Investigation of an Order-up-to Policy with Conditional Expectation Forecasting and Arbitrary Lead-times

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.