A Mixed Integer Linear Program for Optimizing the Utilization of Locomotives with Maintenance Constraints

  • Sarah FrischEmail author
  • Philipp Hungerländer
  • Anna Jellen
  • Dominic Weinberger
Conference paper
Part of the Operations Research Proceedings book series (ORP)


In this paper we investigate the Locomotive Scheduling Problem, i.e., the optimization of locomotive utilization with prior known transports that must be performed. Railway timetables are typically planned a year in advance and then revised, updated and fixed for shorter time periods, e.g., for a week, during the year. Our aim is to assign locomotives to the trains such that the locomotive utilization is maximized considering maintenances. We model this optimization problem on a sparse weighted directed multigraph that defines the input variables for our proposed Mixed Integer Linear Program (MILP). We consider two different objective functions: We minimize over the number of deadhead kilometers, i.e., kilometers from a locomotive driven without pulling a train, and over the number of locomotives used. Finally, we conduct a computational study to compare the performance of our MILP with the different proposed objective functions and show how the MILP can be used within a rolling horizon approach.


Locomotive scheduling problem Maintenance constraints Mixed integer linear programming 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sarah Frisch
    • 1
    Email author
  • Philipp Hungerländer
    • 1
  • Anna Jellen
    • 1
  • Dominic Weinberger
    • 1
  1. 1.Department of MathematicsAlpen-Adria-Universität KlagenfurtKlagenfurtAustria

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