8 th -10th. THE ROLE OF AN ORDERING POLICY AS AN INVENTORY AND COST CONTROLLER Takamichi Hosoda*, and Stephen M. Disney Logistics Systems Dynamics Group, CardiffBusinessSchool,CardiffUniversity,AberconwayBuilding,Colum Drive, Cardiff, CF10 3EU, UK *Corresponding author. Email: hosodat@cardiff.ac.uk , disneysm@cardiff.ac.uk . Abstract 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. Keywords : supply chain management, bullwhip effect, inventory variance, cost minimization, order-up-to policy, myopic policy, forecast Introduction Arrow et al. (1951) introduced the (S, s) ordering policy; Karlin (1960) provides the order-up-to (OUT) policy, which is the s = S case of the (S, s) policy. Karlin shows that if the purchase cost is linear, the optimal policy in each period is characterized by a single critical number, S, which could vary in successive periods. In 1975, assuming an ARMA (Box et al., 1994) demand process, minimum mean square error forecast (MMSE) method, proportional holding and stockout costs and zero lead-time, Johnson and Thompson (1975) shows that the OUT policy is optimal. This policy is often called the myopic inventory policy. Heyman and Sobel (1984) provide an introduction to the myopic policy. On the other hand, Vassian (1955) describes an ordering policy which minimizes the variance of the inventory level for a given forecasting policy. Pinkham (1957) extends Vassian (1955) and presents a linear production rule that achieves an optimal balance between the inventory and the order variance. Here, we investigate the relationship between the OUT policy, the myopic policy, and Vassian’s ordering policy. In the next section we describe the relationship between these policies and some characteristics of them. It has been long recognized that the forecasting method employed has an impact on the performance of an ordering policy (e.g. Badinelli, 1990; Xu et al., 2001; Kim and Ryan, 2003; Dejonckheere et al., 2003). Thus, we will analyze the effect of three different forecasting methods on the inventory variance ratio. The inventory variance ratio is expressed as 2 2 inv D σ σ / (Disney and Towill, 2003a), where 2 inv σ denotes the variance of inventory level and 2 D σ denotes the variance of demand. We will also show that the OUT policy is optimal with linear inventory holding and shortage costs and a time delay in replenishment. Furthermore, we will investigate the order variance ratio. This is expressed as 2 2 O D σσ / (Chen et al., 2000), where 2 O σ refers to the variance of orders. This metric is commonly referred to as “bullwhip”. We conclude our paper with some managerial insights and provide a short discussion on the trade-off between the inventory and the order variance with different forecasting techniques.