Maritime transportation forms the backbone of the world merchandise trade. In this paper, we consider a problem that combines three interconnected subproblems in tramp shipping: the fleet adjustment problem, the cargo selection problem, and the ship routing problem. For cargo selection, we consider the decision behaviors under the setting of Contract of Affreightment (COA), in which cargoes should be rejected or accepted as a batch. In view of the uncertainties observed in maritime transportation, we formulate the problem in a robust way so that the solutions can protect the profitability of shipping companies against variations in voyage costs. We first provide compact mixed integer linear programming formulations for the problem and then convert them into a strengthened set covering model. A tailored branch-and-price-and-cut algorithm is developed to solve the set covering model. The algorithm is enhanced by a multi-cut generation technique aimed at tightening the lower bounds and a primal heuristic aimed at finding high-quality upper bounds. Extensive computational results show that our algorithm yields optimal or near-optimal solutions to realistic instances within short computing times and that the enhancement techniques significantly improve the efficiency of the algorithm.

海上运输是世界商品贸易的支柱。在本文中，我们考虑的问题是流浪运输中三个相互联系的子问题：车队调整问题，货物选择问题和船舶选路问题。对于货物的选择，我们考虑在货运合同（COA）设置下的决策行为，在这种行为中，应拒绝或接受一批货物。鉴于海上运输中存在不确定性，我们以强有力的方式提出问题，以便解决方案可以保护船公司的利润率不受航行成本变化的影响。我们首先为问题提供紧凑的混合整数线性规划公式，然后将它们转换为增强的集合覆盖模型。开发了量身定制的分支和价格和切割算法来解决集合覆盖模型。该算法通过旨在限制下限的多割生成技术和旨在找到高质量上限的原始启发式算法得到增强。大量的计算结果表明，我们的算法可在较短的计算时间内为现实实例提供最佳或接近最优的解决方案，并且增强技术可显着提高算法的效率。