The Maritime Inventory Routing Problem (MIRP) has gained attention in combinatorial optimization in the last decades. The problem has several variations, mostly originated from real-world problems. This work presents a literature review of the solution approaches proposed for different MIRP variations, focusing on matheuristic methods that combine heuristic and optimal approaches and are frequently used to solve MIRPs. This work also studies the use of Relax-and-Fix and Fix-and-Optimize matheuristics for solving a specific MIRP variant proposed in the literature. The proposed algorithms were tested over two discrete-time formulations for which different components such as valid inequalities and additional constraints were proposed. Several computational tests were performed to evaluate the contribution of the formulation components and algorithms features on the solution quality and processing time. An automatic configuration tool was used to define the parameter values for the algorithms, as well as the choice of the formulation components to be used in the tests. The results demonstrated that the proposed algorithms are potentially effective for solving the MIRP when applied to a public dataset, obtaining three new best-known solutions from a total of twenty-eight instances.

在过去的几十年里，海上库存路由问题（MIRP）在组合优化中受到了关注。该问题有多种变体，主要源自现实世界的问题。这项工作对针对不同 MIRP 变体提出的解决方法进行了文献综述，重点介绍了结合启发式和优化方法并经常用于解决 MIRP 的数学方法。这项工作还研究了使用 Relax-and-Fix 和 Fix-and-Optimize 数学算法来解决文献中提出的特定 MIRP 变体。所提出的算法在两个离散时间公式上进行了测试，其中提出了不同的组件，例如有效的不等式和附加约束。进行了多项计算测试以评估配方组件和算法特征对解决方案质量和处理时间的贡献。自动配置工具用于定义算法的参数值，以及测试中使用的配方组件的选择。结果表明，当应用于公共数据集时，所提出的算法对于解决 MIRP 可能有效，从总共 28 个实例中获得三个新的最知名的解决方案。