Analyzing a Family of Formulations for Cyclic Crew Rostering

Authors Thomas Breugem, Twan Dollevoet , Dennis Huisman

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Author Details

Thomas Breugem
  • Technology and Operations Management, INSEAD, Fontainebleau, France
Twan Dollevoet
  • Erasmus University Rotterdam, The Netherlands
Dennis Huisman
  • Erasmus University Rotterdam, The Netherlands
  • Netherlands Railways, The Netherlands

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Thomas Breugem, Twan Dollevoet, and Dennis Huisman. Analyzing a Family of Formulations for Cyclic Crew Rostering. In 20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020). Open Access Series in Informatics (OASIcs), Volume 85, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


In this paper, we analyze a family of formulations for the Cyclic Crew Rostering Problem (CCRP), in which a cyclic roster has to be constructed for a group of employees. Each formulation in the family is based on a partition of the roster. Intuitively, finer partitions give rise to a formulation with fewer variables, but possibly more constraints. Coarser partitions lead to more variables, but might allow to incorporate many of the constraints implicitly. We derive analytical results regarding the relative strength of the different formulations, which can serve as a guideline for formulating a given problem instance. Furthermore, we propose a column generation approach, and use it to compare the strength of the formulations empirically. Both the theoretical and computational results demonstrate the importance of choosing a suitable formulation. In particular, for practical instances of Netherlands Railways, stronger lower bounds are obtained, and more than 90% of the roster constraints can be modeled implicitly.

Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
  • Crew Planning
  • Roster Sequence
  • Column Generation
  • Railway Optimization


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