Dynamic analysis of the damped trend proportional order-up-to policy

Using the Kalman filter we build a state-space model of the proportional order-up-to (POUT) policy with an autoregressive integrated moving average (ARIMA) demand process. The POUT policy is closely related to the order-to-up (OUT) policy with the addition of a proportional feedback controller in the inventory and work-in-progress feedback loops. Our modelling approach allows us to analyse the behaviour of the damped trend POUT policy when the damped trend forecasting method predicts ARIMA(1,1,2) demand. We derive and analyse the demand and inventory variances. We also find the covariance between the demand forecast and the inventory forecast in an attempt to obtain the order variance. Both the demand and the order variances are infinite under the non-stationary ARIMA(1,1,2) process. Thus, the traditional bullwhip measure (the ratio of the order variance divided by the demand variance) is indeterminate. However, we can study the difference between order and demand variance and the difference between the OUT and POUT policies responses.