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

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, economics - operating costs, operations - scheduling, planning - service level, planning - network design


Timetabling, Vehicle scheduling, Integrated approach, Bi-objective optimization, ∊-Constraint


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.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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