This paper studies the vessel fleet deployment problem for liner shipping under uncertain shipment demands. The aim is to minimize the sum of vessel chartering cost and route operating cost, while controlling the risk of shipment demand overflow, i.e., the risk of demand exceeding the shipping capacity. We use moment knowledge to construct an ambiguous set to portray the unknown probability distributions of the demands. We establish chance constraints with risk tolerance for shipping service routes, in a distributionally robust (DR) framework. We propose a mixed integer programming reformulation to approximate the concerned problem with DR chance constraints. We show that the state-of-the-art approach is a special case of our designed approximation method, and we prove the sufficient and necessary conditions such that our approximation method outperforms the state-of-the-art approach, respecting the given risk level. We conduct numerical experiments to demonstrate the advantages of our approximation method. We also show that our novel approximation approach can significantly save the total cost.

本文研究了不确定运输需求下班轮运输的船队部署问题。目的是在控制装运需求溢出风险（即，需求超过装运能力的风险）的同时，将船舶租赁费用和航线运营成本的总和最小化。我们使用矩知识来构造一个模棱两可的集合，以刻画需求的未知概率分布。在分布稳健（DR）的框架中，我们为运输服务路线建立了具有风险承受能力的机会约束。我们提出了一种混合整数规划的重构方法，以近似解决具有DR机会约束的相关问题。我们表明，最先进的方法是我们设计的近似方法的特例，并且我们证明了充分必要的条件，以便在考虑到给定风险水平的前提下，我们的近似方法优于最新方法。我们进行数值实验以证明我们的近似方法的优点。我们还表明，我们新颖的近似方法可以大大节省总成本。