Abstract: With the increase of greenhouse gases emissions and climate change, many governments face growing pressure to reduce carbon emissions. Thus, they implement various low-carbon policies such as carbon cap, carbon cap-and-trade, carbon tax etc., in order to encourage enterprises to adopt low carbon technology and low carbon supply chain management. Hence, it is meaningful to study operation optimization of supply chain network under carbon policies. In this paper, a closed-loop supply chain network including multi manufacturing/remanufacturing plants and multi demand markets is given. Two carbon tax policies including flat tax policy and progressive tax policy are considered. The carbon taxes paid by plants under the two policies are given. The equilibrium conditions of the members in the network under different policies are analyzed. Two closed-loop supply chain network equilibrium models are developed. A Modified Projection Method is proposed. Finally, numerical examples are shown to analyze the effect of carbon tax rates for different policies on new product production outputs, forward and reverse product transaction quantities, demands, prices, investment for carbon emission abatement, carbon emissions, carbon taxes and profits of members in the network. It is found that, with the increase of carbon rate under the two policies, the transaction quantities of forward and reverse product, demands decrease gradually, thus the transaction prices of product increase. Moreover, the increase of carbon rate bring less carbon emissions, more carbon tax paid by firms, hence the profits of firms decease greatly. In addition, it is found that the firms under progressive tax policy pay less carbon tax than one under flat tax policy, hence they can obtain more profits.

Key words: supply chain network; flat tax policy; progressive taxpolicy; network equilibrium