This paper develops a mathematical model using differential equations and considers a bullwhip effect in a supply chain network with multiple retailers and distributors. To ensure the stability of the entire system and reduce the bullwhip effect, a robust control method and an inventory replenishment policy are proposed. This shows that the choice of the output matrix may reduce the bullwhip effect. It has also observed in the inventory replenishment mechanism may be a negative impact on the robustness of the bullwhip effect. However, the inventory replenishment behavior may lead to the bullwhip effect on the presented model. This means that the complex supply relationships may have a significant role in controlling or reducing the bullwhip effect of fluctuations. Manuscript profile