Graphs and algorithms
Integer and combinatorial optimization
Integer and combinatorial optimization
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
New methods for multi-commodity flows
Computers & Mathematics with Applications
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Problems involving allocation of shared resources, such as sections of railway track, can often be solved efficiently using network optimization algorithms. In this paper we discuss a problem which involves scheduling different kinds of trains on a railway network consisting of a mix of double and single track, and which incorporates rather complicated practical constraints. The mathematical model of the problem is an integer network optimization problem with side constraints, and is difficult or impossible to solve exactly in reasonable time. Even finding a feasible solution is non-trivial. We present an efficient approximate algorithm which can find good feasible solutions for real-world networks quickly with modest computing resources.