Annals of Operations Research

, Volume 213, Issue 1, pp 95–114 | Cite as

Stable multi-skill workforce assignments

  • Murat FıratEmail author
  • C. A. J. Hurkens
  • Alexandre Laugier


This paper analyzes stability in multi-skill workforce assignments of technicians and jobs. In our stability analysis, we extend the notion of blocking pairs as stated in the Marriage model of Gale-Shapley to the multi-skill workforce assignment. It is shown that finding stable assignments is NP-hard. A special case turns out to be solvable in polynomial time. For the general case, we give a characterization of the set of stable assignments by means of linear inequalities involving binary variables. We propose an integer programming (IP) model to construct optimal stable assignments with several objectives. In the computational results, we observe that it is easier to attain stability in instances with easy jobs and we consider a range of instances to show how fast the solution time increases. Open questions and further directions are discussed in the conclusion section.


Multi-skill workforce schedules Stable assignments Instability Blocking pair University admissions problem Three-dimensional matching problem Optimal stable assignments 



This research is supported by France Telecom/TUE Research agreement No. 46145963. Thanks are due to Gerhard J. Woeginger for helpful discussions on complexity results and due to Judith C.M. Keijsper for her remarks on the notation of this paper. The reviewers deserve special thanks due to their comments on our proofs and on our IP models. Their comments helped a lot in improving the content of this paper.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Murat Fırat
    • 1
    Email author
  • C. A. J. Hurkens
    • 1
  • Alexandre Laugier
    • 2
  1. 1.Department of Mathematics and Computer ScienceTU EindhovenEindhovenThe Netherlands
  2. 2.France Telecom/R&D/BIZZ/DIAM 905Sophia-Antipolis CedexFrance

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