This study is concerned with the problem of routing vehicles stationed at a central depot to supply customers with known demands, in such a way as to minimize the total distance travelled. The problem is referred to as the vehicle routing problem and is a generalization of the multiple traveling salesmen problem that has many practical applications. A branch-and-bound algorithm for the exact solution of the vehicle routing problem is presented. The algorithm finds the optimal number of vehicles as well as the minimum distance routes. A numerical example is given.