解决多仓配送车辆路径规划难题,支持多时段与货物兼容约束。
A Rolling-Space Branch-and-Price Algorithm for the Multi-Compartment Vehicle Routing Problem with Multiple Time Windows
- 用分支定价算法结合标签法求解复杂配送问题
- 提出滚动空间策略,有效处理大规模实例
- 适合物流调度、供应链优化等实际场景应用
本文研究多仓配送车辆路径问题(MCVRPMTW),该问题是经典带时间窗车辆路径问题的扩展,考虑车辆配备多个独立货仓,且客户需在多个服务时间窗口内完成配送。问题包含三大关键仓组特性:(i) 货仓数量可灵活配置,(ii) 货物与货仓的兼容性,(iii) 货物间的相互兼容性;同时支持司机休息等实际运营要求。为求解该问题,本文设计一种精确的分支定价(B&P)算法,其中定价子问题通过标签算法求解,并引入多种加速策略以减少对称性、稳定列生成的对偶解并优化分支过程。针对大规模实例,提出融合聚类技术的滚动空间B&P算法。在基于真实工业应用构建的实例上进行的大量计算实验验证了方法的有效性,并提供了有价值的管理启示。
原文摘要 · Abstract (English)
This paper investigates the multi-compartment vehicle routing problem with multiple time windows (MCVRPMTW), an extension of the classical vehicle routing problem with time windows that considers vehicles equipped with multiple compartments and customers requiring service across several delivery time windows. The problem incorporates three key compartment-related features: (i) compartment flexibility in the number of compartments, (ii) item-to-compartment compatibility, and (iii) item-to-item compatibility. The problem also accommodates practical operational requirements such as driver breaks. To solve the MCVRPMTW, we develop an exact branch-and-price (B&P) algorithm in which the pricing problem is solved using a labeling algorithm. Several acceleration strategies are introduced to limit symmetry during label extensions, improve the stability of dual solutions in column generation, and enhance the branching process. To handle large-scale instances, we propose a rolling-space B&P algorithm that integrates clustering techniques into the solution framework. Extensive computational experiments on instances inspired by a real-world industrial application demonstrate the effectiveness of the proposed approach and provide useful managerial insights for practical implementation.
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