This paper addresses demand uncertainty and its propagation in supply chains. The supply chain is considered as a linear time invariant (LTI) system driven by stochastic customer demand. Under general ARMA demand patterns and arbitrary lead times, a unified and structured framework based on the classical minimum variance control theory is proposed for decentralized supply chain management (SCM). Optimal forecasting, the traditional order-up-to policy and the generalized order-up-to policy are directly derived according to the minimum variance criterion. Given these strategies, stochastic properties of the supply chain are studied using LTI system theory in both the time and the frequency domain. Findings from previous literature are reinterpreted from a control-theory-oriented perspective, and new characteristics of the generalized order-up-to policy are deduced and analyzed. On the basis of the statistical analysis, an optimization model is constructed to minimize the variable operation costs which are related to the parameters of the SCM strategies.