具有广义一致性要求的路由优化

Kai Wang, L. Zhen, Jun Xia, Roberto Baldacci, Shuaian Wang
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引用次数: 5

摘要

一致性车辆路线问题(ConVRP)的目标是设计多天的同步路线,以服务于一组客户,同时使总出行成本最小化。它规定客户应该在大致相同的时间(时间一致性)由几个熟悉的司机(司机一致性)访问。本文将ConVRP推广到任何级别的驾驶员一致性,并增加了路线一致性,即每个驾驶员在规划日最多可以穿越一定比例的不同路线弧线,保证路线熟悉度。为了解决这一问题,我们开发了两组基于分区的公式,一个基于路线,另一个基于时间表。我们研究了用于导出列子集(路线和时间表)的两种公式的线性松弛的有效下界;子集中是每个配方的最优解决方案的列。然后,我们求解任何一个公式的简化问题,以获得最优解。数值结果表明,我们的精确方法可以有效地求解文献中大多数中等规模的ConVRP实例,也可以求解一些新生成的多达50个客户的实例。我们的精确解决方案探讨了在实践中采用一致性措施方面的一些管理发现。首先,保持相当高的一致性需求并不一定总是导致成本的大幅增加。其次,通过采用高水平的驱动程序一致性,可以潜在地保证高水平的时间一致性。第三,保持高水平的时间一致性和驱动程序一致性可能导致较低水平的路由一致性。
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Routing Optimization with Generalized Consistency Requirements
The consistent vehicle routing problem (ConVRP) aims to design synchronized routes on multiple days to serve a group of customers while minimizing the total travel cost. It stipulates that customers should be visited at roughly the same time (time consistency) by several familiar drivers (driver consistency). This paper generalizes the ConVRP for any level of driver consistency and additionally addresses route consistency, which means that each driver can traverse at most a certain proportion of different arcs of routes on planning days, which guarantees route familiarity. To solve this problem, we develop two set partitioning-based formulations, one based on routes and the other based on schedules. We investigate valid lower bounds on the linear relaxations of both of the formulations that are used to derive a subset of columns (routes and schedules); within the subset are columns of an optimal solution for each formulation. We then solve the reduced problem of either one of the formulations to achieve an optimal solution. Numerical results show that our exact method can effectively solve most of the medium-sized ConVRP instances in the literature and can also solve some newly generated instances involving up to 50 customers. Our exact solutions explore some managerial findings with respect to the adoption of consistency measures in practice. First, maintaining reasonably high levels of consistency requirements does not necessarily always lead to a substantial increase in cost. Second, a high level of time consistency can potentially be guaranteed by adopting a high level of driver consistency. Third, maintaining high levels of time consistency and driver consistency may lead to lower levels of route consistency.
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