Summary: The bullwhip effect refers to the phenomenon of demand distortion in a supply chain. By eliminating or controlling this effect, it is possible to increase product profitability. The main focus of this work is on applying a control technique, based on the divergence of the system, to reduce the bullwhip effect in a single-product one echelon supply chain, in which an Order-Up-To (OUT) order policy is applied. First, the relationships between the bullwhip effect, the stability of the supply chain and the total costs are analyzed. Second, the divergence-based control strategy is applied to stabilize the supply chain dynamics with a considerable reduction of the total costs \((>30\%)\) and, in relevant cases, of the bullwhip effect.