Collaborative Research: Robust Optimization of Rich Vehicle Routing Problems Under Uncertainty

本项目考虑了货运和服务交付过程中车队的使用情况，旨在提高在考虑运营不确定性的情况下优化这些流程的能力，例如与运输网络相关的不确定性（例如，交通状况、道路封闭或车辆故障），或与交付目标本身相关的不确定性（例如，客户需求、时间可用性或地理位置）。从实际的角度来看，在这种情况下做出作业决策时，如果不考虑不确定性，可能会对作业者造成重大的经济和声誉影响，因为作业条件的微小变化可能会导致精心规划和“优化”的作业变得极不理想或完全不可行的。此外，车辆路线操作的有效优化和风险管理框架，如本项目开发的框架，可以通过减少交通拥堵和污染排放等运输系统的不良副作用来造福环境。为了解决这一重要问题，本项目应用并推进了鲁棒优化（RO）的理论领域，鲁棒优化在科学文献中作为一个有前途的框架出现，用于优化受参数不确定性影响的数学模型。该项目力求在优化车辆路线操作所使用的数学模型的背景下，将RO的应用系统化，并简化实践者对其理论和方法创新的采用。该项目通过为研究生和本科生提供货运和服务交付操作、优化方法和算法、不确定性量化和分析以及科学计算等问题的培训，以及为K-12学生提供STEM推广，进一步影响了教育。本项目旨在开发一个优化框架，用于系统处理丰富车辆路径问题（vrp）中的不确定性。vrp考虑车队及其在货运和服务交付操作中的最佳利用。丰富的VRP设置特别说明了在实践中回答的复杂操作现实。从实际的角度来看，设计考虑到操作不确定性的货运和服务交付系统是很有趣的，因为如果不这样做，可能会导致解决方案不可行或极不理想。该项目应用了鲁棒优化（RO）框架，这在vrp的背景下没有得到太多的考虑。考虑到“最坏情况”的情况，该框架寻求优化问题，这是由一个不确定性集决定的，该不确定性集被适当地选择以反映决策者对风险和模糊性的容忍度。从可跟踪性的角度来看，基于ro的方法是有利的，并且不需要精确的分布知识。预期的方法学贡献包括(a)健壮的公式、切割平面和有效的精确解方法的发展，(b)健壮的可行性检查和有效的元启发式解方法，以及(c)相关的可处理的、实际相关的、容易根据风险承受能力进行调整的不确定性集。此外，我们计划编译新的基准实例和计算性能概要的综合集合，这将有助于刺激该领域的研究工作。高效的富vrp优化和风险管理框架，如本项目开发的框架，可以对采用这些框架的公司的竞争力、服务质量和可持续性产生重要影响。此外，它们还减少了运输系统带来的不必要的副作用，如交通拥堵和污染排放，从而有利于环境。该项目将通过为研究生和本科生提供货运和服务交付操作、优化方法和算法、不确定性量化和分析以及科学计算等问题的培训，以及为K-12学生提供STEM推广，从而进一步影响教育。

This project considers the utilization of a fleet of vehicles during freight and service delivery operations, and aims to enhance the ability to optimize such processes in view of operational uncertainty, such as uncertainty related to the transportation network (e.g., traffic conditions, road closings or vehicle break-downs), or uncertainty related to the delivery targets themselves (e.g., customer demands, time availabilities, or geographic locations). From a practical perspective, failure to take into account uncertainty when making operational decisions in this context may have significant economic and reputational repercussions for operators, as slight changes in operational conditions may lead even a carefully planned and "optimized" operation to become highly suboptimal or outright infeasible. Furthermore, efficient optimization and risk-management frameworks for vehicle routing operations, such as the one developed in this project, can benefit the environment by reducing unwanted side-effects of delivery systems such as traffic congestion and pollution emissions. In addressing this important issue, this project applies and advances the theoretical field of Robust Optimization (RO), which has emerged in the scientific literature as a promising framework to optimize mathematical models subject to parameter uncertainty. The project seeks to systematize the application of RO in the context of mathematical models used for the optimization of vehicle routing operations and to streamline the adoption of its theoretical and methodological innovations by practitioners. The project further impacts Education by providing training to graduate and undergraduate students on issues of freight and service delivery operations, optimization methods and algorithms, uncertainty quantification and analysis, and scientific computation, as well as enabling STEM outreach to K-12 students.This project aims to develop an optimization framework for the systematic treatment of uncertainty in rich Vehicle Routing Problems (VRPs). VRPs consider a fleet of vehicles and their optimal utilization in freight and service delivery operations. Rich VRP settings particularly account for complicated operational realities that are answered in practice. From a practical perspective, it is of interest to design freight and service delivery systems that take into account operational uncertainties, since failure to do so may lead to solutions that are infeasible or highly suboptimal. The project applies the Robust Optimization (RO) framework, which has not been considered much in the context of VRPs. The framework seeks to optimize the problem in view of a "worst-case" scenario, as dictated by an uncertainty set that is suitably selected to reflect the decision maker's tolerance for risk and ambiguity. An RO-based approach can be advantageous from a tractability viewpoint and does not require precise distributional knowledge. The expected methodological contributions include the development of (a) robust formulations, cutting planes, and efficient exact solution approaches, (b) robust feasibility checks and efficient metaheuristic solution approaches, and (c) associated uncertainty sets that are tractable, practically relevant, and easily tuned according to risk tolerance. Furthermore, we plan to compile comprehensive collections of new benchmark instances and computational performance profiles, which will help to stimulate research efforts in the area. Efficient rich-VRP optimization and risk-management frameworks, such as the one developed in this project, can have an important impact in the competitiveness, service quality and sustainability of companies that adopt them. Furthermore, they benefit the environment by reducing unwanted side-effects of delivery systems, such as traffic congestion and pollution emissions. The project will further impact Education via providing training to graduate and undergraduate students on issues of freight and service delivery operations, optimization methods and algorithms, uncertainty quantification and analysis, and scientific computation, as well as enabling STEM outreach to K-12 students.