Stochastic Optimization Models and Methods for the Sharing Economy

随着一波以资源共享为基础的产业的引进，美国经济正在经历一场巨大的变革。突出的例子包括ZipCar和Motivate等汽车共享服务，Uber和Lyft等“类似出租车”的服务，以及Airbnb。这种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，以确保用户对服务保持忠诚。例如，在车辆共享中，重要的是用户能够在他们需要的时间和地点以高可靠性获得车辆。本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，特别强调了车辆共享。核心问题与车队规模和整个城市的车队部署有关。这些问题由于车辆使用的高度时效性和随机性而变得复杂。提出了一套解决这些问题的模型和方法，包括容量大小的长期规划方法和车辆供需近实时对齐的短期规划方法。长期规划方法是基于构建随机模型，同时准确地模拟车辆共享操作，并证明具有可以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。这些性质将通过组合论证来建立一组充分条件，这些条件允许在整数格上定义的问题上应用线性规划（因为一个位置的车辆数量和位置的容量是整数）。然后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。这种组合和耦合论证的结合可能广泛适用于共享经济中出现的问题，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，使其能够对地面情况做出近乎实时的反应。在车辆共享系统中，这些工具将指导车辆的重新定位，以更好地与当前和预期的需求保持一致，使用长期规划工具的结果作为指导。在建议的工作中，一个统一的原则是开发在通常操作条件下优化预期性能的方法，以确保高效操作，同时对冲最坏情况，为意外发展提供重要的鲁棒性。这项工作的目标是提供由新的理论结果支持的实际解决方案，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.