Welfare maximization for bus transit systems with timed transfers and financial constraints

Abstract

SUMMARYConventional and flexible bus services may be combined to better serve regions with a wide range of characteristics. If demand densities and resulting service frequencies are low, the coordination of bus arrivals at transfer stations may significantly reduce passenger transfer times. A method is proposed for integrating, coordinating, and optimizing bus services while considering many-to-many travel patterns, demand elasticity, financial constraints, and appropriate service type for various regions. The objective is to maximize welfare, that is, the sum of producer and consumer surplus. The problem is solved with a hybrid optimization method, in which a genetic algorithm with bounded integer variables is selected for solving one of the subproblems. The service types, fares, headways, and service zone sizes are jointly optimized. Sensitivity analyses explore how the choice among conventional and flexible busses depends on the demand, subsidy, and demand elasticity parameters. The results also show that welfare can increase due to coordination, and these increases are found to be higher in cases with high demand or low subsidy.

Time control point strategy coupled with transfer coordination in bus schedule design

“…To avoid bus blockages at time control points shared by several bus lines, the constraints expressed by Equations (13)(14)(15) are thus proposed.…”

“…where J is a set of consecutive time instants, in chronological order, spanning the overall time horizon of the study; j denotes a particular time instant in set J; B s is the number of bus berths at time control point s; and φ s is the maximum bus dwell time at control point s in units of minutes, which can be estimated from historical data and should be rounded up to the nearest integer. Constraints (13)(14)(15) imply that the number of buses arriving at control point s during each interval of φ s consecutive time instants should be fewer than B s . To illustrate the three constraints earlier, suppose that J = [17 : 00,17 : 01,…,19 : 29]; the arrival time 17:29, for example, will then be assigned to the 30th time instant.…”

“…Equation (9) Subject to: Fundamental constraints: Equations (1-3), (5,6), (10)(11)(12), (16,17), (19), (24,25) Bus blockage constraints: Equations (14,15), (20), (22), (23) 3. NUMERICAL EXPERIMENTS Three bus lines -No 32, No.…”

“…To evaluate the effect of bus blockage constraints (13)(14)(15), the authors dropped these three constraints in the developed MINLP model. With the same data setting in Section 3.1, the authors used CPLEX to solve the associated MILP model excluding the bus blockage constraints to obtain the optimal scheduled arrival time solutions when ξ = 15 presented in Table VI.…”

“…Therefore, the total transfer waiting time when ξ = 15 is 1 minute, as presented in Table IV. In brief, the bus blockage constraints (13)(14)(15)) are effective and have been well incorporated into the MINLP model.…”