Stochastic Optimization Models and Methods for the Sharing Economy

随着一波基于资源共享的产业的兴起，美国经济正在经历巨大的变化。突出的例子包括 ZipCar 和 Motivate 等车辆共享服务、Uber 和 Lyft 等“类出租车”服务以及 Airbnb。此类服务不仅依赖于分散用户之间的实时信息流，而且还依赖于确保高可靠性水平，以确保用户保持对服务的忠诚度。例如，在车辆共享中，重要的是订户能够在他们想要的时间和地点以高可靠性获得车辆。该提案探讨了与共享经济相关的物流问题的随机优化模型和方法，特别强调车辆共享。核心问题涉及整个城市的车队规模和车队部署。由于车辆使用的严重时间依赖性和随机性，这些问题变得更加复杂。提出了一套解决这些问题的模型和方法，其中包括容量规模的长期规划方法和车辆供需近实时调整的短期规划方法。长期规划方法基于构建随机模型，该模型同时准确地模拟车辆共享操作，并证明拥有可通过有效的优化技术（特别是整数线性规划）利用的数学结构。这些属性将通过组合参数来建立，以建立一组充分条件，允许人们对整数格上定义的问题应用线性规划（因为某个位置的车辆数量和位置的容量是整数）。然后将通过使用随机耦合技术为所讨论的随机模型建立这些充分条件。这种组合和耦合论点的结合可能广泛适用于共享经济中出现的问题之外，正如模拟优化测试问题库中大量类似结构的问题所证明的那样。除了这些长期规划工具外，还将开发短期工具，以便对实地情况做出近乎实时的响应。在车辆共享系统中，此类工具将利用长期规划工具的结果作为指导，指导车辆重新定位，以更好地满足当前和预期的需求。拟议工作中的一个统一原则是开发在通常操作条件下优化预期性能的方法，以确保高效运行，同时对冲最坏情况事件，为意外发展提供重要水平的稳健性。这项工作的目标是提供由新理论结果支持的实用解决方案，这些结果建立了强大的平均情况和最坏情况保证。

The US economy is undergoing a dramatic change with the introduction of a wave of industries based on the sharing of resources. Prominent examples include vehicle-sharing services like ZipCar and Motivate, "taxi-like" services like Uber and Lyft, and Airbnb. Such services rely not just on real-time information flow between dispersed users, but also on ensuring high reliability levels to ensure that users remain loyal to the service. For example, in vehicle sharing it is important that subscribers are able to obtain vehicles when and where they want them with high reliability. This proposal explores stochastic optimization models and methodology for logistical questions associated with the sharing economy, with particular emphasis on vehicle sharing. Central questions relate to fleet sizing and fleet deployment across a city. These questions are complicated by the heavily time-dependent and stochastic nature of vehicle usage.A suite of models and methods for tackling these problems is proposed that includes both long-term planning methodology for capacity sizing and short-term planning methodology for near real-time alignment of supply and demand of vehicles. The long-term planning methods are based on constructing stochastic models that simultaneously accurately model vehicle-sharing operations and provably possess mathematical structure that can be exploited through efficient optimization techniques, particularly integer linear programming. These properties will be established through combinatorial arguments to establish a set of sufficient conditions that allow one to apply linear programming on problems that are defined on integer lattices (since the number of vehicles at a location, and the capacity of locations are integral). These sufficient conditions will then be established for the stochastic models in question through the use of stochastic coupling techniques. This combination of combinatorial and coupling arguments may be broadly applicable beyond problems arising in the sharing economy, as evidenced by a plethora of similarly structured problems in a repository of simulation-optimization test problems. In addition to these long-term planning tools, short-term tools will be developed that enable a near real-time response to conditions on the ground. In vehicle-sharing systems, such tools would guide the repositioning of vehicles to better align with current and anticipated demand, using the results from long-term planning tools as a guide. A unifying principle in the proposed work is to develop methods that optimize expected performance under usual operating conditions to ensure efficient operation, while hedging against worst-case events to provide an important level of robustness to unexpected developments. The goal of this is work is provide practical solutions supported by new theoretical results that establish both strong average-case and worst-case guarantees.