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Optimizing carbon emissions in green logistics for time-dependent routing
Transportation Research Part B: Methodological ( IF 5.8 ) Pub Date : 2025-01-24 , DOI: 10.1016/j.trb.2025.103155
Yiming Liu, Yang Yu, Roberto Baldacci, Jiafu Tang, Wei Sun

This paper considers a green vehicle routing problem termed the time-dependent green vehicle routing problem with time windows (TDGVRPTW). The TDGVRPTW is an extension of the green vehicle routing problem with time windows in green logistics. It considers time-dependent vehicle speed and aims to minimize carbon emissions. Since the travel times and carbon emissions between locations depend on the departure time from the starting location, optimizing carbon emissions requires determining the optimal departure times from the depot and customers. This paper presents a branch-price-and-cut (BPC) algorithm to solve the TDGVRPTW. The problem is formulated based on a set-partitioning model. To solve the pricing problem associated with the set-partitioning model, we first define backward non-dominated time-dependent arcs and optimal timed routes. We also introduce three types of routes, forward, backward, and patchwork optimal timed routes, and analyze their characteristics. Then, we introduce a method to adjust the times in backward and patchwork optimal timed routes from the latest to the earliest. We prove that this method guarantees correctness and effectively reduces complexity. We propose a bidirectional labeling algorithm to generate routes. The pricing problem employs state-of-the-art techniques, including limited memory subset row cuts (lm-SRCs), ng-route relaxation, and bucket graphs to enhance the algorithm’s efficiency. The BPC algorithm is tested on a set of instances derived from benchmark cases in the literature. Its various components and pricing strategies are evaluated, and its performance is compared with other algorithms from the literature. The results confirm the effectiveness of the proposed algorithm and its newly designed components in solving the TDGVRPTW.

中文翻译:


优化绿色物流中的碳排放,实现时间相关路线



本文考虑了一个绿色车辆路径问题,称为具有时间窗的瞬态绿色车辆路径问题 (TDGVRPTW)。TDGVRPTW 是绿色物流中具有时间窗的绿色车辆路径问题的扩展。它考虑了随时间变化的车速,旨在最大限度地减少碳排放。由于位置之间的行驶时间和碳排放量取决于从起始位置出发的时间,因此优化碳排放量需要确定从站点和客户出发的最佳出发时间。本文提出了一种 branch-price-and-cut (BPC) 算法来解决 TDGVRPTW。该问题是基于集合分区模型制定的。为了解决与集合分区模型相关的定价问题,我们首先定义向后非主导时间依赖弧和最佳定时路线。我们还介绍了三种类型的路由,前进、向后和拼凑的最优定时路由,并分析了它们的特点。然后,我们介绍了一种将时间向后调整的方法,并将最佳定时路线从最新到最早拼凑在一起。我们证明这种方法保证了正确性并有效降低了复杂性。我们提出了一种双向标记算法来生成路由。定价问题采用了最先进的技术,包括有限内存子集行切割 (lm-SRC)、ng-route 松弛和桶图,以提高算法的效率。BPC 算法在从文献中的基准案例派生的一组实例上进行了测试。评估了它的各种组件和定价策略,并将其性能与文献中的其他算法进行了比较。 结果证实了所提出的算法及其新设计的组件在求解 TDGVRPTW 方面的有效性。
更新日期:2025-01-24
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