We envision a multimodal transportation system where Mobility-on-Demand (MoD) service is used to serve the first mile and last mile of transit trips. For this purpose, the current research formulates an optimization model for designing an integrated MoD and urban transit system. The proposed model is a mixed-integer non-linear programming model that captures the strategic behavior of passengers in a multimodal network through a passenger assignment model. It determines which transit routes to operate, the frequency of the operating routes, the fleet size of vehicles required in each transportation analysis zone to serve the demand, and the passenger flow on both road and transit networks. A Benders decomposition approach with several enhancements is proposed to solve the given optimization program. Computational experiments are presented for the Sioux Falls multimodal network. The results show a significant improvement in the congestion in the city center with the introduction and optimization of an integrated transportation system. The proposed design allocates more vehicles to the outskirt zones in the network (to serve the first mile and last mile of transit trips) and more frequency to the transit routes in the city center. The integrated system significantly improves the share of transit passengers and their level of service in comparison to the base optimized transit system. The sensitivity analysis of the bus and vehicle fleet shows that increasing the number of buses has more impact on improving the level of service of passengers compared to increasing the number of MoD vehicles. The article also offers managerial insights on deploying such multimodal service.

我们设想了一个多式联运系统，其中使用按需移动 (MoD) 服务来为中转行程的第一英里和最后一英里提供服务。为此，当前的研究制定了一个优化模型，用于设计集成的 MoD 和城市交通系统。所提出的模型是一个混合整数非线性规划模型，通过乘客分配模型捕获多模式网络中乘客的策略行为。它确定要运营的公交路线、运营路线的频率、每个交通分析区域为满足需求所需的车队规模，以及道路和公交网络上的客流。提出了一种具有多种增强功能的 Benders 分解方法来求解给定的优化程序。针对 Sioux Falls 多模式网络提供了计算实验。结果表明，随着综合交通系统的引入和优化，市中心的拥堵状况得到了显着改善。拟议的设计将更多的车辆分配到网络中的郊区（以服务于公交出行的第一英里和最后一英里），并为市中心的公交路线分配更多的频率。与基础优化过境系统相比，集成系统显着提高了过境乘客的份额及其服务水平。公交车和车队的敏感性分析表明，与增加 MoD 车辆的数量相比，增加公交车的数量对提高乘客服务水平的影响更大。