Operation and charging optimization for electric multimodal mobility system

This paper addresses the joint optimization of vehicle operation and charging for electric mobility-on-demand (MoD) services integrated with public transport (PT) in multimodal mobility systems. Existing modeling approaches often fail to capture key complexities in such systems, particularly the energy constraints and en-route charging behavior of electric MoD fleets and the temporal dynamics required for realistic coordination with scheduled PT services. We propose a tractable expanded network flow model that optimizes electric multimodal mobility systems by capturing interactions among customers, electric MoD vehicles, and PT services over time. The model explicitly represents customer activities, including traveling, waiting, and inter/intramodal transfers; electric MoD operations, such as routing, rebalancing, idling, and charging; and the schedules and routes of PT services. A key theoretical contribution is the proof of total unimodularity of an integer version of the model, ensuring realistic integer solutions and computational tractability. We validated the model using real-world data from Färingsö island, Stockholm, by analyzing Scenario 0: a baseline with PT-only service, Scenario 1: integration of MoD with the full existing PT network, and Scenario 2: integration of MoD with a reduced PT network where selected routes are retained. Results show that Scenario 1 improves travel distance and time by 14.97% and 2.70%, respectively, and reduces waiting time by approximately 60%. In Scenario 2, over 60% of PT vehicle operations can be removed while maintaining an overall customer experience through increased MoD coverage. The model further reveals insights into concentrated intermodal transfers, fluctuating charging demand, and fleet size sensitivity, offering valuable guidance for integrated system design and operations.