Stochastic Optimization Models and Methods for the Sharing Economy

随着基于资源共享的产业浪潮的引入，美国经济正在经历一场戏剧性的变化。突出的例子包括ZipCar和Motivate等车辆共享服务，Uber和Lyft等“类似出租车”的服务，以及Airbnb。这类服务不仅依赖于分散用户之间的实时信息流，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，用户能够随时随地获得他们想要的车辆并具有高可靠性，这一点很重要。该提案探索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。核心问题涉及舰队规模和整个城市的舰队部署。由于车辆使用具有严重的时间依赖性和随机性，这些问题变得复杂起来。提出了一套解决这些问题的模型和方法，其中包括容量大小的长期规划方法和近实时车辆供需协调的短期规划方法。长期规划方法建立在构建随机模型的基础上，该随机模型同时准确地模拟汽车共享运营，并且被证明具有可以通过有效的优化技术，特别是整数线性规划来利用的数学结构。这些性质将通过组合论证建立一组充分条件，允许对整数格上定义的问题应用线性规划(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。这种组合和耦合论点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，还将开发能够对实地情况作出近乎实时反应的短期工具。在车辆共享系统中，这种工具将指导车辆的重新定位，以便更好地与当前和预期的需求保持一致，并以长期规划工具的结果为指导。拟议工作中的一项统一原则是开发在正常运行条件下优化预期性能的方法，以确保高效运行，同时对冲最坏情况的事件，以提供对意外发展的重要健壮性。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，这些新的理论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.