Stabilization of two-echelon supply networks with uncertain demand, multiple delays and switching topology using robust control

Abstract

In this paper, a two-level supply network (SN) system composed of multiple retailers and multiple distributors is developed. The dynamic equations for each echelon are described individually considering the varying possibility of vertical and lateral transshipment of product. Then a SN model is formulated with switched topologies, multiple time-varying delays and uncertain customer demand. By use of the switched Lyapunov stability theory and the average dwell time approach, sufficient conditions of linear matrix inequalities is proposed for the existence of robust $$\hbox {H}\infty $$ state feedback controller. This control strategy guarantee the reduction of inventory levels, delivery rates and orders fluctuations under the worst fluctuation of demand as well as the mitigation of the bullwhip effect (BE). A real case example is presented to demonstrate the effectiveness of the proposed inventory control. The simulation proves that proportionality between vertical and lateral delays as well as cooperation rates have significant impacts on the achievement of best tradeoff between improving inventory dynamics and reducing order fluctuations.