Closed-Loop Supply Chain Network Equilibrium with Environmental Indicators

In this paper, we propose a closed-loop supply chain network equilibrium model with environmental indicators through variational inequality theory, which is composed by raw material suppliers, manufacturers, retailers, demand markets, and recovery centers. In view of sustainable development, the Ministry of Environmental Protection legislates by imposing emission penalties to prevent the manufacturers from violating laws and regulations but offering premiums to stimulate the recovery centers to recycle used products. The penalties and premiums should be greater than the corresponding shadow prices as environmental indicators determined by the model, which is constructive for decision making of the authorities. We describe their behavior, derive optimality conditions, and establish the variational inequality in accordance with the closed-loop supply chain network equilibrium conditions. Based on the existence of solution to the model under reasonable assumptions, a numerical example is provided for illustration.