This vehicle scheduling problem with multiple depots and multiple vehicle types (VMM) is to determine the optimal vehicle routes to minimize the total travel costs. The object of this paper is to develope an exact algorithm for the VMM. In this paper the VMM is transformed into a mathematical model of the vehicle problem with multiple depots. Then an efficient branch and bound algorithm is developed to obtain an exact solution for this model. In order to enhance the efficiency, this algorithm emphasizes the follows; First, a heuristic algorithm is developed to get a good initial upper bound. Second, an primal-dual approach is used to solve subproblems which are called the quasi-assignment problem, formed by branching strategy is presented to reduce the number of the candidate subproblems.