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Stable multi-skill workforce assignments

Abstract

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.

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Acknowledgements

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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Correspondence to Murat Fırat.

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Fırat, M., Hurkens, C.A.J. & Laugier, A. Stable multi-skill workforce assignments. Ann Oper Res 213, 95–114 (2014). https://doi.org/10.1007/s10479-012-1224-0

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Keywords

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