带时间窗和线性重量相关费用的集货车辆路径问题的分支定价切割算法
Branch-and-price-and-cut for the Split-collection Vehicle Routing Problem with Time Windows and Linear Weight-related Cost
摘要：
本文提出了一种新的车辆路径问题，同时涉及时间窗，分裂收集和线性重量相关的成本，这是一个推广的分裂交付车辆路径问题的时间窗（SDVRPTW）。这个问题包括确定最低成本的车辆路线，以服务于一组客户，同时尊重车辆容量和时间窗口的限制。单位距离的行驶成本是车辆重量的线性函数，并且可以通过多辆车辆来满足客户需求。为了解决这个问题，我们提出了一个精确的分支和价格和切割算法，其中的定价子问题是一个资源受限的基本最小费用路径问题。我们首先证明了定价子问题的最优解至少与一个极端的收集模式相关联，然后设计了一个定制的和新颖的标签设置算法来解决它。计算结果表明，我们提出的算法可以有效地处理SDVRPTW和我们的问题。
英文摘要：
This paper addresses a new vehicle routing problem that simultaneously involves time windows, split collection and linear weight-related cost, which is a generalization of the split delivery vehicle routing problem with time windows (SDVRPTW). This problem consists of determining least-cost vehicle routes to serve a set of customers while respecting the restrictions of vehicle capacity and time windows. The travel cost per unit distance is a linear function of the vehicle weight and the customer demand can be fulfilled by multiple vehicles. To solve this problem, we propose a exact branch-and-price-and-cut algorithm, where the pricing subproblem is a resource-constrained elementary least-cost path problem. We first prove that at least an optimal solution to the pricing subproblem is associated with an extreme collection pattern, and then design a tailored and novel label-setting algorithm to solve it. Computational results show that our proposed algorithm can handle both the SDVRPTW and our problem effectively.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
