We analyse an infinite horizon two-echelon supply chain inventory problem. First-order auto-regressive demand pattern is assumed and each participant adopts the order-up-to (OUT) policy with the minimum mean square error forecasting scheme to generate replenishment orders. To control the dynamics of the supply chain, we incorporate a proportional controller into the OUT policy, which we call a generalised OUT policy, at the first echelon player only. We aim to minimise the sum of the variances of the net inventory at the two echelons. We find that the supply chain inventory variance can be reduced by over a third with our generalised OUT policy. To enjoy this cost saving, the attitude of first echelon player to cost increases is an essential factor. Interestingly, a significant amount of benefit comes from the first player doing what is the best for the overall supply chain, rather than what is the best for local cost minimisation.