This study addresses an interesting tugboat scheduling problem considering uncertainty in both container ship arrival and tugging process times for large container ports. The uncertain ship arrival and tugging process times are formulated as a finite set of discrete scenarios that can be generated from historical port traffic data. We deal with the uncertainty by integrating proactive and reactive scheduling strategies such that this study is distinct from most existing studies in the literature. The proactive scheduling strategy considers the expected degree of variability and uncertainty during the execution of a tugboat fleet schedule while the reactive scheduling strategy properly adjusts the initial schedule to cope with unexpected scenarios with minimum recovery cost. A mixed-integer linear programming model for the proposed tugboat scheduling problem is established. For a large-scale problem, an ad-hoc algorithm is designed to generate tugging chains such that the large-scale problem can be tackled effectively. The extensive numerical experiments are finally carried out to demonstrate the practical significances of the models and algorithms developed by this study.

这项研究解决了一个有趣的拖船调度问题，考虑到大型集装箱港口的集装箱船到达和拖船过程时间的不确定性。不确定的船舶到达和拖曳过程时间被公式化为可从历史港口流量数据生成的有限离散场景集。我们通过集成主动和被动调度策略来处理不确定性，从而使该研究与文献中大多数现有研究不同。主动调度策略在执行拖船船队调度时会考虑预期的可变性和不确定性程度，而被动调度策略会适当地调整初始调度以最小的恢复成本来应对意外情况。针对提出的拖船调度问题，建立了混合整数线性规划模型。对于大规模问题，设计了一种自组织算法来生成牵引链，以便可以有效解决大规模问题。最后进行了广泛的数值实验，以证明本研究开发的模型和算法的实际意义。