A procedure to adjust transit trip departure times through minimizing the maximum headway

Transit frequency is usually determined at the heavier load route segment, whereas at other segments the operation may be inefficient due to situations characterized by empty seats. The transit schedulers attempt to overcome this problem by deleting manually some departure times to allow for the initiation of certain trips beyond the beginning of the route and/or termination-before the end of the route. The outcome of this process is the reduction of the number of vehicles required to carry on the timetable. This work describes an automated procedure for the scheduler to adjust the number of departures at each route timepoint to that required from a passenger load standpoint. Given a complete timetable, the procedure reduces the number of departures with the objective to minimize the maximum headway to be obtained, where the headway is associated with passenger wait time. This minimax headway problem is solved through: (i) representation of the problem on a directed network with a special pattern; (ii) applying a modified shortest-path algorithm on the network to determine the minimax headway; and (iii) applying an algorithm to ensure that the exact number of required departures will be included in the optimal solution. Finally, some computational results and an example are demonstrated.