EurOMA International Conference on Operations and Global Competitiveness Budapest, Hungary, June 19-22, 2005 INVESTIGATION OF AN ORDER-UP-TO POLICY WITH CONDITIONAL EXPECTATION FORECASTING AND ARBITRARY LEAD-TIMES Gerard Gaalman 1 and Stephen Disney 2 1.University of Groningen, Faculty of Management and Organization, P.O. Box 800, 9700 AV Groningen, The Netherlands. Tel: 0031-50-3637196. E-mail: g.j.c.gaalman@rug.nl 2. Logistics Systems Dynamics Group, Cardiff Business School, Cardiff University, Aberconway Building, Colum Drive, Cardiff, CF10 3EU, UK. E-mail: disneysm@cardiff.ac.uk ABSTRACT We study the bullwhip and inventory variance problem in a single echelon of a supply chain with arbitrary lead-times. We assume three different classes of demand; uncorrelated white noise demand, autoregressive (AR) demand and autoregressive moving average (ARMA) demand. We use conditional expectation to generate minimum mean square error forecasts of demand to use in the Order-Up-To (OUT) replenishment policy. We notice that in some instances of the demand patterns this alone is enough to avoid the bullwhip effect. But this smoothing property is not realized for all demands. We introduce a proportional feedback controller into the OUT policy that allows us to meet the smoothing objective for all demands. To achieve this we use both state space and transfer function analysis. Although both methods yield different, useful insights into our problem during analysis, both approaches converge to the same solutions. Keywords: Order-Up-To policy, bullwhip, inventory variance, ARMA demand INTRODUCTION The purpose of an ordering policy is to control production or distribution in such a way that supply is matched to demand, inventory levels are maintained within acceptable levels and capacity requirements are kept to a minimum. In doing so, however, the bullwhip effect may arise (Lee, Padmanabhan and Whang, 1997). It has been estimated that the economic consequences of the bullwhip effect can be as much as 30% of factory gate profits (Metters, 1997). The Order Up To (OUT) policy is a standard ordering algorithm in many MRP systems that is used to achieve the customer service, inventory and capacity trade-off (Gilbert, 2005). This policy is often used by companies to coordinate orders for multiple items from the same supplier, where setup costs may be reasonably ignored. Conceptually, the OUT policy is very easy to understand. Periodically, we review our inventory position and place an “order” to bring the inventory position “-up-to” a defined level. However, because of the lead-time between placing an order and receiving the goods into stock, we need to forecast demand. Common forecasting techniques to exploit here include moving average and exponential smoothing (Chen, Drezner, Ryan and Simchi-Levi, 2000; and Dejonckheere, Disney, Lambrecht and Towill, 2003; Kim and Ryan, 2003). These techniques are useful for identifying environmental changes when the mean demand moves from one level to another. However, if demand possesses a linear trend or an explosive geometric growth, other forecasting techniques such as double or triple exponential smoothing may be more appropriate (Dejonckheere, Disney, Lambrecht and Towill, 2002).