In this paper, we introduce two algorithms to address the two-echelon capacitated location-routing problem (2E-CLRP). We introduce a branch-and-cut algorithm based on the solution of a new two-index vehicle-flow formulation, which is strengthened with several families of valid inequalities. We also propose an adaptive large-neighbourhood search (ALNS) meta-heuristic with the objective of finding good-quality solutions quickly. The computational results on a large set of instances from the literature show that the ALNS outperforms existing heuristics. Furthermore, the branch-and-cut method provides tight lower bounds and is able to solve small- and medium-size instances to optimality within reasonable computing times.

中文翻译：

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两梯队有能力的位置路由问题的下限和上限

在本文中，我们介绍了两种算法来解决两梯队电容定位路由问题（2E-CLRP）。我们引入了一种基于新的双指标车流公式的解决方案的分支和切割算法，该算法通过几个有效不等式进行了加强。我们还提出了一种自适应大邻域搜索 (ALNS) 元启发式方法，目的是快速找到高质量的解决方案。文献中大量实例的计算结果表明，ALNS 优于现有的启发式算法。此外，分支和切割方法提供了严格的下界，并且能够在合理的计算时间内解决中小型实例的最优问题。