Annals of Operations Research

, Volume 273, Issue 1–2, pp 479–500 | Cite as

Complexity, bounds and dynamic programming algorithms for single track train scheduling

  • Jonas HarberingEmail author
  • Abhiram Ranade
  • Marie Schmidt
  • Oliver Sinnen
S.I.: OR in Transportation


In this work we consider the single track train scheduling problem. The problem consists of scheduling a set of trains from opposite sides along a single track. The track has intermediate stations and the trains are only allowed to pass each other at those stations. Traversal times of the trains on the blocks between the stations only depend on the block lengths but not on the train. This problem is a special case of minimizing the makespan in job shop scheduling with two counter routes and no preemption. We develop a lower bound on the makespan of the train scheduling problem which provides us with an easy solution method in some special cases. Additionally, we prove that for a fixed number of blocks the problem can be solved in pseudo-polynomial time.


Machine scheduling Train scheduling Complexity analysis Counter routes 



The authors were partially funded by the DFG under Grant Number SCHO1140/3-2 and by the European Union Seventh Framework Programme (FP7-PEOPLE-2009-IRSES) under Grant Number 246647 with the New Zealand Government (project OptALI). We also thank the Simulationswissenschaftliches Zentrum Clausthal-Göttingen (SWZ) for financial support.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Georg-August-University of GöttingenGöttingenGermany
  2. 2.Indian Institute of Technology BombayMumbaiIndia
  3. 3.Erasmus University RotterdamRotterdamThe Netherlands
  4. 4.University of AucklandAucklandNew Zealand

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