面向 “最后一公里” 的卡车-无人机协同配送路径建模综述
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四川大学商学院

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TP391.9;F259.2

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A Review of Mathematical Models for Vehicle Routing Problem with Drones in Last Mile Delivery
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    摘要:

    本文综述了面向“最后一公里”的卡车-无人机协同配送优化建模研究进展,构建了“场景驱动-参数刻画-建模基础-模型拓展”一体化综述框架。首先,梳理快递、即时与应急等典型配送场景的车机协同特征与差异化需求,揭示不同场景对模型优化目标侧重与约束优先级的影响;其次,总结资源与运行、时间与能耗、路网与需求等核心参数的刻画方式,阐明其对可行域边界、协同强度,以及成本与能耗结构的作用;接着,构建覆盖基础协同模式、优化目标和约束体系的分类框架与建模单元;最后,对多主体、异构、动态、不确定、多点访问、同时取送货、需求可拆分及多配送中心等扩展模型进行对照分析。综述表明,现有研究仍存在若干关键不足:不同配送场景的订单结构、服务承诺与组织流程尚未清晰映射到协同模式、目标口径与约束模块的选择;参数刻画偏静态同质且对交通、气象、空域、需求波动等现实因素的响应不足;运营过程、平台规则、政策监管与多维目标权衡的刻画尚不充分;拓展模型关键假设、同步规则与可行域结构等方面缺少统一表达。未来可面向场景-模型映射、动态与情景相关参数体系、贴近运营的目标-约束一体化建模、关键假设与同步规则的统一表达,以及模块化可复用建模构件等方向进行深化。

    Abstract:

    This paper reviews the modelling progress of the vehicle routing problem with drones (VRPD) for last-mile delivery, and proposes an integrated review framework structured around four pillars: scenario drivers, parameter characterization, modelling fundamentals and model extensions. First, it examines the heterogeneous truck-drone collaborative characteristics and differentiated optimization requirements across representative last mile delivery scenarios, including express parcel delivery, instant delivery, and emergency delivery. Second, this paper summarizes the main description approaches for core parameters of resources and operations, time and energy, and road networks and demand, elucidating their roles in shaping feasibility boundaries, collaboration intensity, and cost/energy structures. Next, it develops a taxonomy and reusable modelling building blocks covering optimization objectives, constraint systems, and collaboration structures. Finally, this paper conducts a comparative analysis of key model extensions, including multi-truck and multi-drone VRPD, heterogeneous VRPD, dynamic VRPD, stochastic VRPD, multi-visit VRPD, split-delivery VRPD, pickup and delivery VRPD, multi-depot VRPD. The review indicates several common gaps in the literature: the demand structures, service commitments, and operational processes of different delivery scenarios have not yet been clearly mapped to the selection of collaboration modes, objective formulations, and constraint modules; parameter characterization is often static and homogeneous and responds inadequately to fluctuations in traffic, weather, airspace availability, and demand; operational processes, platform rules, regulatory constraints, and multi-dimensional objective trade-offs are still insufficiently modelled; and extended models still lack unified expressions for key assumptions, synchronization rules, and feasibility structures. Future research should therefore focus on strengthening scenario-to-model mappings, developing dynamic parameter systems, integrating objectives and constraints with real operational mechanisms, standardizing the expression of critical assumptions and synchronization rules, and constructing modular, reusable modelling components.

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  • 收稿日期:2026-01-03
  • 最后修改日期:2026-04-18
  • 录用日期:2026-04-21
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