A Lagrangian heuristic algorithm for a real-world train timetabling problem
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
Optimal Real-Time Traffic Control in Metro Stations
Operations Research
Train timetable problem on a single-line railway with fuzzy passenger demand
IEEE Transactions on Fuzzy Systems
Modeling Network Transition Constraints with Hypergraphs
Transportation Science
Modeling Network Transition Constraints with Hypergraphs
Transportation Science
Railway track allocation: models and methods
OR Spectrum
Non-cyclic train timetabling and comparability graphs
Operations Research Letters
Rescheduling rail networks with maintenance disruptions using Problem Space Search
Computers and Operations Research
Computers and Industrial Engineering
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We present a novel optimization approach for the timetabling problem of a railway company, i.e., scheduling of a set of trains to obtain a profit maximizing timetable, while not violating track capacity constraints. The scheduling decisions are based on estimates of the value of running different types of service at specified times. We model the problem as a very large integer programming problem. The model is flexible in that it allows for general cost functions. We have used a Lagrangian relaxation solution approach, in which the track capacity constraints are relaxed and assigned prices, so that the problem separates into one dynamic program for each physical train. The number of dual variables is very large. However, it turns out that only a sm all fraction of these are nonzero, which one may take advantage of in the dual updating schemes. The approach has been tested on a realistic example suggested by the Swedish National Railway Administration. This example contains 18 passenger trains and 8 freight trains to be scheduled during a day on a stretch of single track, consisting of 17 stations. The computation times are rather modest and the obtained timetables are within a few percent of optimality.