H∞ Control of a State Matrix Model of Multiechelon Supply Chains System and Its Bullwhip Effect

A state matrix model of a multiechelon supply chains system is built, and its bullwhip effect is analyzed. A new method to quantify the bullwhip effect is presented and described by a l₂ norm of the discrete-time transfer function of the multiechelon supply chains system, where the output is the sum of the variance of the production and the variance of the inventory, the input is the variance of the customer´s demand in downstream. It is the minimum of the up bounded of the bullwhip effect. To reduce the bullwhip effect, we apply the linear matrix inequality approach to design a Hinfin control strategy in the worse case that the end customer´s demand is the most fluctuation. The essence of the method is that the optimum strategy of the supply chain managements in the worse case. To prove it, we give a number example.