Trains’ movements on a railway network are regulated by official timetables. Deviations and delays occur quite often in practice, demanding fast rescheduling and rerouting 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. This 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 specific sets of variables and constraints. Similarly to the classical Benders’ decomposition approach, slave and master communicate through suitable feasibility cuts in the variables of the master. Extensive tests on real-life instances from single and double-track lines in Italy showed significant improvements over current dispatching performances. A decision support system based on this exact approach has been in operation in Norway since February 2014 and represents one of the first operative applications of mathematical optimization to train dispatching.

Train movements in railway lines are generally controlled by human dispatchers. As disruptions often occur, dispatchers take real-time scheduling and routing decisions in the attempt to minimize deviations from the ocial timetable. This optimization problem is called Train Dispatching. We represent it as a Mixed Integer Linear Programming model, and solve it by 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 in short computing time. 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 year 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.

No abstract

No abstract

No abstract