带时间窗的厢式货车与助力车组合路径规划问题：建模、变种及求解方法
The Combined Van-and-Mopeds Routing Problem with Time Windows: Formulation, Variants, and Solution Methods
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中文总结 AI 辅助
研究带时间窗的厢式货车与助力车组合路径规划问题，提出MILP公式及扩展变种，用字典序两阶段优化框架并结合图稀疏化技术，还开发CBCR启发式算法，能求解不同规模实例，扩展了问题可处理性。
中文摘要 AI 辅助
我们引入并研究了带时间窗的厢式货车与助力车组合路径规划问题（CVMRPTW），这是一种异构车队车辆路径规划问题的新变种，由欧洲密集城市的最后一英里包裹配送所激发。在CVMRPTW中，一辆厢式货车作为移动基地，按需部署助力车以到达厢式货车无法到达或效率低下区域的客户。主要目标是在保证满足所有交付时间窗的同时，尽量减少助力车的使用数量。我们提出了一种混合整数线性规划（MILP）公式，通过22个结构化约束族来捕捉车辆同步、容量跟踪和时间窗合规性，并将其扩展到三个具有实际操作动机的变种：标准模型、主动等待厢式货车变种和公共仓库变种。一个字典序两阶段优化框架允许在不牺牲主要目标的情况下优化次要目标——路径持续时间、组合行驶时间和组合距离。三种图稀疏化预处理技术可将变量和约束的数量减少多达25%。对于超出精确求解器实际限制的实例，我们开发了基于聚类的组合路径规划（CBCR）启发式算法，该算法将问题分解为聚类阶段、聚类级精确求解和路径重建阶段。对来自里斯本和斯图加特的OpenStreetMap数据的实际实例进行的计算实验表明，MILP可在一小时内将多达48个客户的实例求解到可行性，并且CBCR启发式算法在有利条件下可将可处理性扩展到多达80个客户的实例。
英文摘要
We introduce and study the Combined Van-and-Mopeds Routing Problem with Time Windows (CVMRPTW), a novel variant of the heterogeneous fleet vehicle routing problem motivated by last-mile parcel delivery in dense European cities. In the CVMRPTW, a single van serves as a mobile base from which on-demand mopeds are deployed to reach customers located in areas inaccessible or inefficient for vans. The primary objective is to minimise the number of mopeds used while guaranteeing that all delivery time windows are met. We propose a Mixed-Integer Linear Programming (MILP) formulation that captures vehicle synchronisation, capacity tracking, and time-window compliance through 22 structured constraint families, and extend it to three operationally motivated variants: the standard model, the active-waiting-van variant, and the common-depot variant. A lexicographic two-stage optimisation framework allows secondary objectives-route duration, combined travel time, and combined distance-to be optimised without sacrificing the primary objective. Three graph-sparsification preprocessing techniques reduce the number of variables and constraints by up to 25%. For instances beyond the practical limits of exact solvers, we develop the Cluster-Based Combined Routing (CBCR) heuristic, which decomposes the problem into a clustering phase, a cluster-level exact solve, and a route-reconstruction phase. Computational experiments on real-world instances derived from OpenStreetMap data for Lisbon and Stuttgart show that the MILP solves instances with up to 48 customers to feasibility within one hour, and that the CBCR heuristic extends tractability to instances with up to 80 customers under favourable conditions.
