Abstract: Assuming that a local government has launched a regional carbon trading market on the purpose of maximizing the profit of the whole production system which is under supervision, a variational inequality is used to construct a supernetwork framework including a supply chain subnetwork and a carbon trading subnetwork. It is assumed that the supplier always play the role of buyer and the manufacturer as the seller in carbon market. The profit-maximized subjective function of each firm in is formulated based and their optimal pricing and production decisions are discussed on the network which also contains a self-benefited carbon trading center. Based on this specific problem and combined with previous work, the proof of the existence, uniqueness and sufficient and necessary conditions of the optimal solution are comprehensively provided. A Korpelevich modified projection algorithm is addressed for solving the problem. With a numerical example, a convergent result is found out. With a comparison analysis between the scenarios of "participating in trading" and "not participating in trading", the result shows some valuable managerial insights on the decision making of the company and the government under the low-carbon environment.

Key words: carbon trading, supply chain, supernetwork model