On-demand transit has significantly changed the landscape of personal transportation. Even traditional public transit is being overhauled by employing similar strategies, leading to the introduction of new services such as on-demand public transit (ODPT). ODPT links a geographical area using a fleet of vehicles that operate with flexible routes and timetables as opposed to its' fixed route and timetable counterparts. Further, strict regulations on reducing the carbon footprint has enforced transport operators to rely on electric vehicle (EV) fleets in public transit. However, in addition to the requirement to compute routes and schedules in real-time for ODPT services, EVs also impose constraints due to reduced driving ranges. This necessitates highly responsive real-time algorithms to cater for the significantly larger number of computations. To this end, we propose a hybrid methodology, which exploits parallel computing techniques using a clustering algorithm to decompose a large problem into smaller sub-problems, which are subsequently solved using a genetic algorithm. The result obtained from this step is used as an initial solution in a global optimization stage to further improve the quality of results. Experiments using the actual road network show that the proposed method not only improves speed of computation but also the quality of results compared to the state-of-the-art.