We discuss the exploitation of a well-established replenishment rule, the order-up-to policy, to control the supply chain risk resulting from the Bullwhip effect. To avoid this risk within supply chains, two specific recommendations are highly important. First, we provide strong evidence that availability of high fidelity up-to-date delivery lead-time information is essential. This inevitably requires transparency and trust between various ‘players’ within the supply chain. For many practical reasons this is easier to recommend than to actually achieve. Secondly, such reliable data needs to be automatically fed into the replenishment system to enable it to function in an adaptive mode. This step offers a reasonable guarantee of a well-controlled performance. It is also advisable that at the design stage, replenishment rule parameters should be set so that ‘conservative’ operation is achieved. The new theoretical advances described in the paper are validated via simulation models of the delivery process.