We propose a new dynamic row/column management algorithm for the schedule of freight trains in a single/double track railway system. While many works have already been devoted to train scheduling, previously published optimization models all suffer from scalability issues. Moreover, very few of them consider the number of alternate tracks in the sidings for train meets, as well as the delay incurred by trains that take sidings. We propose a non time-indexed model, which takes into account such constraints, and we design a solution scheme with iterative additions/removals of constraints/variables in order to remain with a manageable sized mathematical program, while still ensuring convergence to an optimal solution. Numerical results are presented on data instances of Canada Pacific Railway. We evaluate the performance of the optimization model, and the sensitivity of the train schedules to the length of the operation hours, the length of the trains, and the departure times.