Abstract: Ports, as critical hubs in global trade, are significant sources of greenhouse gas emissions in the shipping industry. The carbon trading market, as a key economic tool for emission reduction strategies, not only provides long-term stability but also imposes additional operational and cost pressures on ports. A port alliance, which fosters port integration and promotes sustainable development through inter-port cooperation, facilitates resource sharing and cross-port investment, thereby alleviating operational and cost pressures. With the strengthening of government controls on carbon emissions and the growing prevalence of port alliances, the decision-making environment for ports has become increasingly complex.
Ports can optimize their facilities through rational investment in development to enhance their handling capacity. However, cargo handling operations increase, so do carbon emissions. To meet government emission requirements, ports need to participate in the carbon trading market by purchasing carbon allowances, which incurs costs. Ports must make rational investment decisions to maximize revenue from both cargo handling and carbon trading activities.
Port investment decisions also affect the transportation strategies of shipping companies. After ports make investment decisions, the capacity of nodes in the transportation network changes, creating a new network. Shipping companies react to this new network by adjusting their container transport and transshipment plans to minimize costs. These shipping strategies, in turn, impact port revenue and carbon emissions, which subsequently influence decisions in the carbon trading market and affect carbon trading prices.
To respond to changes in port demand and reduce emission pressures, this paper considers the carbon trading mechanism for ports and the cooperative strategies within port alliances, establishing a bi-level programming model. In this model, the upper level focuses on optimizing port investment strategies to improve the demand satisfaction capacity of both ports and the shipping system, while reducing the carbon emission intensity of ports. Shipping companies, as one of the entities at the lower level, optimize their transport strategies to minimize shipping costs, while the carbon trading market, as another lower-level entity, sets carbon trading prices based on port carbon emission demand. The alliance cooperation strategy forms a multi-leader and dual-follower game among the parties. To achieve equilibrium in this game, we employ KKT conditions and a diagonalization algorithm to solve an Equilibrium Problem with Equilibrium Constraints(EPEC), which includes multiple single-leader and dual-follower problems. Each problem is formulated as a Mathematical Program with Equilibrium Constraints (MPEC). This ensures that each port makes optimal decisions based on the decision sets of other ports, with no single port able to unilaterally increase its revenue by changing its investment decisions.
Through five years of simulation experiments, it is found that ports with higher cargo handling volumes are more willing to invest in reducing their carbon emission intensity. Regarding trends in carbon trading prices, both a reduction in carbon allowance supply and a decrease in carbon emission intensity lead to higher carbon trading prices. Concerning the effectiveness of port alliances, the presence of a port alliance within a shipping network increases the demand satisfaction rate. The larger the alliance, the higher the demand satisfaction rate. However, when growth is too rapid or emission reduction targets are too ambitious, port alliances may struggle to ensure continued growth in demand satisfaction rates.

Key words: port alliance, carbon trading market, bi-level planning model, MPEC, EPEC

摘要： 随着政府碳排放控制的加强以及港口联盟的普及,港口面临的决策问题变得更加复杂。为了应对港口需求变化并缓解减排压力,本文考虑港口碳交易机制和联盟合作战略,并据此建立双层规划模型。在该模型中,上层的港口优化投资策略来提高港口及航运系统的需求满足能力并降低港口的碳排放强度,航运公司作为下层的一个主体通过优化运输方案来最小化运输成本,碳交易市场作为下层的另一个主体通过港口的碳排放需求来决策碳交易价格。联盟合作策略构成各方之间的多领导者—双追随者博弈,为达到这个博弈的均衡,我们使用KKT条件与对角化算法求解一个具有均衡约束的均衡问题(EPEC),其中包含多个单领导者—双追随者问题,每个问题都被建立为一个均衡约束规划问题(MPEC)。经过5年期的模拟实验,发现在同等资源下,港口联盟在提高港口需求满足率、实现减排目标方面具有较好的效果。

关键词: 港口联盟, 碳交易市场, 双层规划模型, MPEC, EPEC