Timetable setting of single bus line using dynamic programming

The service time of a single bus line is divided into some time periods according to passenger flow intensity; it is supposed that passengers arrive evenly at the stop and bus runs are set evenly in each time period. The bus timetable setting problem is to determine bus run assignments in each time period to minimise the total waiting time of passengers on platforms if the number of total runs is known. This is a typical time-continuous multi-stage decision problem, and the dynamic programming method is appropriate to solve it. Global optimisation procedures using dynamic programming are developed to solve such a multi-stage decision problem. A numerical example is given to demonstrate the efficiency of the proposed method.