In a supply chain system, it is very important to forecast the changes in the market in order to maintain an inventory level that is just enough to satisfy customer demand. However, demand forecasting is responsible for the so-called "bullwhip effect", the exaggeration of demand fluctuation toward upstream nodes. In this study, we present a minimum variance control (MVC) approach to solve this problem. First, customer demand trends are described by a general ARIMA model. The customer demand forecast is used to determine two inventory targets: inventory at hand and inventory on the road. The changes in inventory level are predicted using a model of material balance and information flow. The order policy is obtained by minimizing the errors between predicted inventory levels and set points and using a function that penalizes large changes in orders. Two controller parameters, the penalty cost factor and the relative weight between the changes in inventory and absolute inventory, are used to optimize the excess inventory and backorder subject to the constraint of no "bullwhip". Simulation results show that this approach can track customer demand and maintain a proper inventory level without causing a bullwhip effect, whether the customer demand trend is stationary or not. Furthermore, the performance of the MVC is found to be superior to those of other approaches such as order-up-to-level, proportional and integral (PI) control, and smoothing order policy found in the literature.