2012-10-31Buch DOI: 10.18452/3053
Optimizing existing railway timetables by means of stochastic programming
Vlerk, Maarten H. van der
Haneveld, Willem K. Klein
Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
We present some models to find the best allocation of a limited amount of so-called running time supplements (extra minutes added to a timetable to reduce delays) on a railway line. By the best allocation, we mean the solution under which the sum of expected delays is minimal. Instead of trying to invent a completely new timetable, our aim is to finely adjust an already existing and well-functioning one. We model this inherently stochastic optimization problem by using two-stage recourse models from stochastic programming, following Vromans . We present an improved formulation, allowing for an efficient solution using a standard algorithm for recourse models. We include a case study that we managed to solve about 180 times faster than it was solved in . By comparing our solution with other, seemingly intuitive solutions, we show that finding the best allocation is not obvious, and implementing it in practice promises a significant improvement in the punctuality of trains. A technique to estimate the model parameters from empirical data and an approximating deterministic problem are also presented, along with some practical ideas that are meant to enhance the applicability of our models.
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