The Multi-Period Dynamic Optimization with Carbon Emissions Reduction under Cap-and-Trade

Under low carbon environment, a multi-period emissions reduction problem for manufacturer is investigated in the paper, where we assume that the government sets mandatory carbon emissions limit to all the enterprises by free of charge and allows the carbon emission quota to be traded or banked inter-temporally in the carbon trading market. Using discrete-time optimal control theory, the optimal emission reduction strategies for each period are firstly explored for maximizing the sum of net profit under cap-and-trade. The optimal carbon emissions, permit trading quantity, and the number of buying Certified Emission Reduction (CER) are obtained in each period. Furthermore, the effects of carbon price and initial carbon quota given by the government on the firm's emission reduction strategies are discussed. Finally, numerical examples are illustrated to verify the proposed model, and some managerial inferences for a multi-period emission reduction are provided in conclusions.