The paper analyzes the formation of the bullwhip effect in logistic systems as a significant threat to preserving stability in the face of non-negligible goods transport delay and uncertainty of demand and stock records. The popular order-up-to policy is selected as the method governing the goods flow. A dynamic model of entity interaction is constructed and examined, first, analytically, then in numerical tests for various scenarios of practical significance, e.g., a supply chain with external and local demand signals or real-world European goods distribution system. It has been found that the order-up-to policy does not trigger the bullwhip effect despite the delays in the goods delivery in the nominal operating conditions in supply chains. However, in networked environments, even the basic configuration triggers the bullwhip effect.