Reducing the passenger travel time in practice by the automated construction of a robust railway timetable

Abstract

Automatically generating timetables has been an active research area for some time, but the application of this research in practice has been limited. We believe this is due to two reasons. Firstly, some of the models in the literature impose artificial upper bounds on time supplements. This causes a high risk of generating infeasibilities. Secondly, some models that leave out these upper bounds often generate solutions that contain some very large time supplements because these supplements are not penalised in the objective function. The reason is that these objective functions often do not completely correspond to the true goal of a timetable. We solve both problems by minimising our objective function: total passenger travel time, expected in practice. Since this function evaluates and indirectly steers all time related decision variables in the system, we do not need to further restrict the ranges of any of these variables. As a result, our model does not suffer from infeasibilities generated by such artificial upper bounds for supplements.Furthermore, some measures are taken to significantly speed up the solver times of our model. These combined features result in our model being solved more quickly than previous models. As a result, our method can be used for timetabling in practice. We demonstrate our claims by optimising, in about two hours only, the timetable of all 196 hourly passenger trains in Belgium. Assuming primary delay-distributions with an average of 2% on the minima of each activity, the optimised timetable reduces expected passenger time in practice, as evaluated on the macroscopic level, by 3.8% during peak hours. This paper demonstrates that we added two important missing steps to make cyclic timetabling for passengers really useable in practice: (i) the addition of the objective function of expected passenger time in practice and (ii) the reduction of computation time by addition of well chosen additional constraints.