H∞ control of bullwhip effects in closed-loop supply chain networks with two chains cooperation

With two chains cooperation, Hinfin control methods of bullwhip effects in closed-loop supply chain (CLSC) networks are studied. In each chain, the products which hold by the consumer part are considered as the virtual inventory and the remanufacturing part is defined as a rate to the virtual inventory. The inventory state difference equations of the manufacturers, retailers and consumers are built respectively. Considering CLSCs based on remanufacturing, the model of CLSC networks is established. Bullwhip effects are described as the variance proportion. In the worse case of the demand fluctuation, Hinfin control methods of bullwhip effects in the system are presented with two chains cooperation. To prove it, some number examples are given. The essence of the method is that in the worse case the optimum strategy of the normal manufacturing and order are made by cooperation control of node enterprises in the CLSC networks to restrain bullwhip effects. As a result, it presents a new method to study the stability of CLSC networks and control corporately their bullwhip effects.