This study aims to investigate control strategies for the bullwhip effect based on a dynamic model of the linear supply chain, proposed by Helbing and Lammer (2005), which describes the inventory dynamics and production rates of productive units. We simulated the model for instability and stability conditions defined by mathematical analysis. Through these results, we verified both classical and reverse bullwhip effects associated with instability and stability conditions, respectively. The model revealed a duality once the control strategy proposed by Helbing and Lamer (2005) for the classical bullwhip effect ends up causing a reverse effect, which is equally troubling. In the reverse bullwhip effect, we observed amplification of the production rates in the network chains from the supplier to the customer in a way that the upstream chain was not able to meet the needs of the downstream chain. To withhold both effects, we suggest the dynamic control of the parameters that describe the network based on Helbing and Lammer (2005) model.
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