The Freight Train Routing Problem for Congested Railway Networks with Mixed Traffic

Ralf Borndörfer (), Torsten Klug (), Thomas Schlechte (), Armin Fügenschuh (), Thilo Schang () and Hanno Schülldorf ()
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Ralf Borndörfer: Department of Optimization, Zuse Institute Berlin, 14195 Berlin, Germany
Torsten Klug: Department of Optimization, Zuse Institute Berlin, 14195 Berlin, Germany
Thomas Schlechte: Department of Optimization, Zuse Institute Berlin, 14195 Berlin, Germany
Armin Fügenschuh: Faculty of Mechanical Engineering, Helmut Schmidt University/University of the Federal Armed Forces Hamburg, 22043 Hamburg, Germany
Thilo Schang: Deutsche Bahn Mobility Logistics AG, Transportation Network Development and Transport Models (GSV), 60326 Frankfurt am Main, Germany
Hanno Schülldorf: Deutsche Bahn Mobility Logistics AG, Transportation Network Development and Transport Models (GSV), 60326 Frankfurt am Main, Germany

Transportation Science, 2016, vol. 50, issue 2, 408-423

Abstract: We consider the following freight train routing problem (FTRP). Given is a transportation network with fixed routes for passenger trains and a set of freight trains (requests), each defined by an origin and destination station pair. The objective is to calculate a feasible route for each freight train such that the sum of all expected delays and all running times is minimal. Previous research concentrated on microscopic train routings for junctions or inside major stations. Only recently approaches were developed to tackle larger corridors or even networks. We investigate the routing problem from a strategic perspective, calculating the routes in a macroscopic transportation network of Deutsche Bahn AG. In this context, macroscopic refers to an aggregation of complex and large real-world structures into fewer network elements. Moreover, the departure and arrival times of freight trains are approximated. The problem has a strategic character since it asks only for a coarse routing through the network without the precise timings. We provide a mixed-integer nonlinear programming (MINLP) formulation for the FTRP, which is a multicommodity flow model on a time-expanded graph with additional routing constraints. The model’s nonlinearities originate from an algebraic approximation of the delays of the trains on the arcs of the network by capacity restraint functions. The MINLP is reduced to a mixed-integer linear model (MILP) by piecewise linear approximation. The latter is solved by a state-of-the art MILP solver for various real-world test instances.

Keywords: freight train routing; capacity restraint functions; multicommodity flows; mixed-integer linear and nonlinear programming (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:50:y:2016:i:2:p:408-423

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