公共交通承载货运的建模框架与优化算法综述

A Review of Modeling Frameworks and Optimization Approaches for Freight on Transit in Public Transport

摘要: 随着城市末端物流配送需求规模的持续扩张与服务时效要求的不断提高，传统以路面车辆为主的配送体系正面临运营成本攀升、交通拥堵加剧及环境负外部性显著等系统性挑战。在此背景下，利用城市公共交通系统剩余运力进行货运(Freight on Transit, FoT)作为一种集约、可持续的协同配送模式受到广泛关注。然而，现有研究在运输组织模式的界定与定量分析框架方面仍较为分散，缺乏系统性整合与模式间的比较分析。为此，本文对FoT领域的定量研究文献进行系统性梳理与整合。首先，界定了FoT系统的三阶段流程与四类核心运营要素，并据此归纳出五类典型运输组织模式，系统比较各模式的流程结构、协同机制、优势、局限及适用场景。其次，依据战略、战术与操作层级，梳理并归类出现有研究聚焦的选址分配、列车调度与路径规划三类核心优化问题，综述各类问题的数学建模方法、求解算法及其在不同模式中的研究侧重点。最后，总结现有研究的共识与不足，并展望未来研究方向，包括多模式统一建模、多层级决策耦合建模，以及不确定环境下动态调度机制的引入。研究结果为城市公共交通与末端物流系统的协同设计与优化提供了理论框架，也为高效、低碳的城市货运方案设计提供了参考。

Abstract: With the continuous expansion of urban last-mile logistics demand and increasingly stringent service time requirements, traditional delivery systems relying primarily on road vehicles face systemic challenges, including rising operational costs, worsening traffic congestion, and significant environmental externalities. In this context, utilizing the residual capacity of urban public transport systems for freight transport, known as Freight on Transit (FoT), has attracted widespread attention as an intensive and sustainable collaborative delivery mode. However, existing studies remain fragmented regarding the definition of transport organization patterns and quantitative analysis frameworks, lacking systematic integration and comparative evaluation across modes. This paper provides a systematic review and synthesis of quantitative research in the FoT domain. First, it delineates a three-stage process of FoT systems and identifies four core operational elements, based on which five typical transport organization patterns are summarized, with a systematic comparison of their process structures, coordination mechanisms, advantages, limitations, and applicable scenarios. Second, guided by strategic, tactical, and operational decision levels, the literature is classified into three core optimization problems: facility location and allocation, train scheduling, and routing. For each problem, the review summarizes existing mathematical modeling approaches, solution algorithms, and research emphases in different organizational patterns. Finally, the paper highlights consensus and gaps in current research and outlines future research directions, including unified multi-modal modeling, hierarchical decision coupling, and the incorporation of dynamic scheduling mechanisms under uncertainty. The findings provide a theoretical framework for the collaborative design and optimization of urban public transport and last-mile logistics systems, offering references for the development of efficient and low-carbon urban freight solutions.