This paper studies the integration of the vehicle routing problem with cross-docking (VRPCD). The aim is to find a set of routes to deliver products from a set of suppliers to a set of customers through a cross-dock facility, such that the operational and transportation costs are minimized, without violating the vehicle capacity and time horizon constraints. A two-phase matheuristic based on column generation is proposed. The first phase focuses on generating a set of feasible candidate routes in both pickup and delivery processes by implementing an adaptive large neighborhood search algorithm. A set of destroy and repair operators are used in order to explore a large neighborhood space. The second phase focuses on solving the set partitioning model to determine the final solution. The proposed matheuristic is tested on the available benchmark VRPCD instances and compared with the state-of-the-art algorithms. Experimental results show the competitiveness of the proposed matheuristic as it is able to improve the best known solutions for 80 instances and to obtain the same results for the remaining 10 instances, with an average improvement of 12.6%. On new and larger instances, our proposed matheuristic maintains its solution quality within acceptable CPU times and outperforms a pure ALNS algorithm. We also explicitly analyze the performance of the matheuristic considering the solution quality and CPU time.

本文研究了车辆选路问题与跨站台（VRPCD）的集成。目的是找到一条路线，通过跨码头设施将产品从一组供应商交付给一组客户，从而使运营和运输成本最小化，而又不会违反车辆容量和时间限制。提出了一种基于列生成的两阶段数学方法。第一阶段着重于通过实现自适应大邻域搜索算法，在提取和交付过程中生成一组可行的候选路线。为了探索较大的邻里空间，使用了一组销毁和修复操作员。第二阶段着重于解决集合划分模型以确定最终解决方案。建议的数学模型在可用的基准VRPCD实例上进行了测试，并与最新算法进行了比较。实验结果表明了所提出的数学方法的竞争力，因为它能够针对80个实例改进最著名的解决方案，并针对其余10个实例获得相同的结果，平均提高12.6％。在新的和更大的实例上，我们提出的数学方法可在可接受的CPU时间内保持其解决方案质量，并且性能优于纯ALNS算法。我们还考虑解决方案质量和CPU时间来明确分析数学性能。实验结果表明了所提出的数学方法的竞争力，因为它能够针对80个实例改进最著名的解决方案，并针对其余10个实例获得相同的结果，平均提高12.6％。在新的和更大的实例上，我们提出的数学方法可在可接受的CPU时间内保持其解决方案质量，并且性能优于纯ALNS算法。我们还考虑解决方案质量和CPU时间来明确分析数学性能。实验结果表明了所提出的数学方法的竞争力，因为它能够针对80个实例改进最著名的解决方案，并针对其余10个实例获得相同的结果，平均提高12.6％。在新的和更大的实例上，我们提出的数学方法可在可接受的CPU时间内保持其解决方案质量，并且性能优于纯ALNS算法。我们还考虑解决方案质量和CPU时间来明确分析数学性能。