排放控制区下集装箱班轮运输船期设计与燃油补给联合优化

为解决排放控制区下集装箱班轮运输船期设计和燃油补给联合优化问题，分析了多时间窗、多起讫时间和多装卸效率等合作协议条款与船舶航行、装卸及到/离港时间之间的关联性。结合燃油补给港燃油价格差异和折扣因素，以船公司航线服务周总成本最小化为目标，构建排放控制区下船期设计和燃油补给混合整数非线性规划模型，设计线性割线近似的求解方法。以中远海运集团有限公司AWE1航线为例，数值实验验证了模型及其求解方法的适用性和有效性。结果显示：船期设计与燃油补给联合优化可使船公司航线服务周总成本降低7.41%；随着船舶到港时间窗长度的增大，船公司航线服务周总成本及船舶在排放控制区内平均航速均随之降低。研 究表明，上述合作协议条款不仅有助于船公司更为灵活地调整船舶航速和船期，还有利于减少船舶在排放控制区内的温室气体排放。

Joint Optimization of Vessel Scheduling and Refueling for Container Liner Shipping in Emission Control Areas

This paper investigates the vessel scheduling and refueling for container liner shipping in emission control areas. The relationship between the terms of cooperation agreements was analyzed including multiple time windows, multiple start/end times, multiple loading/unloading rates, and the time of vessel sailing, loading/unloading, and arrival/ departure. In accordance with the factors of fuel price differentiation and its discount at different ports, the vessel scheduling and refueling problem with emission control was formulated as a mixed integer non-linear programming model, which has the goal of minimum total weekly route service cost of liner shipping. The linear secant approximation was also designed to solve the model. Taking the AWE1 route served by China COSCO Shipping Corporation Limited as an example, the paper verified the applicability and effectiveness of the model and the solution method by numerical experiments. The results show that the joint optimization of vessel scheduling and refueling of liner shipping would reduce the total weekly route service cost by 7.41%. The total weekly route service cost and the average vessel sailing speed in emission control areas would decrease with the increase of the length of vessel arrival time window. The result indicates that the terms of cooperation agreement would not only help shipping companies to adjust vessel sailing speed and schedule with more flexibility, but also help reducing vessels’greenhouse gas emissions in emission control areas.