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Polynomially solvable personnel rostering problems

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  • Smet, Pieter
  • Brucker, Peter
  • De Causmaecker, Patrick
  • Vanden Berghe, Greet

Abstract

Personnel rostering is a personnel scheduling problem in which shifts are assigned to employees, subject to complex organisational and contractual time-related constraints. Academic advances in this domain mainly focus on solving specific variants of this problem using intricate exact or (meta)heuristic algorithms, while little attention has been devoted to studying the underlying structure of the problems. The general assumption is that these problems, even in their most simplified form, are NP-hard. However, such claims are rarely supported with a proof for the problem under study. The present paper refutes this assumption by presenting minimum cost network flow formulations for several personnel rostering problems. Additionally, these problems are situated among the existing academic literature to obtain insights into what makes personnel rostering hard.

Suggested Citation

  • Smet, Pieter & Brucker, Peter & De Causmaecker, Patrick & Vanden Berghe, Greet, 2016. "Polynomially solvable personnel rostering problems," European Journal of Operational Research, Elsevier, vol. 249(1), pages 67-75.
    • Handle: RePEc:eee:ejores:v:249:y:2016:i:1:p:67-75
    DOI: 10.1016/j.ejor.2015.08.025
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    Cited by:

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    2. Komarudin & Tim De Feyter & Marie-Anne Guerry & Greet Vanden Berghe, 2020. "The extended roster quality staffing problem: addressing roster quality variation within a staffing planning period," Journal of Scheduling, Springer, vol. 23(2), pages 253-264, April.
    3. Elín Björk Böðvarsdóttir & Niels-Christian Fink Bagger & Laura Elise Høffner & Thomas J. R. Stidsen, 2022. "A flexible mixed integer programming-based system for real-world nurse rostering," Journal of Scheduling, Springer, vol. 25(1), pages 59-88, February.
    4. Lai, David S.W. & Leung, Janny M.Y. & Dullaert, Wout & Marques, Inês, 2020. "A graph-based formulation for the shift rostering problem," European Journal of Operational Research, Elsevier, vol. 284(1), pages 285-300.
    5. Sara Ceschia & Nguyen Dang & Patrick Causmaecker & Stefaan Haspeslagh & Andrea Schaerf, 2019. "The Second International Nurse Rostering Competition," Annals of Operations Research, Springer, vol. 274(1), pages 171-186, March.
    6. Castaño, Fabián & Velasco, Nubia, 2020. "Exact and heuristic approaches for the automated design of medical trainees rotation schedules," Omega, Elsevier, vol. 97(C).
    7. Youngbum Hur & Jonathan F. Bard & Markus Frey & Ferdinand Kiermaier, 2019. "An investigation of shift and break flexibility with real-time break assignments using a rolling horizon approach," Flexible Services and Manufacturing Journal, Springer, vol. 31(1), pages 174-211, March.
    8. Tristan Becker & Pia Mareike Steenweg & Brigitte Werners, 2019. "Cyclic shift scheduling with on-call duties for emergency medical services," Health Care Management Science, Springer, vol. 22(4), pages 676-690, December.

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