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Does Laziness Pay Off? - A Lazy-Constraint Approach to Timetabling

Authors Torsten Klug, Markus Reuther, Thomas Schlechte

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Author Details

Torsten Klug
  • LBW Optimization GmbH, Berlin, Germany
Markus Reuther
  • LBW Optimization GmbH, Berlin, Germany
Thomas Schlechte
  • LBW Optimization GmbH, Berlin, Germany

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Torsten Klug, Markus Reuther, and Thomas Schlechte. Does Laziness Pay Off? - A Lazy-Constraint Approach to Timetabling. In 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022). Open Access Series in Informatics (OASIcs), Volume 106, pp. 11:1-11:8, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Timetabling is a classical and complex task for public transport operators as well as for railway undertakings. The general question is: Which vehicle is taking which route through the transportation network in which order? In this paper, we consider the special setting to find optimal timetables for railway systems under a moving block regime. We directly set up on our work of [T. Schlechte et al., 2022], i.e., we consider the same model formulation and real-world instances of a moving block headway system. In this paper, we present a repair heuristic and a lazy-constraint approach utilizing the callback features of Gurobi, see [Gurobi Optimization, 2022]. We provide an experimental study of the different algorithmic approaches for a railway network with 100 and up to 300 train requests. The computational results show that the lazy-constraint approach together with the repair heuristic significantly improves our previous approaches.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
  • Moving Block
  • Railway Track Allocation
  • Timetabling
  • Train Routing


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  1. Ralf Borndörfer, Torsten Klug, Leonardo Lamorgese, Carlo Mannino, Markus Reuther, and Thomas Schlechte, editors. Handbook of Optimization in the Railway Industry, volume 268. Springer, 2018. URL:
  2. Valentina Cacchiani, Dennis Huisman, Martin Kidd, Leo Kroon, Paolo Toth, Lucas Veelenturf, and Joris Wagenaar. An overview of recovery models and algorithms for real-time railway rescheduling. Transportation Research Part B: Methodological, 63:15-37, 2014. URL:
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  7. Ulrich Pferschy and Rostislav Staněk. Generating subtour elimination constraints for the TSP from pure integer solutions. Central European Journal of Operations Research, 25(1):231-260, February 2016. URL:
  8. Thomas Schlechte, Ralf Borndörfer, Jonas Denißen, Simon Heller, Torsten Klug, Michael Küpper, Niels Lindner, Markus Reuther, Andreas Söhlke, and William Steadman. Timetable optimization for a moving block system. Journal of Rail Transport Planning & Management, 22:100315, June 2022. URL:
  9. Peijuan Xu, Francesco Corman, Qiyuan Peng, and Xiaojie Luan. A train rescheduling model integrating speed management during disruptions of high-speed traffic under a quasi moving block system. Transportation Research Part B, 104:638-666, 2017. URL:
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