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

该项目考虑了货运和服务交付业务期间车队的使用情况，目的是提高优化此类流程的能力，以应对运营不确定性，例如与运输网络相关的不确定性(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(如客户需求、时间可获得性或地理位置)。从实践的角度来看，在这种情况下做出运营决策时不考虑不确定性可能会对运营商产生重大的经济和声誉影响，因为运营条件的轻微变化可能会导致即使是精心规划和“优化”的运营也会变得非常次优或完全不可行。此外，针对车辆路径作业的高效优化和风险管理框架，如本项目中开发的框架，可以通过减少交通拥堵和污染排放等运输系统的有害副作用而有益于环境。在解决这一重要问题时，该项目应用并推进了稳健优化(RO)的理论领域，这是科学文献中出现的一种有前途的框架，用于优化受参数不确定性影响的数学模型。该项目力求在用于优化车辆路线作业的数学模型的背景下，使可再生能源的应用系统化，并简化从业人员对其理论和方法创新的采用。该项目通过向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，进一步影响教育，并使STEM能够扩展到K-12学生。该项目旨在开发一个系统地处理富车辆路径问题(VRP)中不确定性的优化框架。VRP考虑一支车队及其在货运和服务交付业务中的最佳利用。丰富的VRP设置特别考虑了在实践中得到回答的复杂的操作现实。从实践的角度来看，有必要设计考虑到业务不确定性的货运和服务交付系统，因为不这样做可能导致解决办法不可行或极不理想。该项目采用稳健优化(RO)框架，这一框架在VRPS的背景下没有得到太多考虑。该框架力求在“最坏情况”的情况下优化问题，这是由适当选择的不确定性集合决定的，以反映决策者对风险和模棱两可的容忍程度。从可处理性的角度来看，基于RO的方法可能是有利的，并且不需要精确的分布知识。预期的方法论贡献包括：(A)稳健的公式、切割平面和有效的精确解方法，(B)稳健的可行性检查和有效的元启发式求解方法，以及(C)易于处理、实际相关和容易根据风险容忍度调整的相关不确定性集。此外，我们计划汇编新的基准实例和计算性能概况的全面集合，这将有助于刺激该领域的研究工作。高效的RICH-VRP优化和风险管理框架，如本项目中开发的框架，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，它们还可以减少运输系统的副作用，如交通拥堵和污染排放，从而有益于环境。该项目将通过向研究生和本科生提供有关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，进一步影响教育，并使STEM能够接触到K-12学生。

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.