An exact decomposition approach for the real-time Train Dispatching problem (v.2)

Trains movements on a railway network are regulated by official timetables. Deviations and delays occur quite often in practice, demanding fast re-scheduling and re-routing decisions in order to avoid conflicts and minimize overall delay. This is the real-time train dispatching problem. In contrast with the classic ""holistic"" approach, we show how to decompose the problem into smaller subproblems associated with the line and the stations. The decomposition is the basis for a master-slave solution algorithm, in which the master problem is associated with the line and the slave problem is associated with the stations. The two subproblems are modeled as mixed integer linear programs, with their specific sets of variables and constraints. Similarly to the classical Bender's decomposition approach, the slave and the master communicate through suitable feasibility cuts in the variables of the master. By applying our approach to a number of real-life instances from single and double-track lines in Italy, we were able to (quickly) find optimal or near-optimal solutions, with impressive improvements over the performances of the current operating control systems. The new approach will be put in operation in such lines for an extensive on-field test-campaign as of April 2013. Follows SINTEF Technical Report A2327