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.
