Automated, passenger time optimal, robust timetabling, using integer programming

To design an optimal passenger train timetable one should choose a quality criterium or a combination of criteria. We consider the main quality criterium from a passenger perspective: journey time. This means that the expected time all passengers will spend when our timetable is put in practice is minimal, even taking into account typical train delays. From a train operator or rail infrastructure management company perspective, there are further concerns too, like the number of train units that has to take part in this schedule, their frequency, the number of drivers and other crew members. These factors are all related to cost to maintain the schedule but are here considered secondary and indeed, are here kept constant. We consider only the passenger criterium here. We analytically derive total stochastic expected passenger time as a closed formula, linearize it and use it as a goal function for optimizing the schedule using a mixed integer linear programming model. We applied this to all 224 current Belgian train relations, passing 550 train stations and calculated an optimal schedule in 3 hours. We believe this mathematically optimal approach is unique, in its detailed model of expected, stochastic passenger time, in its scale of implementation and in its use of actual current data from practice