This paper investigates a new variant of the consistent vehicle routing problem considering path consistency based on the underlying road network (ConVRP${}_{RN}$). It is the problem of determining a set of consistent paths for vehicles within a certain period (e.g. a week). We propose a flexible strategy to achieve path consistency, providing a discount for the cost of roads that are traversed every day. The objective is to minimize the total travel costs considering the discount for the paths’ consistent parts. We formulate the problem as a set partitioning model and a general arc-flow model, and then solve the problem by a branch-price-and-cut algorithm. The algorithm is based on a two-layer network, including an underlying road-network graph (lower layer) and a serial of customer-based graphs (upper layer). Furthermore, an innovative aggregation technique is proposed to accelerate the algorithm, which is specifically designed for ConVRP${}_{RN}$. Finally, we construct a road network based on the real road-network structure of West Jordan and demonstrate the effectiveness of our approach on a set of numerical experiments. The impact of consistency discount is also analyzed to provide information and inspiration for tactical decision making.

本文研究了基于基础道路网络 (ConVRP) 的考虑路径一致性的一致车辆路径问题的新变体${}_{\mathrm{电阻}N}$）。这是在一定时期（例如一周）内为车辆确定一组一致路径的问题。我们提出了一种灵活的策略来实现路径一致性，为每天经过的道路成本提供折扣。考虑到路径一致部分的折扣，目标是最小化总旅行成本。我们将问题表述为集合划分模型和一般弧流模型，然后通过分支价格和切割算法解决问题。该算法基于两层网络，包括底层道路网络图（下层）和一系列基于客户的图（上层）。此外，提出了一种创新的聚合技术来加速算法，这是专门为 ConVRP 设计的${}_{\mathrm{电阻}N}$. 最后，我们基于 West Jordan 的真实道路网络结构构建了一个道路网络，并在一组数值实验中证明了我们的方法的有效性。还分析了一致性折扣的影响，为战术决策提供信息和启发。