Abstract: This paper focuses on the vessel scheduling problem of container liner shipping with sea contingency time. The proportional coefficient of navigation buffer time on each leg was established based on the empirical data of sea contingency time. The optimal speed for vessel sailing time segmentation interval on each leg with the least fuel consumption was solved using the continuous optimal control principle. Considering the collaborative agreement with multiple vessel arrival time windows, multiple start and end times, and multiple handling rates at ports of call, this study proposed a mixed integer nonlinear programming robust optimization model of liner shipping schedule design with sea contingency time. The goal of the model was minimizing total liner shipping service cost. A piecewise discretization linear approximation algorithm was applied to solve the proposed model. Taking the AWE1 route as an example, the numerical values from 100 scenarios were used in the simulation verification. The results show that the vessel scheduling considering sea contingency time and collaborative agreement can reduce the total cost of liner shipping services by respectively 14.65% and 3.54%, compared to the scheduling without considering sea contingency time and collaborative agreement. The results also indicate that the vessel scheduling of liner shipping plays an important role on routes or during the seasons where severe weather and sea conditions have a great impact on the navigation of vessels. The scheduling considering sea contingency time and collaborative agreement can achieve benefits for the involved carrier, ports and shippers.

Key words: water transportation, vessel scheduling, sea contingency time, collaborative agreement, robust optimization

摘要： 针对考虑海上意外时间的集装箱班轮运输船期设计问题，依据海上意外时间经验数据，设 置航行缓冲时间比例系数。运用连续最优控制原理，求解各航段船舶航行时间细分区间上燃油 消耗最小的优化航速。结合多时间窗、多起讫时刻和多挂靠港口装卸效率合作协议，以班轮运输 服务总成本最小为目标，构建班轮运输船期设计非线性混合整数规划鲁棒优化模型，设计分段离 散化线性逼近算法求解模型。以AWE1(远东-美东1)航线为例，运用100个场景的数值进行模拟 验证。结果显示：与不考虑海上意外时间或无合作协议相比，考虑海上意外时间和合作协议的班 轮运输船期设计分别降低班轮运输服务总成本14.65%和3.54%。研究表明，在恶劣天气和海况 对船舶航行影响较大的航线上或季节里，基于合作协议，设计考虑航行意外时间的鲁棒性船期， 可实现船公司、港口和客户三方共赢。

关键词: 水路运输, 船期设计, 海上意外时间, 合作协议, 鲁棒优化