Passenger railway systems are highly complex systems requiring the solution of several planning problems that can be analyzed and solved through the application of mathematical models and optimization techniques, which generally lead to an improvement in the performance of the system, and also to a reduction in the time required for solving these problems. The planning process is generally divided into several phases. After a description of the whole planning process and of its main phases, the Platforming and Train-Unit Assignment phases are considered in more detail. In the Train Platforming Problem, we are given a set of timetabled trains, and the objective is to find the best assignment of the trains to the platforms (and to the routing paths connecting the arrival/departure tracks to the assigned platforms) in a railway station. An Integer Linear Programming (ILP) formulation is presented, and a column generation procedure is proposed for the solution of the corresponding continuous relaxation. An effective heuristic algorithm, driven by the continuous relaxation of the ILP formulation, is proposed as well. Computational results on real-world instances are reported. A train unit consists of a self-contained train with an engine and a set of wagons with passenger seats. The Train-Unit Assignment Problem calls for the definition of the “best” train units to be assigned to a given set of timetabled trips, each with a given number of passenger seats requested. Heuristic algorithms based on the solution of ILP models are presented. Computational results on real-world instances are reported.
Paolo Toth is Professor of Operational Research at the Faculty of Engineering of the University of Bologna. He is the author of more than 160 papers published in international journals and of the book Knapsack Problems: Algorithms and Computer Implementations (coauthor S. Martello; J. Wiley, Chichester, 1990). He is also Co-Editor of the books Combinatorial Optimization (J. Wiley, Chichester, 1979) and The Vehicle Routing Problem (SIAM Monographs on Discrete Mathematics and Applications, Philadelphia, 2002). He is currently a member of the Editorial Boards of the journals Transportation Science, Networks, Journal of Heuristics, Journal of the Operational Research Society, European Journal of Operational Research and many more. He was President of AIRO (Italian Operational Research Society) 1988-1995; President of EURO (Association of the European Operational Research Societies) 1995-1996; and President of IFORS (International Federation of the Operational Research Societies) 2001-2003. In May 1998, Toth delivered the Harold Larnder Memorial Lecture (annual Award of CORS). In 1998, he was conferred the EURO Gold Medal, the highest distinction within Operational Research in Europe. In May 2003, the University of Montreal conferred him a Doctorate honoris causa in Operational Research. In November 2005, the Transportation Science and Logistics Society of INFORMS conferred on him the Robert Herman Lifetime Achievement Award in Transportation Science.