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From Routes to Resources: A Model for Real-Time Train Dispatching with No-Wait Constraints

Authors Luka Stärk , Ralf Borndörfer , Niels Lindner

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OASIcs.ATMOS.2026.6.pdf
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Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
  • Mathematics of computing → Combinatorial optimization
  • Theory of computation → Mixed discrete-continuous optimization
Keywords
  • Train Dispatching
  • No-Wait Constraints
  • Disjunctive Graph
  • Edge Clique Cover
  • Microscopic Railway Timetabling

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Abstract

Optimization for train dispatching promises to reduce delays. Yet scalable applications are challenging. We present an efficient MIP model, based on generalized disjunctive graphs, for the train dispatching problem with no-wait constraints. For each train, we model its possible movements with microscopic detail as a DAG of operations. We select one train path per DAG and associate it with reservation and release times for the exclusive infrastructure it uses, such that the resulting schedule is conflict-free. When the connecting velocity between consecutive operations is positive, no-wait constraints apply. Additionally, we give a procedure to transform realistic infrastructure constraints based on route exclusions into an equivalent representation on resources by means of edge clique covers and incorporation of overlap exclusions. This makes resource-based dispatching models applicable to real-life infrastructure. We embed the MIP into an iterative algorithm, which we evaluate on the DISPLIB benchmark set and on a real-life dataset from German dispatching regions that we publish together with this paper. We prove optimality for 70 of the 112 DISPLIB instances within short running times, and we find 27 new best known solutions within a 10-minute time limit.

Cite As Get BibTex

Luka Stärk, Ralf Borndörfer, and Niels Lindner. From Routes to Resources: A Model for Real-Time Train Dispatching with No-Wait Constraints. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 6:1-6:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/OASIcs.ATMOS.2026.6

Author Details

Luka Stärk
  • Zuse Institute Berlin, Germany
  • Freie Universität Berlin, Germany
Ralf Borndörfer
  • Zuse Institute Berlin, Germany
  • Freie Universität Berlin, Germany
Niels Lindner
  • Zuse Institute Berlin, Germany
  • Freie Universität Berlin, Germany

Funding

The work for this article has been conducted in the Research Campus MODAL funded by the German Federal Ministry of Research, Technology and Space (BMFTR), fund number 05M25KEM.
  • Stärk, Luka: Partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – The Berlin Mathematics Research Center MATH+ (EXC-2046/2, project ID: 390685689).

Acknowledgements

We thank our industrial partner DB InfraGO AG, in particular the ADA-PMB team, for the kind permission to publish our benchmarking set based on real data. We also thank the three anonymous reviewers, whose comments improved the presentation of this paper.

Supplementary Materials

References

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