Expected Passenger Travel Time as Objective Function for Train Schedule Optimization

Most literature in train schedule optimization concentrates on the constraints of the problem. A few examples are [4, 5, 6, 7, 8]. Very little is found on the optimisation criterium: the objective function [2, 3]. We believe one of the main reasons is that in generating schedules that are robust against delays, this is the harder part of the mathematical modelling. Indeed, unlike the hard constraints, it requires the use of statistics, namely delay statistics. It also requires accurate measurement of these delays or derivation from train logs. We consider total passenger travel time as the most important criterium for judging the quality of a passenger train schedule [1, 9, 10, 11], so this is what we want to minimize as the objective function. Approaches to train scheduling that lack an objective function like this are unable to make an informed decision about the size of supplements. These methods usually resort to inserting buffers on a train traject of up to some maximum percentage of the total train travel time [5]. Such approaches do not take into account the typical delays at a certain location, nor the number of passengers sitting in, entering, leaving or transferring to or from this train at that location. Therefore, it is impossible to calculate the travel time increase or decrease resulting from a buffer on all passenger streams. In our objective function, we use passenger numbers instead of trains as weight factors. While optimizing a schedule, we focus on decreasing this objective function and this implies