关键词: 供应链物流网络, 需求不确定, 低碳政策, 鲁棒优化

Abstract: In response to global warming, the Chinese government will adopt more effective policies and measures, which aim to peak carbon dioxide emissions by 2030 and achieve carbon neutrality by 2060. Such an ambitious goal has brought great challenges to various industries by changing the mode of operation management and implementing the transformation of the low-carbon economy. In terms of the total carbon emissions in China, the transportation sector currently accounts for about 10.4%, of which the road is the main carbon emission contributor, accounting for 87%. It is an important and necessary way to achieve the emission reduction target through the optimization and reconstruction of the cargo transportation system. In terms of government regulation policies, the mostly discussed are carbon emission cap-and-trade and carbon tax. They are set to internalize the cost of carbon emissions, encourage enterprises to actively optimize their logistics network structure, and promote the transport mode from road to cleaner rail and water transport. China began implementing a carbon cap-and-trade policy in eight pilot cities in 2011, and established a carbon emission trading market in 2021. Therefore, the integration of carbon cap-and-trade policy in the design of supply chain logistics networks and the construction of multi-mode transport systems are effective ways for enterprises to transform low-carbon.
   The classic facility location problem focuses on the goals of cost, efficiency, and social welfare improvement while ignoring the environmental impacts of transportation activities. The design of the supply chain logistics network has a significant two-stage property: during the effective period of facility planning decisions, the future product demand is changed by economic and social development and affects the decision of the enterprise. In recent years, probabilistic distributed fuzzy sets have been widely used to reduce their conservatism and improve their robustness by constructing fuzzy sets according to confidence levels from probability distribution information in historical data. In addition, the robust optimization method is an effective method to solve the optimization problem considering uncertainty. Relevant research provides a comprehensive optimization framework for supply chain logistics network design, but this method does not involve how to reconstruct the distributed robust model into a standard programming model that can be directly used by commercial solvers, which can design an efficient solution.
   Therefore, this paper studies the design of a supply chain logistics network under product demand uncertainty and carbon cap-and-trade policy. Considering the uncertainty of future product demand, a norm-based fuzzy set is proposed to describe the probability distribution of uncertain demand. Given the carbon emission reduction and trading policies, a two-stage robust optimization model for supply logistics network design is constructed to optimize the number and scale of distribution centers and the multi-mode transportation scheme of products. Based on the classic three-level network planning, the model comprehensively considers the distribution center construction cost, transportation cost, product shortage cost, and the negative utility of carbon emission trading to minimize the total cost. Considering the separability of the model, this paper reconstructs the main model and submodels and proposes a solution method based on column and constraint decomposition. Finally, the validity of the proposed robust optimization model and decomposition algorithm is verified by a practical case.
   The numerical results show that the proposed distributed robust optimization method can improve the robustness of the decision scheme and reduce its investment effectively. The greater the demand uncertainty, the greater the number and scale of distribution centers expected to be built, which in turn increases the corresponding expected construction costs, transportation costs, carbon acquisition, and total costs. In order to realize the carbon emission reduction target, government departments can encourage enterprises to implement low-carbon production planning and operation in combination with policies such as subsidies for low-carbon transport modes. It is also important to strengthen the supervision of carbon emissions and assess the emission reduction performances under different incentive measures. When the carbon quota is abundant, enterprises should pay more attention to reducing the transportation cost. And when the quota is scarce, the focus will be on how to reduce transport carbon emissions.

Key words: supply chain logistics network, uncertain demand, low-carbon policy, robust optimization