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Balanced Assignments of Periodic Tasks

Authors Héloïse Gachet, Frédéric Meunier

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Applied computing → Transportation
Keywords
  • Fair schedule
  • Eulerian digraph
  • Markov chain
  • interval graph

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Abstract

This work deals with a problem of assigning periodic tasks to employees in such a way that each employee performs each task with the same frequency in the long term. The motivation comes from a collaboration with the main French railway company, the SNCF. An almost complete solution is provided under the form of a necessary and sufficient condition that can be checked in polynomial time. A complementary discussion about possible extensions is also proposed.

Cite As Get BibTex

Héloïse Gachet and Frédéric Meunier. Balanced Assignments of Periodic Tasks. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 5:1-5:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/OASIcs.ATMOS.2024.5

Author Details

Héloïse Gachet
  • École nationale des ponts et chaussées, Champs-sur-Marne, France
  • SNCF, DTIPG, Saint-Denis, France
Frédéric Meunier
  • École nationale des ponts et chaussées, Champs-sur-Marne, France

Funding

This research was partially supported by the SNCF as part of a CIFRE PhD.

Acknowledgements

The authors are also grateful to Jean-François Delmas for pointing out the situation of "normal numbers," whose existence status shares some similarity with that of balanced feasible assignments; see Section 4.1.

References

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