Integrated Periodic Timetabling and Vehicle Circulation Scheduling

Periodic timetabling is one of the most well researched problems in the public transport optimization literature. However, the impact timetabling has on the number of required vehicles, which directly translates to operator costs, is rarely considered. Therefore, in this paper, we consider the problem of jointly optimizing the timetable and the vehicle circulation schedule, which specifies the cyclic sequences of trips vehicles perform. In order to be able to solve realistic instances, we improve an earlier proposed formulation by contraction techniques, valid inequalities and symmetry-breaking constraints. Ultimately, this allows us to explore the trade-off between the number of vehicles and the attractiveness of the timetable from the passengers' perspective. An extensive computational study demonstrates the effectiveness of the improved formulation. Moreover, using this approach we are able to find timetables requiring substantially fewer vehicles at the cost of minimal increases of the average travel time of passengers.