Optimal Freight Train Classification using Column Generation
Markus Bohlin,Florian Dahms,Holger Flier,Sara Gestrelius +3 more
- 01 Jan 2012
- Vol. 25, pp 10-22
TL;DR: A new extended integer programming model is formed and a column generation approach based on branch-and-price to solve problem instances of industrial size is designed based on historical data from the Hallsberg hump yard in Sweden.
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Abstract: We consider planning of freight train classification at hump yards using integer programming. The problem involves the formation of departing freight trains from arriving trains subject to scheduling and capacity constraints. To increase yard capacity, we allow the temporary storage of early freight cars on specific mixed-usage tracks. The problem has previously been modeled using a direct integer programming model, but this approach did not yield lower
bounds of sufficient quality to prove optimality. In this paper, we
formulate a new extended integer programming model and design a column generation approach based on branch-and-price to solve
problem instances of industrial size. We evaluate the method on
historical data from the Hallsberg hump yard in Sweden, and compare
the results with previous approaches. The new method managed to find
optimal solutions in all of the 192 problem instances tried. Furthermore, no instance took more than 13 minutes to solve
to optimality using fairly standard computer hardware.
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Citations
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A matheuristic approach to integrate humping and pullout sequencing operations at railroad hump yards
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Branch-And-Price: Column Generation for Solving Huge Integer Programs
Cynthia Barnhart,Ellis L. Johnson,George L. Nemhauser,Martin W. P. Savelsbergh,Pamela H. Vance +4 more
TL;DR: In this paper, column generation methods for integer programs with a huge number of variables are discussed, including implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branch-and-bound tree.
A Primer in Column Generation
Jacques Desrosiers,Marco E. Lübbecke +1 more
- 01 Jan 2005
TL;DR: In this article, a didactic introduction to the use of column generation technique in linear and in particular in integer programming is given, and the relevant basic theory and more advanced ideas which help in solving large scale practical problems are discussed.
Multistage methods for freight train classification
TL;DR: In this paper, the authors developed a novel encoding of classification schedules, which allows characterizing train classification methods simply as classes of schedules, and applied this efficient encoding, they achieved a simpler, more precise analysis of well-known classification methods.