Nonlinear modeling and performance analysis of a closed-loop supply chain in the presence of stochastic noise

ABSTRACT We study four-echelon supply chains consisting of manufacturer, wholesaler, retailer and customer with recovery center as hybrid recycling channels. In order to gain a larger market share, the retailer often takes the sales as a decision-making variable. For this purpose, in this supply chain, the retailer limits the forecast of market demand in future periods with expected logic. It also manages demand by leveraging prices and choosing market. In this paper, first, we investigate the state-space model of this supply chain system and examine the effect of complex dynamic and stochastic noise on the bullwhip effect. We analytically prove that this factor leads to the bullwhip effect. So, first, we filtered the information between nodes with extended Kalman filter after which we regulated the destructive effects of the bullwhip phenomenon by designing a non-linear quadratic Gaussian optimal controller. Eventually, the simulation results indicate the efficiency of the proposed method.