An integrated approach for timetabling and vehicle scheduling problems to analyze the trade-off between level of service and operating costs of transit networks

[Display omitted] •We develop a complete integration of timetabling and vehicle scheduling problems.•Our methodology formulates a bi-objective problem and use the ∊-constraint algorithm.•Obtained solutions can be used to measure the compromise between quality and costs.•We answer questions such as how many passengers are benefited by using one more bus? In transit systems there is a critical trade-off between the level of service and operating costs. At the planning level, for a given network design, this trade-off is captured by the timetabling (TT) and vehicle scheduling (VS) problems. In the TT problem we try to maximize the number of passengers benefited by well timed transfers, while in the VS problem we seek to minimize the operating costs, which are related to the fleet size. This paper presents two integer linear programming models for the TT and VS problems, and combines them in a bi-objective integrated model. We propose and implement an ∊-constraint method to jointly solve this TT and VS bi-objective problem. This allows to analyze the trade-off between these two criteria in terms of Pareto fronts. Numerical experiments show that our proposed approach can solve scenarios with up to 50 bus lines.