A Dynamic Row/Column Management Algorithm for Freight Train Scheduling

We propose a new dynamic row/column management algorithm for freight train scheduling in a single track railway system. While many papers have already been devoted to train scheduling, previously published optimization models still suffer from scalability issues, even for single track railway systems. Moreover, very few of them take into account the capacity constraints, i.e., the number of alternate tracks in the railway stations/sidings in order for the trains to meet/bypass. We propose an optimization model which takes such constraints into account, while still handling efficiently the other meaningful constraints. We design an original solution scheme with iterative additions/removals of constraints/variables in order to remain with a manageable sized mixed integer linear program at each iteration, without threatening to reach the optimal solution. Numerical results are presented on several data instances of CPR (Canadian Pacific Railway) on the Vancouver-Calgary corridor, one of the most busy corridor in their railway system. Therein, the proposed model and algorithm are used as a planning tool to evaluate the network capacity, i.e., how much the number of trains can be increased without impacting significantly the average travel times between the source and destination stations of the various trains in the corridor. Larger data instances than those previously published are solved accurately (epsilon-optimal solutions) for the schedule of freight trains.