Assignment Based Resource Constrained Path Generation for Railway Rolling Stock Optimization

Authors Boris Grimm, Ralf Borndörfer, Julian Bushe

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Author Details

Boris Grimm
  • Freie Universtät Berlin, Germany
  • Zuse Institute Berlin, Germany
Ralf Borndörfer
  • Freie Universtät Berlin, Germany
  • Zuse Institute Berlin, Germany
Julian Bushe
  • Zuse Institute Berlin, Germany

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Boris Grimm, Ralf Borndörfer, and Julian Bushe. Assignment Based Resource Constrained Path Generation for Railway Rolling Stock Optimization. In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 13:1-13:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


The fundamental task of every passenger railway operator is to offer an attractive railway timetable to the passengers while operating it as cost efficiently as possible. The available rolling stock has to be assigned to trips so that all trips are operated, operational requirements are satisfied, and the operating costs are minimum. This so-called Rolling Stock Rotation Problem (RSRP) is well studied in the literature. In this paper we consider an acyclic version of the RSRP that includes vehicle maintenance. As the latter is an important aspect, maintenance services have to be planned simultaneously to ensure the rotation’s feasibility in practice. Indeed, regular maintenance is important for the safety and reliability of the rolling stock as well as enforced by law in many countries. We present a new integer programming formulation that links a hyperflow to model vehicle compositions and their coupling decisions to a set of path variables that take care of the resource consumption of the individual vehicles. To solve the model we developed different column generation algorithms which are compared to each other as well as to the MILP flow formulation of [Ralf Borndörfer et al., 2016] on a test set of real world instances.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
  • Railway Rolling Stock Optimization
  • Integer Programming
  • Column Generation


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