In recent years, intelligent transportation systems made it possible for operators to adapt in real-time the transportation supply to travel demand via new mobility services. Among these services, ride-sharing is becoming popular. The dynamic ride-sharing problem involves two sub-problems: (1) How to serve the upcoming trips (Optimal fleet management) and (2) How to accurately predict the travel times to determine vehicles availability and pick up/drop off times. In this paper, we express the optimal fleet management problem as a constrained multi objective integer linear programming. Our aim is to find the global optimal solution for the ride-sharing problem without uncertainty in demand to have a vision of these services performance in optimal situation. Then we compare the results and experiments with the exact optimal condition. We have designed an algorithm to find the exact solution for matching problem based on the branch and bound algorithm. To solve the second sub-problem, we define two different models to assess the impact of traffic conditions on the dynamic ride-sharing system performance for large-scale problems.