Both for-profit and nonprofit peer-to-peer (P2P) ridesharing services have gained enormous popularity in recent years due to their advantages over solo driving and public transit. We study the rideshare matching and routing problem in a nonprofit P2P ridesharing system consisting of a matching agency, drivers and riders. The matching agency is a government or a not-for-profit organization and its objective is to maximize the societal benefits of ridesharing. The drivers involved are commuters and hence have their own travel plans, which are executed regardless of whether riders are matched with them. We consider both static and dynamic versions of the nonprofit P2P ridesharing problem. Existing modeling and solution approaches for similar P2P ridesharing problems can only solve relatively small problem instances optimally. We propose an exact solution algorithm for the static version of the problem by taking advantage of its special characteristics. This exact solution approach formulates and solves the problem as a set packing formulation using route-based variables, and uses an efficient graph-based approach to generate all necessary vehicle routes in the formulation quickly. We also develop a column generation (CG) based heuristic approach for the static problem. Finally, we propose two dynamic dispatching policies for the dynamic version of the problem. Our proposed exact algorithm solves very large problem instances (e.g., with 600 drivers and 1800 riders) of the static problem and our CG based heuristic can find near-optimal solutions for even larger instances of the static problem in short computation time. Our dynamic dispatching policies can generate near-optimal solutions for the dynamic problem in real-time fashion. We also generate some important insights based on some taxi trip data in Washington DC. First, P2P ridesharing can bring significant cost-saving, especially when the participants have a relatively flexible schedule. For every 10% increase in schedule flexibility, there is an about 4% to 7% increase in cost-saving. Second, the cost-saving due to ridesharing increases with the vehicle capacity, but this increase slows down quickly when the vehicle capacity reaches 4. Third, ridesharing generates more cost savings during peak hours and in urban areas.

近年来，无论是营利性还是非营利性的P2P共享服务，都比单人驾驶和公共交通更具优势。我们在由匹配机构，驾驶员和骑手组成的非营利性P2P乘车共享系统中研究乘车共享匹配和路线问题。匹配机构是政府或非营利组织，其目标是最大程度地实现拼车的社会利益。涉及的驾驶员是通勤者，因此具有自己的旅行计划，无论是否与他们匹配，都将执行该旅行计划。我们考虑非营利性P2P拼车问题的静态和动态版本。对于类似的P2P拼车问题，现有的建模和解决方案只能最优地解决相对较小的问题实例。通过利用其特殊特性，我们为问题的静态版本提出了一种精确的求解算法。这种精确的解决方案使用基于路线的变量将问题解决并解决为固定装箱方案，并使用有效的基于图的方法来快速生成配方中所有必要的车辆路线。我们还针对静态问题开发了基于列生成（CG）的启发式方法。最后，我们针对问题的动态版本提出了两种动态调度策略。我们提出的精确算法解决了静态问题的非常大的问题实例（例如，有600名驾驶员和1800名车手），而我们基于CG的启发式算法可以在较短的计算时间内为更大的静态问题实例找到接近最优的解决方案。我们的动态调度策略可以实时生成动态问题的最佳解决方案。我们还会根据华盛顿特区的一些出租车旅行数据得出一些重要见解。首先，P2P乘车共享可以节省大量成本，尤其是当参与者的时间表相对灵活时。进度灵活性每增加10％，节省的成本就会增加4％至7％。第二，由于乘车共享而节省的成本随车辆容量的增加而增加，但是当车辆的容量达到4时，这种增加会迅速减慢。第三，乘车共享在高峰时段和城市地区可节省更多成本。P2P乘车共享可以节省大量成本，尤其是当参与者的时间表相对灵活时。进度灵活性每增加10％，节省的成本就会增加4％至7％。第二，由于乘车共享节省的成本随车辆容量的增加而增加，但是当车辆容量达到4时，这种增加的速度会迅速降低。第三，在高峰时段和城市地区，乘车共享可以节省更多的成本。P2P乘车共享可以节省大量成本，尤其是在参与者的时间表相对灵活的情况下。进度灵活性每增加10％，节省的成本就会增加4％至7％。第二，由于乘车共享而节省的成本随车辆容量的增加而增加，但是当车辆的容量达到4时，这种增加会迅速减慢。第三，乘车共享在高峰时段和城市地区可节省更多成本。