The multidepot vehicle scheduling problem (MDVSP) is a fundamental public transport challenge. To address the large‐scale model and inherent solution symmetry associated with the traditional trip‐to‐trip connection‐based approach for MDVSP, a new trip‐to‐route (T2R) connection‐based approach is proposed. Considering real‐world problem characteristics with numerous trips sharing common origin–destination stations and travel times on one route, this approach aggregates same vehicle possible trip sequences into a T2R connection. Two time‐space network aggregation (TSNA) flow formulation versions, route pair‐based TSNA and station pair‐based TSNA, were constructed. Furthermore, TSNA equivalence under any given decomposition strategy, including first‐in‐first‐out, with the multicommodity network flow (MCNF) model was demonstrated. Given the favorable separable TSNA structure, an alternating direction method of multipliers (ADMM)‐based procedure is proposed to decompose the MDVSP into multiple subproblems that can be linearized and readily solved using commercial solvers. The quality of the solutions was assessed using lower bounds obtained from the Lagrangian relaxation problem. The effectiveness and superiority of the proposed MDVSP models and algorithms were subsequently confirmed using random data sets and real‐world instances.

中文翻译：

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现场多站点车辆调度场景的聚合制定

多站点车辆调度问题（MDVSP）是一个基本的公共交通挑战。为了解决与 MDVSP 传统的基于行程到行程连接的方法相关的大规模模型和固有解对称性，提出了一种新的基于行程到路线 (T2R) 连接的方法。考虑到现实世界的问题特征，即一条路线上的众多行程共享共同的起点站-目的地站和行程时间，这种方法将相同的车辆可能的行程序列聚合到 T2R 连接中。构建了两种时空网络聚合（TSNA）流公式化版本：基于路径对的 TSNA 和基于站对的 TSNA。此外，还证明了在任何给定的分解策略（包括先进先出）下，TSNA 与多商品网络流 (MCNF) 模型的等效性。考虑到有利的可分离 TSNA 结构，提出了一种基于乘子交替方向法 (ADMM) 的过程，将 MDVSP 分解为多个子问题，这些子问题可以线性化，并且可以使用商业求解器轻松求解。使用从拉格朗日松弛问题获得的下限来评估解的质量。随后使用随机数据集和现实世界实例证实了所提出的 MDVSP 模型和算法的有效性和优越性。