This paper presents a novel mathematical model for real-time high-capacity ride-sharing that dynamically assigns trips to vehicles based on current demand and vehicle locations. The model addresses three key challenges in ride-sharing: batch assignment of requests to vehicles, continuous assignment of incoming requests, and fleet rebalancing. The algorithm starts with a greedy assignment and improves it using constrained optimization, leading to high-quality solutions that converge to optimality over time. The method is validated using 3 million taxi trips from New York City and is shown to handle up to ten passengers per vehicle. It is applicable to autonomous vehicle fleets and incorporates vehicle rebalancing to high-demand areas. The model is general and can be used for various real-time multi-vehicle, multi-task assignment problems. The algorithm is implemented as an integer linear program (ILP) and is shown to be anytime optimal, returning good solutions quickly and improving them over time. The method is robust to changes in time window length, request density, and congestion levels. It is also efficient and can be parallelized, making it suitable for large-scale applications. The paper also presents results showing the impact of different vehicle capacities and maximum waiting times on ride-sharing performance. The method is validated using real-world data and is shown to improve ride-sharing efficiency, reduce travel delays, and lower operational costs.This paper presents a novel mathematical model for real-time high-capacity ride-sharing that dynamically assigns trips to vehicles based on current demand and vehicle locations. The model addresses three key challenges in ride-sharing: batch assignment of requests to vehicles, continuous assignment of incoming requests, and fleet rebalancing. The algorithm starts with a greedy assignment and improves it using constrained optimization, leading to high-quality solutions that converge to optimality over time. The method is validated using 3 million taxi trips from New York City and is shown to handle up to ten passengers per vehicle. It is applicable to autonomous vehicle fleets and incorporates vehicle rebalancing to high-demand areas. The model is general and can be used for various real-time multi-vehicle, multi-task assignment problems. The algorithm is implemented as an integer linear program (ILP) and is shown to be anytime optimal, returning good solutions quickly and improving them over time. The method is robust to changes in time window length, request density, and congestion levels. It is also efficient and can be parallelized, making it suitable for large-scale applications. The paper also presents results showing the impact of different vehicle capacities and maximum waiting times on ride-sharing performance. The method is validated using real-world data and is shown to improve ride-sharing efficiency, reduce travel delays, and lower operational costs.