Planning the route system for urban buses

Abstract

It is assumed that the number of buses to be operated during the various periods of the day, which is the primary factor determining costs, has already been determined and is a problem constraint. The method determines the frequencies on each route but no attempt at scheduling is made. The city is divided into zones and the number of journeys to be made by the public between each pair of zones is a data input expressed in matrix form. The objective function, to be minimized, is the sum of the journey time (which includes allowance for transfer times) plus discomfort penalties proportional to the number of passengers who cannot find seats. The planning method has two phases. In the first, desirable routes, which may be added to an initial set of routes, are generated; and routes, which may be deleted from the augmented set of routes, are pointed out. The routes to be added are selected from a set of candidate routes each of which is based on a route skeleton consisting of four zones with the extremes restricted to a set of terminal zones. In the second phase, optimal frequencies for a set of routes, under the constraint of a given number of available buses, are determined by a gradient method. The optimal value of the objective function in the second phase serves as a more accurate evaluator of a generated set of routes. Fortran programs implementing the two phases have been run for the Haifa area which was represented by 41 zones. The route determining algorithm produces a set of routes in 3 min C.P.U. on an I.B.M. 360 50 . The frequency program effectively minimized the objective function for 20 routes in 15 min run time on an I.B.M. 360 44 . There is strong evidence that the programs provide useful results and they appear to be useful planning tools.