Container terminals play a vital role as representative logistic facilities for contemporary trade by handling outbound, inbound, and transshipment containers to and from the sea and hinterland. The increasing number of containers and vessels poses new challenges to port management and resource scheduling, because of scarce land, high labour cost, and limited technical equipment. This study investigates the berth allocation planning problem at a tactical level considering uncertain operation time. Based on the historical data, we formulate a data-driven expanded robust optimisation model to minimise the total cost of deviations between the planned and expected berthing time of the vessel. To solve the model, we firstly use $K$-means clustering to construct the uncertainty set. Secondly, we present a column-and-constraint generation algorithm to solve the model. Extensive computational experiments are conducted to verify the effectiveness of the proposed model and algorithm. Experiment results show that the proposed model can not only guarantee the out-of-sample performance, which overcomes the vulnerability of the sample average approximation approach but also avoid the over-conservatism of the traditional robust optimisation model.

集装箱码头通过处理往来于海洋和腹地的出站，入站和转运集装箱，在当代贸易中扮演着重要的后勤设施的角色。由于土地稀缺，劳动力成本高和技术设备有限，集装箱和船只数量的增加对港口管理和资源调度提出了新的挑战。这项研究考虑了不确定的运营时间，在战术层面上研究了泊位分配计划问题。根据历史数据，我们制定了一个数据驱动的扩展鲁棒优化模型，以最大程度地减少船舶计划停泊时间与预期停泊时间之间的总成本。为了解决模型，我们首先使用$ķ$-均值聚类以构造不确定性集。其次，我们提出了一种列约束生成算法来求解该模型。进行了大量的计算实验，以验证所提出的模型和算法的有效性。实验结果表明，该模型不仅可以保证样本外性能，克服了样本均值逼近方法的脆弱性，而且避免了传统鲁棒优化模型的过度保守性。