Exact and heuristic solution methods for time-constrained vehicle routing

时间约束车辆路径问题包括确定覆盖一组任务的最低成本车辆路线，使得每个任务在预定义的时间窗口内执行，并且每条路线的车辆容量得到尊重。由于在货运中的不同应用，存在几个问题变体。在这个方案中，我们开发了数学优化模型和方法，以帮助规划者确定最佳可能的车辆路线。优化方法可以分为两类：精确方法寻求最优解，可能需要大量的计算时间；启发式方法速度快得多，但提供的解质量好，可能不是最优解。我们探索了精确方法的三个研究方向和启发式方法的一个研究方向。此外，我们还针对两个具体的车辆路径问题提出了优化方法：具有时间窗和同步约束的分配式送货车辆路径问题，允许同时访问每个客户；以及具有时间窗和后进先出约束的提货和送货车辆路径问题，该问题包括在客户处提货，并以与提货作业相反的顺序将货物送到特定地点。从科学的角度来看，本研究的结果具有较强的方法论意义，将适用于不同运输方式下的车辆路径问题，甚至适用于其他领域出现的某些问题。从商业角度来看，这些结果将有助于货运公司更好地管理其车辆的使用，因此将有助于提高加拿大公司的生产率。最后，从学术角度来看，本研究将为加拿大优化软件开发公司完成学业后所需的三名博士生和两名硕士研究生提供资金支持和培训。

Time-constrained vehicle routing problems consist of determining least-cost vehicle routes to cover a set of tasks such that each task is executed within a predefined time window and vehicle capacity is respected for each route. Several problem variants exist, arising from different applications in freight transportation. In this proposal, we develop mathematical optimization models and methods to help the planners in determining the best possible vehicle routes. The optimization methods can be classified into two categories: an exact method seeks an optimal solution and can require substantial computational time; a heuristic method is much faster but provides a good-quality solution that may not be optimal. We explore three research directions for exact methods and one for heuristics. Furthermore, we develop optimization methods for two specific vehicle routing problems: the split delivery vehicle routing problem with time windows and synchronization constraints that allows multiple visits to each customer if they occur simultaneously; and the pickup and delivery vehicle routing problem with time windows and last-in, first-out constraints that consists of picking up merchandise at customers to deliver it at specific locations in the reverse order of the corresponding pickup operations. From a scientific point of view, the results of this research are rather methodological and will be applicable to a wide variety of vehicle routing problems in different mode of transportation and even to certain problems arising in other domains. From a commercial point of view, these results will help the freight companies to better manage the utilization of their vehicles and will therefore contribute to increase the productivity of Canadian companies. Finally, from an academic point of view, this research will provide financial support and training to three PhD students and two MSc students that will be in demand by the Canadian optimization software development companies after completing their studies.