2012-10-31Buch DOI: 10.18452/8428
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 runningtime supplements (extra minutes added to a timetable to reduce delays) on a railway line. Bythe 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 alreadyexisting and well-functioning one. We model this inherently stochastic optimization problemby using two-stage recourse models from stochastic programming, following Vromans . Wepresent an improved formulation, allowing for an efficient solution using a standard algorithmfor recourse models. We include a case study that we managed to solve about 180 times fasterthan 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 practicepromises a significant improvement in the punctuality of trains. A technique to estimate themodel parameters from empirical data and an approximating deterministic problem are alsopresented, along with some practical ideas that are meant to enhance the applicability of ourmodels.
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