Liner shipping companies need to satisfy the shipping demand from both the long-term contracts and the spot market. In general, the container shipping demand of the long-term contract has more stable volumes but lower freight rates compared with the spot market demand. It is thus a critical problem for the shipping companies how to provide discriminative shipping services to these two types of shipping demand through contract selection and container slot allocation to simultaneously increase the shipping profit and control its variations resulting from the demand variations. To handle this problem, a two-stage stochastic programming model is constructed in this paper which adopts the Conditional-Value-at-Risk (CVaR) to measure the profit variations. In the first stage, the shipping company selects the long-term contracts from a candidate contract set to sign with customers under the uncertainties in the show-up rates of containers in long-term contracts, and the volumes and the freight rates of the spot market demands. In the second stage, after all uncertainties have been realized, the shipping company determines the slot allocation for both the contract and spot demands. With the introduction of the CVaR, classical Benders decomposition cannot be directly applied to solve the risk-averse model. This paper thus develops a risk-averse Benders decomposition method tailored for the model. Numerical experiments are also conducted to verify the effectiveness of the solution method and provide some meaningful managerial insights.

班轮运输公司需要同时满足长期合同和现货市场的航运需求。总体而言，长期合约的集装箱海运需求相比现货市场需求量量较为稳定，但运价较低。因此，如何通过合同选择和集装箱舱位分配，为这两种航运需求提供有区别的航运服务，同时增加航运利润并控制因需求变化而导致的航运利润变化，是航运公司面临的一个关键问题。为了解决这个问题，本文构建了一个两阶段随机规划模型，该模型采用条件风险价值（CVaR）来衡量利润变化。在第一阶段，航运公司在长期合同中集装箱到场率、现货市场需求量和运价等不确定性的情况下，从候选合同集中选择长期合同与客户签订。在第二阶段，在所有不确定性都已实现后，船公司根据合同和现货需求确定舱位分配。随着 CVaR 的引入，经典的 Benders 分解不能直接应用于解决风险规避模型。因此，本文开发了一种为模型量身定制的风险规避 Benders 分解方法。还进行了数值实验以验证解决方法的有效性并提供一些有意义的管理见解。