The Bullwhip effect is a well-known phenomenon, which affects the supply chain management process. It produces variations in a customer’s demand pattern, which amplify as they pass through the production, supply and distribution processes. The deviation gets amplified upstream at each level of the chain, in the form of replenishment orders. Forrester stated that the amplification is due to problems arising from non-zero lead times and inaccurate forecasting made by each member of the chain in the face of demand variability. This paper analyzes the effect of the fluctuation in lead times due to transportation (delivery times) on the distortion of replenishment/manufacturing orders generated by each member of a traditional supply chain, and the impact of that distortion on fill rate, inventory costs and transportation costs, by using a dynamic simulation model for the management of the demand in multilevel supply chains.