The Mobility-on-Demand (MOD) services, like the ones offered by Uber and Lyft, are transforming urban transportation by providing more sustainable and convenient service that allows people to access anytime and anywhere. In most U.S. cities with sprawling suburban areas, the utilization of public transit for commuting is often low due to lack of accessibility. Thereby the MOD system can function as a first-and-last-mile solution to attract more riders to use public transit. Seamless integration of ride-shared MOD service with public transit presents enormous potential in reducing pollution, saving energy, and alleviating congestion.

This research proposes a general mathematical framework for solving a multi-modal large-scale ride-sharing problem under real-time context. The framework consists of three core modules. The first module partitions the entire map into a set of more scalable zones to enhance computational efficiency. The second module encompasses a mixed-integer-programming model to concurrently find the optimal vehicle-to-request and request-to-request matches in a hybrid network. The third module forecasts the demand for each station in the near future and then generates an optimized vehicle allocation plan to best serve the incoming rider requests.

To ensure its applicability, the proposed model accounts for transit frequency, MOD vehicle capacity, available fleet size, customer walk-away condition and travel time uncertainty. Extensive experimental results prove that the proposed system can bring significant vehicular emission reduction and deliver timely ride-sharing service for a large number of riders. The main contributions of this study are as follows:

• Design of a general framework for planning a multi-modal ride-sharing system in cities with under-utilized public transit system;

• Development of an efficient real-time algorithm that can produce solutions of desired quality and scalability and redistribute the available fleet corresponding to the future demand evolution;

• Validation of the potential applicability of the proposed system and quantitatively reveal the trade-off between service quality and system efficiency.