Periodic Timetabling: Travel Time vs. Regenerative Energy

While it is important to provide attractive public transportation to the passengers allowing short travel times, it should also be a major concern to reduce the amount of energy used by the public transport system. Electrical trains can regenerate energy when braking, which can be used by a nearby accelerating train. Therefore, apart from the minimization of travel times, the maximization of brake-traction overlaps of nearby trains is an important objective in periodic timetabling. Recently, this has been studied in a model allowing small modifications of a nominal timetable. We investigate the problem of finding periodic timetables that are globally good in both objective functions. We show that the general problem is NP-hard, even restricted to a single transfer station and if only travel time is to be minimized, and give an algorithm with an additive error bound for maximizing the brake-traction overlap on this small network. Moreover, we identify special cases in which the problem is solvable in polynomial time. Finally, we demonstrate the trade-off between the two objective functions in an experimental study.