An exact algorithm for multiple depos bus scheduling

In this paper the authors present an exact algorithm for solving the multiple depot bus scheduling problem. The algorithm uses two well known linear programming relaxations of the problem. The first, a pure network flow problem, is used to obtain a dual feasible solution to the second relaxation, a multi-commodity network flow problem, which is solved using dual simplex. Branch and bound is then used to obtain the optimal integer solution. This technique is then used to solve exact problems much greater than any previously reported technique. Results are presented for problems with up to 600 trips and 3 depots.