Abstract: As one of the main sources of indirect carbon emissions, suppliers are a significant part of the carbon emissions of the whole supply chain. On the other hand, as the starting point of the supply chain, the selection of suppliers is directly related to the benefits and market competitiveness of downstream manufacturers. However, few literatures consider carbon emission in supplier selection decision. Further, some important factors, including the types of purchased products, uncertain customer demands, and carbon emission, have not been simultaneously studied in dealing with dynamic supplier selection problems. Therefore two carbon emission regulations, including carbon cap-and-trade and carbon tax, are considered in the process of solving dynamic supplier selection and lot-sizing decision problems. The calculation of carbon emissions is related to several factors, including vehicle loads, fuel, and distance and so on. In addition, being confronted with uncertain market demand and changing inventory, how to choose suppliers, how to allocate orders, how much to purchase at different times and how to minimize supply chain cost under different carbon emission regulations are the main problems to be solved in this paper. By means of optimality theory, a mixed integer nonlinear programming model is formulated to explore the dynamic supplier selection and procurement lot-sizing decision by different modes dealing with carbon emission in the case of multi-period, multi-supplier, multi-product and uncertain demand. Analysis is made to different modes dealing with carbon emission including carbon tax and carbon cap-and-trade. In order to solve complex large-scale problems in a short time, a modified discrete particle swarm optimization(MDPSO)is proposed by designing mutation operator and perturbation factor and is compared with several commonly-used improved particle swarm optimization. Then exact method, approximate method and improved heuristic method are applied to solve the mixed integer programming problem of different scales and analysis is made to compare them. Finally, numerical examples are given to verify validity and feasibility of the model proposed. The empirical results show that different modes of carbon emission treatment have different effects on supply chain management decision-making. Carbon tax can be used as a tool to effectively control total carbon emissions without significantly increasing the total cost of the supply chain. Under carbon cap-and-trade mode, it is found that the change of carbon cap has no effect on carbon emission. Carbon trading price can be used as a regulatory tool to balance the total cost and carbon emissions of the supply chain. Furthermore, the improved particle swarm optimization algorithm proposed(MDPSO)in this paper can solve the problem of large-scale supplier selection and procurement lot-sizing in a short time at the expense of solution accuracy to a small extent(less than 2%). In practice, the research can be used as a tool for enterprises to make quantitative decision, which theoretically enriches supplier selection and procurement lot-sizing decision.

Key words: mixed integer nonlinear programming；supplier selection；lot-sizing；carbon emission