Liner container shipping company satisfies container shipping demand from both long-term contracts and spot market. Different from the shipping demand from long-term contracts whose freight rate is usually negotiated between the shipping company and the customer, the freight rate of the spot demand is usually determined by the shipping company itself. This paper thus focuses on how to determine the optimal freight rate of spot containers for each origin and destination (OD) pairs of a shipping network to maximize the total profit. To further reflect industry practice, two types of uncertainties are considered, i.e., the uncertain spot demand volume due to stochastic slot booking arrivals and cancelations, and the uncertain remaining ship capacity for the spot demand after satisfying other demand types with higher priority (e.g. delayed containers). This problem is first formulated as a two-stage stochastic nonlinear and nonconvex programming model. A tailored spatial branch-and-bound-and-Benders algorithm is then developed to obtain the global optimal solution of the model. Numerical experiments also demonstrate the efficiency of the solution algorithm and the applicability of the proposed model in improving the profit from the spot shipping demand.

班轮集装箱运输公司可以满足长期合同和现货市场的集装箱运输需求。不同于长期合同的运输需求，后者通常是由运输公司和客户之间协商运费的，现货需求的运费通常是由运输公司自己确定的。因此，本文着重于如何为运输网络的每个始发地和目的地（OD）对确定现货集装箱的最佳运费，以最大程度地提高总利润。为了进一步反映行业实践，考虑了两种类型的不确定性，即，由于随机定舱预订的到来和取消而导致的现货需求量不确定，以及在满足其他优先级更高的需求类型（例如延迟）之后，现货需求的剩余剩余运力不确定。容器）。首先将该问题表述为两阶段随机非线性和非凸规划模型。然后，开发了量身定制的空间分支定界弯曲算法，以获得模型的全局最优解。数值实验还证明了求解算法的效率以及所提模型在提高现货运输需求利润中的适用性。