NDLI: Timetabling optimization of a single railway track line with sensitivity analysis

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Timetabling optimization of a single railway track line with sensitivity analysis

Content Provider	Springer Nature Link
Author	Castillo, Enrique Gallego, Inmaculada Ureña, José María Coronado, José María
Copyright Year	2008
Abstract	The paper deals with the timetabling problem of a single-track railway line. To solve the timetabling problem, we propose a three-stage approach combining several optimization criteria. Initially and mainly, the maximum relative travel time (ratio of travel time to minimum possible travel time) is minimized subject to a set of constraints, including departure time, train speed, minimum and maximum dwell time, and headway at track segments and stations. Since this problem has many solutions, the process is repeated for other trains, keeping the relative travel times of the critical train fixed, until all trains have been assigned their optimal relative travel times. In the second stage, the prompt allocation of trains is a secondary objective, and finally, in the third stage, the one minimizing the sum of the station dwell times of all trains, keeping the relative travel times constant, is selected to reduce fuel consumption, as a tertiary objective. To consider the user preferences in the optimization problems, the user preference departure time is used instead of the actual planned departure times. In order to guarantee that the exact or a very good approximate global optimum is attained, an algorithm based on the bisection rule is used. This method allows the computation time to be reduced in at least one order of magnitude for 42 trains. The problem of sensitivity analysis is also discussed, and closed form formulas for the sensitivities in terms of the dual variables are given. Several examples of applications are presented to illustrate the goodness of the proposed method. The results show that an adequate selection of intermediate stations and of the departure times are crucial in the good performance of the line and that inadequate spacings between consecutive trains can block the line. In addition, it is shown that, in order to improve performance, regional trains must be scheduled just ahead of or following the long distance trains, rather than having independent schedules. The sensitivities are shown to be very useful in identifying critical trains, segments, stations, departure times, and headways and in suggesting line infrastructure changes.
Starting Page	256
Ending Page	287
Page Count	32
File Format	PDF
ISSN	11345764
Journal	Top
Volume Number	17
Issue Number	2
e-ISSN	18638279
Language	English
Publisher	Springer-Verlag
Publisher Date	2008-07-08
Publisher Institution	Spanish Society of Statistics and Operations Research
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Train timetabling Single track Bisection method Global optimum Railways Sensitivity analysis Special problems of linear programming Mixed integer programming Minimax problems Game Theory/Mathematical Methods Industrial and Production Engineering Statistics for Business/Economics/Mathematical Finance/Insurance Optimization Operations Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Discrete Mathematics and Combinatorics Management Science and Operations Research Information Systems and Management Modeling and Simulation

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