ra0001">A supply chain with stochastic lead-time and ARMA demand is considered.
ra0002">Exact expressions are obtained for the distributions of order and inventory.
ra0003">Under order crossover, the order-up-to policy does not minimize inventory variance.
ra0004">Inventory variance minimization by proportional policy also reduces bullwhip.
ra0005">This ability is compromised under some demand auto-correlation cases.