Modelling the number and location of sidings on a single line railway. (English) Zbl 0889.90062

Summary: This article puts forward a model to determine the required number and position of sidings on a single track rail corridor. The sidings are positioned to minimize both the risk of delays and the delays caused by train conflicts, for a given cyclic train schedule. The key feature of the model is the allowance of variable train velocities and non-uniform departure times. A decomposition procedure, used to partition the mixed integer nonlinear program into easily solvable sub-models was found to converge quickly. Numerical results, using actual train schedules, indicate considerable savings in terms of both conflict delay and risk of delay when track sidings are positioned using the model. Simulations are used to demonstrate how the model can be used determine the required number of sidings given a pre-defined level of service.


90B06 Transportation, logistics and supply chain management
90C11 Mixed integer programming


Full Text: DOI


[1] Petersen, E. R.; Taylor, A. J., A structured model for rail line simulation and optimisation, Transportation Sci., 16, 192-205 (1982)
[2] Petersen, E. R.; Taylor, A. J., Design of a single-track rail line for high speed trains, Transportation Res. A., 21, 47-57 (1987)
[3] Kraft, E. R., Analytical models for rail line capacity analysis, (Transportation Res. Forum Proc., 24 (1983)), 153-162
[4] Higgins, A.; Ferreira, L.; Kozan, E., Modelling delay risks associated with train schedules, Transportation Planning Technol., 19, 89-108 (1995)
[5] Higgins, A., Optimisation of Train Schedules to Minimise Transit Time and Maximise Reliability, (Ph.D. Thesis (1996), Faculty of Science, Queensland University of Technology)
[6] Reynolds, R., Adequacy of Transport Infrastructure: Rail, (Bureau of Transport and Communications Economics: Working Paper 14.2 (1995), GPS: GPS Canberra, Australia)
[7] Geoffrion, A. M., Generalised benders decomposition, J. Optimisation Theory Appl., 10, 237-263 (1972) · Zbl 0229.90024
[8] Koskosidis, Y. A.; Powell, W. B.; Solomon, M. M., An optimisation-based heuristic for vehicle routing and scheduling with soft time window constraints, Transportation Sci., 26, 69-85 (1992) · Zbl 0762.90022
[9] Sklar, M. G.; Armstrong, R. D.; Samm, S., Heuristics for scheduling aircraft and crew during airlift operations, Transportation Sci., 24, 63-76 (1990)
[10] Higgins, A.; Kozan, E.; Ferreira, L., Optimal Scheduling of Trains on a Single Line Track, Transportation Res. B, 30, 147-161 (1996)
[11] Krasy, D.; Harker, P.; Chen, B., Optimal pacing of trains in freight railroads, Opns Res., 39, 82-99 (1991)
[12] Jovanovic, D., Improving Railroad On-time Performance: Models, Algorithms and Applications, (Ph.D. Thesis (1989), Department of Decision Sciences, The Wharton School. University of Pennsylvania)
[13] Brooke, A.; Kendrick, D.; Meeraus, A., GAMS: A User’s Guide (1988), Scientific Press
[14] Hohenbalken, D. V., Simplical decomposition in non-linear programming algorithms, Math. Prog., 13, 49-68 (1977)
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.