The berth allocation problem (BAP) has been extensively studied in the literature, which seeks to determine berths and times for upcoming ships. The previous studies do not distinguish berths and ships among different liner carriers. By taking into account the increasing use of dedicated berths in practice, this paper proposes a special BAP where berths and ships could be distinguished among different liner carriers. For our BAP under a cooperative environment, we propose a mixed-integer programming model. Based on an assignment model with binary variables, our BAP can be reduced to the liner carrier clustering problem. To generate stable liner carrier clusters used in our assignment model, queueing theory and core theory are applied. A three-stage optimization method is proposed to solve our BAP. Namely, stage I proposes a queueing theory approach for various liner carrier clusters, and based on core theory stage II determines the stability of different liner carrier clusters. Based on the results obtained in stages I and II, stage III solves the liner carrier clustering problem. Numerical experiments are carried out to demonstrate the effectiveness of the proposed method.

泊位分配问题 (BAP) 已在文献中进行了广泛研究，旨在确定即将到来的船舶的泊位和时间。以前的研究没有区分不同班轮运输船之间的泊位和船舶。考虑到在实践中越来越多地使用专用泊位，本文提出了一种特殊的 BAP，可以在不同的班轮承运人之间区分泊位和船舶。对于合作环境下的 BAP，我们提出了混合整数编程模型。基于具有二元变量的分配模型，我们的 BAP 可以简化为线性载波聚类问题。为了生成我们的分配模型中使用的稳定线性载波集群，应用了排队理论和核心理论。提出了一种三阶段优化方法来解决我们的 BAP。即，第一阶段提出了各种班轮航母集群的排队理论方法，第二阶段基于核心理论确定了不同航母集群的稳定性。基于阶段 I 和 II 获得的结果，阶段 III 解决了线性载波聚类问题。进行数值实验以证明所提出方法的有效性。