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An Integer Multicommodity Flow Model Applied to the Rerostering of Nurse Schedules

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  • Margarida Moz
  • Margarida Pato

Abstract

The problem of rerostering service schedules is very common in organizations that work shifts around the clock every day of the year with a set number of employees. Whenever one or more workers announce that they will not be able to attend to tasks previously assigned in their schedule, those tasks must be performed at the expense of alterations in the schedules of other workers. These changes should not conflict with the rules laid down by the administration and employment contracts and should affect the previous schedules as little as possible. This is a difficult real problem calling for a computational tool to cope with it easily. In the paper the issue is described in detail in the context of nurse scheduling and formulated as an integer multicommodity flow problem with additional constraints, in a multi-level acyclical network. A heuristic was implemented as a first approach to solving the problem. Subsequently the integer linear programming formulation of the multicommodity flow model and two linear relaxations were tested using CPLEX [2] optimizers. The computational results reported regard real instances from a Lisbon state hospital. Satisfactory rosters were obtained within acceptable computational times in all instances tested, either with the integer optimizer, or with the heuristic. This being so, refinements will be undertaken to embed these methodologies in a decision support system that may assist the head nurse in her daily rerostering activities. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • Margarida Moz & Margarida Pato, 2003. "An Integer Multicommodity Flow Model Applied to the Rerostering of Nurse Schedules," Annals of Operations Research, Springer, vol. 119(1), pages 285-301, March.
    • Handle: RePEc:spr:annopr:v:119:y:2003:i:1:p:285-301:10.1023/a:1022907212477
    DOI: 10.1023/A:1022907212477
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    Citations

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    Cited by:

    1. Deborah L. Kellogg & Steven Walczak, 2007. "Nurse Scheduling: From Academia to Implementation or Not?," Interfaces, INFORMS, vol. 37(4), pages 355-369, August.
    2. Hassani, Rachid & Desaulniers, Guy & Elhallaoui, Issmail, 2021. "Real-time bi-objective personnel re-scheduling in the retail industry," European Journal of Operational Research, Elsevier, vol. 293(1), pages 93-108.
    3. Zsolt Ercsey & Zoltán Kovács, 2024. "Multicommodity network flow model of a human resource allocation problem considering time periods," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 32(4), pages 1041-1059, December.
    4. Na Li & Xiaorui Li & Paul Forero, 2022. "Physician scheduling for outpatient department with nonhomogeneous patient arrival and priority queue," Flexible Services and Manufacturing Journal, Springer, vol. 34(4), pages 879-915, December.
    5. Maenhout, Broos & Vanhoucke, Mario, 2013. "Reconstructing nurse schedules: Computational insights in the problem size parameters," Omega, Elsevier, vol. 41(5), pages 903-918.
    6. Wolbeck, Lena & Kliewer, Natalia & Marques, Inês, 2020. "Fair shift change penalization scheme for nurse rescheduling problems," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1121-1135.
    7. Ana Paias & Marta Mesquita & Margarida Moz & Margarida Pato, 2021. "A network flow-based algorithm for bus driver rerostering," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 543-576, June.
    8. Mesquita, Marta & Moz, Margarida & Paias, Ana & Pato, Margarida, 2015. "A decompose-and-fix heuristic based on multi-commodity flow models for driver rostering with days-off pattern," European Journal of Operational Research, Elsevier, vol. 245(2), pages 423-437.
    9. Borgonjon, Tessa & Maenhout, Broos, 2022. "An exact approach for the personnel task rescheduling problem with task retiming," European Journal of Operational Research, Elsevier, vol. 296(2), pages 465-484.
    10. Khodakaram Salimifard & Sara Bigharaz, 2022. "The multicommodity network flow problem: state of the art classification, applications, and solution methods," Operational Research, Springer, vol. 22(1), pages 1-47, March.
    11. Toni I. Wickert & Pieter Smet & Greet Vanden Berghe, 2021. "Quantifying and enforcing robustness in staff rostering," Journal of Scheduling, Springer, vol. 24(3), pages 347-366, June.
    12. Maenhout, Broos & Vanhoucke, Mario, 2018. "A perturbation matheuristic for the integrated personnel shift and task re-scheduling problem," European Journal of Operational Research, Elsevier, vol. 269(3), pages 806-823.
    13. Babak Akbarzadeh & Ghasem Moslehi & Mohammad Reisi-Nafchi & Broos Maenhout, 2020. "A diving heuristic for planning and scheduling surgical cases in the operating room department with nurse re-rostering," Journal of Scheduling, Springer, vol. 23(2), pages 265-288, April.
    14. Christopher N. Gross & Andreas Fügener & Jens O. Brunner, 2018. "Online rescheduling of physicians in hospitals," Flexible Services and Manufacturing Journal, Springer, vol. 30(1), pages 296-328, June.

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