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The nurse rostering problem: A critical appraisal of the problem structure

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  • Glass, Celia A.
  • Knight, Roger A.

Abstract

This paper is concerned with the problem of nurse rostering within hospitals. We analyse a class of four benchmark instances from the nurse rostering literature to provide insight into the nature of the problem. By highlighting the structure of the problem we are able to reduce the relevant solution space. A mixed integer linear programme is then able to find optimal solutions to all four instances of this class of benchmark problems, each within half an hour. Our second contribution is to extend current mathematical approaches to nurse rostering to take better account of the practical considerations. We provide a methodology for handling rostering constraints and preferences arising from the continuity from one scheduling period to the next.

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  • Glass, Celia A. & Knight, Roger A., 2010. "The nurse rostering problem: A critical appraisal of the problem structure," European Journal of Operational Research, Elsevier, vol. 202(2), pages 379-389, April.
    • Handle: RePEc:eee:ejores:v:202:y:2010:i:2:p:379-389
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    References listed on IDEAS

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    1. Mark Isken, 2004. "An Implicit Tour Scheduling Model with Applications in Healthcare," Annals of Operations Research, Springer, vol. 128(1), pages 91-109, April.
    2. Michael J. Brusco & Larry W. Jacobs, 2000. "Optimal Models for Meal-Break and Start-Time Flexibility in Continuous Tour Scheduling," Management Science, INFORMS, vol. 46(12), pages 1630-1641, December.
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    5. Burke, Edmund K. & Curtois, Timothy & Post, Gerhard & Qu, Rong & Veltman, Bart, 2008. "A hybrid heuristic ordering and variable neighbourhood search for the nurse rostering problem," European Journal of Operational Research, Elsevier, vol. 188(2), pages 330-341, July.
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    Cited by:

    1. Yücel Öztürkoğlu, 2020. "A Different Approach to Nurse Scheduling Problem: Lagrangian Relaxation," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 8(2), pages 237-248, December.
    2. Caballini, Claudia & Paolucci, Massimo, 2020. "A rostering approach to minimize health risks for workers: An application to a container terminal in the Italian port of Genoa," Omega, Elsevier, vol. 95(C).
    3. Valouxis, Christos & Gogos, Christos & Goulas, George & Alefragis, Panayiotis & Housos, Efthymios, 2012. "A systematic two phase approach for the nurse rostering problem," European Journal of Operational Research, Elsevier, vol. 219(2), pages 425-433.
    4. 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.
    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. Florian Mischek & Nysret Musliu, 2019. "Integer programming model extensions for a multi-stage nurse rostering problem," Annals of Operations Research, Springer, vol. 275(1), pages 123-143, April.
    7. Pieter Smet & Burak Bilgin & Patrick De Causmaecker & Greet Vanden Berghe, 2014. "Modelling and evaluation issues in nurse rostering," Annals of Operations Research, Springer, vol. 218(1), pages 303-326, July.
    8. Lü, Zhipeng & Hao, Jin-Kao, 2012. "Adaptive neighborhood search for nurse rostering," European Journal of Operational Research, Elsevier, vol. 218(3), pages 865-876.
    9. Sophie Veldhoven & Gerhard Post & Egbert Veen & Tim Curtois, 2016. "An assessment of a days off decomposition approach to personnel shift scheduling," Annals of Operations Research, Springer, vol. 239(1), pages 207-223, April.
    10. Ran Liu & Xiaolan Xie, 2018. "Physician Staffing for Emergency Departments with Time-Varying Demand," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 588-607, August.
    11. Mohammad Reza Hassani & J. Behnamian, 2021. "A scenario-based robust optimization with a pessimistic approach for nurse rostering problem," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 143-169, January.
    12. Marta Rocha & José Oliveira & Maria Carravilla, 2014. "A constructive heuristic for staff scheduling in the glass industry," Annals of Operations Research, Springer, vol. 217(1), pages 463-478, June.
    13. Xiang Li & Haoyue Fan & Jiaming Liu & Qifeng Xun, 2022. "Staff scheduling in blood collection problems," Annals of Operations Research, Springer, vol. 316(1), pages 365-400, September.
    14. Van den Bergh, Jorne & Beliën, Jeroen & De Bruecker, Philippe & Demeulemeester, Erik & De Boeck, Liesje, 2013. "Personnel scheduling: A literature review," European Journal of Operational Research, Elsevier, vol. 226(3), pages 367-385.
    15. Burak Bilgin & Patrick Causmaecker & Benoît Rossie & Greet Vanden Berghe, 2012. "Local search neighbourhoods for dealing with a novel nurse rostering model," Annals of Operations Research, Springer, vol. 194(1), pages 33-57, April.
    16. Sara Ceschia & Rosita Guido & Andrea Schaerf, 2020. "Solving the static INRC-II nurse rostering problem by simulated annealing based on large neighborhoods," Annals of Operations Research, Springer, vol. 288(1), pages 95-113, May.

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    Keywords

    Integer programming Nurse rostering;

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