A branch-and-bound approach for robust railway timetabling

Gábor Maróti*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


This paper studies the robust cyclic timetabling problem. The goal is to modify a given reference timetable to enhance its robustness against small stochastic disturbances. The robustness is measured by the expected total delay of the realised timetable. Kroon et al. (Transp Res Part B 42(6):553–570, 2008) propose a stochastic programming approach and implement it for Netherlands Railways (NS). While the model’s outcome is accepted by practitioners, relevant planning problems are rendered intractable by computation times of up to several days. In this paper we describe a Branch-and-Bound algorithm for solving the stochastic program of Kroon et al. (Transp Res Part B 42(6):553–570, 2008). We propose specific node selection rules, variable selection rules, constructive heuristics and lower bounds. We carry out computational tests on large real-life problem instances. The results confirm that our algorithm is able to considerably improve the robustness of the reference solutions. This is achieved with computation times of a few minutes. However, the weak lower bounds we use leave a considerable optimality gap. Therefore, our algorithm is best described as a heuristic solution method.

Original languageEnglish
Pages (from-to)73-94
Number of pages22
JournalPublic Transport
Issue number1-2
Publication statusPublished - 1 Jul 2017


  • Branch-and-bound
  • Robust timetabling
  • Stochastic programming


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