Optimal Train Dispatching by Benders'-Like Reformulation

Train movements on railway lines are generally controlled by human dispatchers. Because disruptions often occur, dispatchers make real-time scheduling and routing decisions in an attempt to minimize deviations from the official timetable. This optimization problem is called train dispatching. We represent it as a mixed integer linear programming model, and solve it with a Benders'-like decomposition within a suitable master/slave scheme. Interestingly, the master and the slave problems correspond to a macroscopic and microscopic representation of the railway, recently exploited in heuristic approaches to the problem. The decomposition, along with some new modeling ideas, allowed us to solve real-life instances of practical interest to optimality. Automatic dispatching systems based on our macro/micro decomposition-in which both master and slave are solved heuristically-have been in operation in several Italian lines since 2011. The exact approach described in this paper outperforms such systems on our test bed of real-life instances. Furthermore, a system based on another version of the exact decomposition approach has been in operation since February 2014 on a line in Norway.