zbMATH — the first resource for mathematics

Railway scheduling by network optimization. (English) Zbl 0716.90057
Summary: 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 incorporate 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.
Reviewer: Reviewer (Berlin)

90B35 Deterministic scheduling theory in operations research
90C35 Programming involving graphs or networks
90-08 Computational methods for problems pertaining to operations research and mathematical programming
90C10 Integer programming
Full Text: DOI
[1] Anderson, E.J.; Nash, P., Linear programming in infinite dimensional spaces, (1987), Wiley Chichester, England
[2] Boland, N.; Mees, A.I., New methods for multicommodity flows, Computers and mathematics with applications, 20, 1, 29-38, (1990) · Zbl 0708.90024
[3] Ford, L.R.; Fulkerson, D.R., Flows in networks, (1962), Princeton University Press · Zbl 0139.13701
[4] Garey, M.R.; Johnson, D.S., Computers and intractibility: A guide to the theory of NP-completeness, (1979), Freeman San Francisco
[5] Gondran, M.; Minoux, M., Graphs and algorithms, (1984), Wiley Chichester, England, translated by S. Vajda · Zbl 1117.06010
[6] Lomonosov, M.V., Combinatorial approaches to multiflow problems, Discrete applied mathematics, 11, 1, 1-93, (1985) · Zbl 0598.90036
[7] Minoux, M., Résolution des problèmes de multiflots entiers dans LES grands réseaux, Rairo, 3, 21-40, (1975) · Zbl 0317.90056
[8] Nedelkovic, N.B.; Norton, N.C., Computerized train scheduling, (13-15 May, 1985), Australian Transport Research Forum Melbourne
[9] Nemhauser, G.L.; Wolsey, L.A., Integer and combinatorial optimization, (1988), Wiley New York · Zbl 0469.90052
[10] Rockafellar, R.T., Network flows and monotropic optimization, (1984), Wiley New York · Zbl 0596.90055
[11] Whittle, P., Optimization under constraints, (1971), Wiley Chichester, England · Zbl 0218.90041
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.