Ridepooling services play an increasingly important role in modern transportation systems. With soaring demand and growing fleet sizes, the underlying route planning problems become increasingly challenging. In this context, we consider the dial-a-ride problem (DARP): Given a set of transportation requests with pick-up and delivery locations, passenger numbers, time windows, and maximum ride times, an optimal routing for a fleet of vehicles, including an optimized passenger assignment, needs to be determined. We present tight mixed-integer linear programming (MILP) formulations for the DARP by combining two state-of-the-art models into novel location-augmented-event-based formulations. Strong valid inequalities and lower and upper bounding techniques are derived to further improve the formulations. We then demonstrate the theoretical and computational superiority of the new model: First, the formulation is tight in the sense that, if time windows shrink to a single point in time, the linear programming relaxation yields integer (and hence optimal) solutions. Second, extensive numerical experiments on benchmark instances show that computational times are on average reduced by 49.7% compared to state-of-the-art event-based approaches.

翻译：拼车服务在现代交通系统中扮演着日益重要的角色。随着需求激增与车队规模扩大，其底层路径规划问题变得愈发复杂。在此背景下，我们研究拨召服务问题：给定一组具有上下车地点、乘客数量、时间窗及最长乘车时间约束的运输请求，需要确定包含优化乘客分配的车队最优路径规划。通过将两种先进模型结合为新型的基于位置增强事件的建模框架，我们提出了拨召服务问题的紧致混合整数线性规划模型。为进一步改进模型，我们推导了强有效不等式及上下界技术。随后，我们证明了新模型在理论与计算上的优越性：首先，该模型具有紧致性，即当时间窗收缩至单一时间点时，线性规划松弛可产生整数解（从而获得最优解）；其次，在基准测试案例上的大量数值实验表明，相较于先进的基于事件的方法，计算时间平均减少49.7%。