Regulating the Bullwhip Effect in Supply Chain with Hybrid Recycling Channels Using Linear Quadratic Gaussian Controller

In this paper, a discrete time state space model for a four-level supply chain system including factory, wholesaler, retailer, and customer is designed with a recovery center as recycling hybrid channels. Due to the lack of coordination between the chain level and the unhealthy exchange of information in the system, almost all supply chain dynamics involve stochastic noise. For the first time, in this paper, we investigated that stochastic noise led to the bullwhip effect. Also, we probed the effect of lead time, various forecasting methods, and aggressive ordering on the bullwhip effect in the proposed supply chain. In order to mitigate the bullwhip effect, the Kalman filter method was proposed. Therefore, by using linear quadratic Gaussian controllers, not only the effect of the bullwhip effect was adjusted but also the system became stable. Eventually, the simulation results of Meshkin match factory indicate the efficiency of the proposed method.