This paper investigates a reliable ship fleet planning problem with the uncertainties of container shipping demand, transport costs and freight rates in liner shipping services, and this problem is formulated as a two-stage robust optimization model. In our model, the first-stage decision is to determine the types and quantities of ships, as well as their allocation to different routes, and the second-stage is to fulfill container shipping demand after uncertain information is revealed. Compared to the models proposed in existing researches, our model involves multiple uncertainties aforementioned, and it can also capture the correlation between demand and freight rates. Due to the difficulty of directly solving the two-stage robust optimization model, the column-and-constraint generation algorithm and the benders-dual cutting plane algorithm are developed to address this model. Based on a real shipping network case, extensive computational experiments are conducted to test the practical significance of the presented model and the applicability of our algorithm. The computational results indicate that considering multiple uncertainties simultaneously can significantly save the worst-case costs, demonstrating that the developed two-stage robust optimization model provides a valuable decision-making reference for liner companies seeking to enhance the reliability of ship fleet planning.

中文翻译：

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班轮运输服务的可靠船队规划问题


本文研究了班轮服务中集装箱运输需求、运输成本和运价的不确定性，研究了可靠的船队规划问题，并将该问题表述为两阶段鲁棒优化模型。在我们的模型中，第一阶段的决策是确定船舶的类型和数量，以及它们对不同航线的分配，第二阶段是在不确定信息泄露后满足集装箱运输需求。与现有研究中提出的模型相比，我们的模型涉及上述多种不确定性，并且它还可以捕捉需求和运费之间的相关性。由于难以直接求解两阶段鲁棒优化模型，该文开发了 column-and-constraint 生成算法和 benders-dual cutting plane 算法来解决该模型的问题。基于真实的航运网络案例，进行了大量的计算实验，以检验所提模型的实际意义和我们算法的适用性。计算结果表明，同时考虑多个不确定性可以显著节省最坏情况的成本，表明所开发的两阶段鲁棒优化模型为寻求提高船队规划可靠性的班轮公司提供了有价值的决策参考。