不确定旅行时间下车辆路由的广义风险指数:公式、性质和精确解框架

Zhenzhen Zhang, Yu Zhang, Roberto Baldacci
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引用次数: 0

摘要

我们考虑的是一个具有时间窗口的车辆路由问题,该问题的目标是为同质车队确定路线,使其在规定的时间窗口内最大限度地到达客户所在地,同时确保总旅行成本不超过规定的预算。具体来说,我们优化了一种新的性能指标,该指标考虑了与晚到客户地点相关的风险,称为广义风险指数(GRI)。GRI 作为特例涵盖了几个现有的风险指数,并产生了新的指数。我们展示了其突出的管理和计算特性,以更好地激发其动机。我们提出了基于集合划分的问题替代模型。为了获得最优解,我们开发了一个结合路径枚举和分支-价格-切割算法的精确解框架,其中 GRI 是在路径枚举和列生成子问题中处理的。我们主要通过利用 GRI 和预算约束的特性来减少求解空间,同时又不失最优性。我们在文献中收集的一系列实例上对所提出的方法进行了测试。结果表明,在减少延迟方面,GRI 的新实例优于现有的几个风险指数。精确方法可以优化解决多达 100 个节点的实例。它能持续解决多达 50 个节点的实例,在可管理的实例规模上比最先进的方法高出一倍多。资助:本研究得到了国家自然科学基金[Grants 72101187, 72371204, 72021002, and 71901180]、卡塔尔国家研究基金[Grant ARG01-0430-230029]、四川省自然科学基金[24NSFSC6232]和西南财经大学光华人才项目的资助。补充材料:在线附录见 https://doi.org/10.1287/trsc.2023.0345 。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Generalized Riskiness Index in Vehicle Routing Under Uncertain Travel Times: Formulations, Properties, and Exact Solution Framework
We consider a vehicle routing problem with time windows under uncertain travel times where the goal is to determine routes for a fleet of homogeneous vehicles to arrive at the locations of customers within their stipulated time windows to the maximum extent while ensuring that the total travel cost does not exceed a prescribed budget. Specifically, a novel performance measure that accounts for the riskiness associated with late arrivals at the customers, called the generalized riskiness index (GRI), is optimized. The GRI covers several existing riskiness indices as special cases and generates new ones. We demonstrate its salient managerial and computational properties to motivate it better. We propose alternative set partitioning-based models of the problem. To obtain the optimal solution, we develop an exact solution framework combining route enumeration and branch-price-and-cut algorithms, in which the GRI is dealt with in route enumeration and column generation subproblems. We mainly reduce the solution space by exploiting the GRI and budget constraints’ properties without losing optimality. The proposed method is tested on a collection of instances derived from the literature. The results show that a new instance of the GRI outperforms several existing riskiness indices in mitigating lateness. The exact method can solve instances with up to 100 nodes to optimality. It can consistently solve instances involving up to 50 nodes, outperforming state-of-the-art methods by more than doubling the manageable instance size. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72101187, 72371204, 72021002, and 71901180], the Qatar National Research Fund [Grant ARG01-0430-230029], Natural Science Foundation of Sichuan Province [24NSFSC6232], and Guanghua Talent Project of the Southwestern University of Finance and Economics. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0345 .
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