OR Spectrum

, Volume 36, Issue 3, pp 631–668 | Cite as

Robust load planning of trains in intermodal transportation

  • Florian BrunsEmail author
  • Marc Goerigk
  • Sigrid Knust
  • Anita Schöbel
Regular Article


In this paper, the problem of robust load planning for trains in intermodal container terminals is studied. The goal of load planning is to choose wagon settings and assign load units to wagons of a train such that the utilization of the train is maximized, and setup and transportation costs in the terminal are minimized. However, in real-world applications, many of the parameters needed for the model are not known exactly. Since feasibility of the resulting load distribution has always to be guaranteed, we decided to use a robust approach. In particular, we apply the concepts of strict and adjustable robustness to enhance the load planning problem. Based on a formulation developed in Bruns and Knust (OR Spectrum 34:511–533, 2012) for the deterministic load planning problem, we propose mixed-integer linear programming formulations for most of the respective robust counterparts, dependent on the type of uncertainty. An experimental study shows that most of the robust problems can be solved within runtimes of a few minutes, which is good enough for real-world applications. Furthermore, our results indicate that robust solutions may improve the planning considerably, and that it is promising to add robustness even to large mixed-integer programs with many and diverse technical constraints.


Load planning Intermodal transportation Robustness  Strict robustness Adjustable robustness 



We gratefully acknowledge the help of two anonymous referees who gave several constructive comments to improve the paper. Additionally, we thank Marco Lenk (Deutsche Umschlaggesellschaft Schiene-Straße mbH) for providing information about uncertainties in the practical load planning setting.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Florian Bruns
    • 1
    Email author
  • Marc Goerigk
    • 2
  • Sigrid Knust
    • 1
  • Anita Schöbel
    • 2
  1. 1.Institute of Computer ScienceUniversity of OsnabrückOsnabrückGermany
  2. 2.Institute for Numerical and Applied MathematicsGeorg-August-UniversityGöttingenGermany

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