In this study, we propose a container slot allocation problem for a liner shipping service. A liner containership provides a regular shipping service with a fixed itinerary and schedule. In practice, the liner containership may not be fully loaded, which results in a loss of revenue. We therefore segment shippers into two classes: contract shippers and spot shippers. A contract shipper has a contract with the shipping company and negotiates a fixed minimum quantity, so that the shipping company can secure a steady revenue. The remaining containership slots are open to spot shippers, allowing the shipping company to obtain ad hoc revenue. The container slot allocation problem is investigated in this study using a two-stage stochastic mixed-integer nonlinear programming model. We use the sample average approximation based on Lagrangian relaxation and dual decomposition techniques to effectively solve the model. Finally, we conduct a case study to evaluate the applicability and effectiveness of the proposed model and the solution algorithm.

在这项研究中，我们提出了班轮运输服务的集装箱舱位分配问题。班轮集装箱船提供具有固定行程和时间表的定期运输服务。在实践中，班轮集装箱船可能不会满载，从而导致收入损失。因此，我们将托运人分为两类：合同托运人和现货托运人。合同托运人与船公司签订合同，协商固定的最低数量，以便船公司获得稳定的收入。剩余的集装箱船位对现货托运人开放，使航运公司获得临时收入。本研究使用两阶段随机混合整数非线性规划模型研究集装箱槽位分配问题。我们使用基于拉格朗日松弛和对偶分解技术的样本平均近似来有效地求解模型。最后，我们进行了一个案例研究，以评估所提出的模型和求解算法的适用性和有效性。