IDEAS home Printed from https://ideas.repec.org/a/spr/flsman/v34y2022i4d10.1007_s10696-021-09426-7.html
   My bibliography  Save this article

The emergency department physician rostering problem: obtaining equitable solutions via network optimization

Author

Listed:
  • Paola Cappanera

    (University of Florence)

  • Filippo Visintin

    (University of Florence)

  • Roberta Rossi

    (University of Florence)

Abstract

In this study, we address workload balancing in Emergency Department Physician Rostering Problems. We propose a two-phase approach to deal with two common workload balancing issues: (1) the even distribution of worked weekends and weekend night shifts across physicians in the long term, and (2) the even distribution of morning and afternoon shifts in the medium term. To implement such an approach, we have developed two Integer Linear Programming (ILP) models, one for each phase. In the first phase, we determine the weekends that each physician will be on duty over the long term planning horizon (6-months) while evenly distributing the workload (worked weekends and weekend night shifts) across physicians. In the second phase, month by month, we iteratively determine the workday shifts of each physician while pursuing the even distribution of workload (morning and afternoon shifts) across physicians. The second phase relies on the solution of the first phase, i.e., the weekend shifts assigned to each physician in the first phase are considered preassigned shifts in the second phase. In both phases, we consider the constraints deriving from collective as well as individual contractual agreements (e.g. constraints limiting the maximum number of night shifts each physician can work every month, their maximum weekly and monthly workload, etc.) as well as individual physician’s preferences and desiderata. The problems addressed in the two phases differ in terms of the planning horizon, objective function, and constraints, yet they are both modeled as multicommodity ow problems and share the same network structure. Also, we define some families of simple yet effective, valid inequalities that are crucial to address the computational complexity of the first-phase problem. The proposed optimization models have been tested on real data from a leading European Hospital and on benchmark instances from the literature. The models’ effectiveness has been assessed through six key performance indicators purposely defined. Results demonstrate that the presented models allow considering the complex nature of physicians rostering problems and obtaining well-balanced and thus equitable work schedules.

Suggested Citation

  • Paola Cappanera & Filippo Visintin & Roberta Rossi, 2022. "The emergency department physician rostering problem: obtaining equitable solutions via network optimization," Flexible Services and Manufacturing Journal, Springer, vol. 34(4), pages 916-959, December.
  • Handle: RePEc:spr:flsman:v:34:y:2022:i:4:d:10.1007_s10696-021-09426-7
    DOI: 10.1007/s10696-021-09426-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10696-021-09426-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10696-021-09426-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jens Brunner & Günther Edenharter, 2011. "Long term staff scheduling of physicians with different experience levels in hospitals using column generation," Health Care Management Science, Springer, vol. 14(2), pages 189-202, June.
    2. 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.
    3. Jens Brunner & Jonathan Bard & Rainer Kolisch, 2009. "Flexible shift scheduling of physicians," Health Care Management Science, Springer, vol. 12(3), pages 285-305, September.
    4. Melanie Erhard, 2021. "Flexible staffing of physicians with column generation," Flexible Services and Manufacturing Journal, Springer, vol. 33(1), pages 212-252, March.
    5. Yann Ferrand & Michael Magazine & Uday S. Rao & Todd F. Glass, 2011. "Building Cyclic Schedules for Emergency Department Physicians," Interfaces, INFORMS, vol. 41(6), pages 521-533, December.
    6. Paola Cappanera & Giorgio Gallo, 2004. "A Multicommodity Flow Approach to the Crew Rostering Problem," Operations Research, INFORMS, vol. 52(4), pages 583-596, August.
    7. A.T. Ernst & H. Jiang & M. Krishnamoorthy & B. Owens & D. Sier, 2004. "An Annotated Bibliography of Personnel Scheduling and Rostering," Annals of Operations Research, Springer, vol. 127(1), pages 21-144, March.
    8. Ernst, A. T. & Jiang, H. & Krishnamoorthy, M. & Sier, D., 2004. "Staff scheduling and rostering: A review of applications, methods and models," European Journal of Operational Research, Elsevier, vol. 153(1), pages 3-27, February.
    9. Erhard, Melanie & Schoenfelder, Jan & Fügener, Andreas & Brunner, Jens O., 2018. "State of the art in physician scheduling," European Journal of Operational Research, Elsevier, vol. 265(1), pages 1-18.
    10. Christopher N. Gross & Jens O. Brunner & Manfred Blobner, 2019. "Hospital physicians can’t get no long-term satisfaction – an indicator for fairness in preference fulfillment on duty schedules," Health Care Management Science, Springer, vol. 22(4), pages 691-708, December.
    11. Paola Cappanera & Maria Grazia Scutellà, 2011. "Color-Coding Algorithms to the Balanced Path Problem: Computational Issues," INFORMS Journal on Computing, INFORMS, vol. 23(3), pages 446-459, August.
    12. 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.
    13. A Gunawan & H C Lau, 2013. "Master physician scheduling problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(3), pages 410-425, March.
    14. Frederik Knust & Lin Xie, 2019. "Simulated annealing approach to nurse rostering benchmark and real-world instances," Annals of Operations Research, Springer, vol. 272(1), pages 187-216, January.
    15. Stolletz, Raik & Brunner, Jens O., 2012. "Fair optimization of fortnightly physician schedules with flexible shifts," European Journal of Operational Research, Elsevier, vol. 219(3), pages 622-629.
    16. Millar, Harvey H. & Kiragu, Mona, 1998. "Cyclic and non-cyclic scheduling of 12 h shift nurses by network programming," European Journal of Operational Research, Elsevier, vol. 104(3), pages 582-592, February.
    17. Doi, Tsubasa & Nishi, Tatsushi & Voß, Stefan, 2018. "Two-level decomposition-based matheuristic for airline crew rostering problems with fair working time," European Journal of Operational Research, Elsevier, vol. 267(2), pages 428-438.
    18. Bard, Jonathan F. & Purnomo, Hadi W., 2005. "Preference scheduling for nurses using column generation," European Journal of Operational Research, Elsevier, vol. 164(2), pages 510-534, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vincent Augusto & Nadia Lahrichi & Ettore Lanzarone & Taesik Lee & Jie Song, 2022. "Analytics and Optimization in Healthcare Management," Flexible Services and Manufacturing Journal, Springer, vol. 34(4), pages 821-823, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Wolbeck, Lena Antonia, 2019. "Fairness aspects in personnel scheduling," Discussion Papers 2019/16, Free University Berlin, School of Business & Economics.
    3. Toni I. Wickert & Alberto F. Kummer Neto & Márcio M. Boniatti & Luciana S. Buriol, 2021. "An integer programming approach for the physician rostering problem," Annals of Operations Research, Springer, vol. 302(2), pages 363-390, July.
    4. David Rea & Craig Froehle & Suzanne Masterson & Brian Stettler & Gregory Fermann & Arthur Pancioli, 2021. "Unequal but Fair: Incorporating Distributive Justice in Operational Allocation Models," Production and Operations Management, Production and Operations Management Society, vol. 30(7), pages 2304-2320, July.
    5. Melanie Erhard, 2021. "Flexible staffing of physicians with column generation," Flexible Services and Manufacturing Journal, Springer, vol. 33(1), pages 212-252, March.
    6. Damcı-Kurt, Pelin & Zhang, Minjiao & Marentay, Brian & Govind, Nirmal, 2019. "Improving physician schedules by leveraging equalization: Cases from hospitals in U.S," Omega, Elsevier, vol. 85(C), pages 182-193.
    7. Jan Schoenfelder & Christian Pfefferlen, 2018. "Decision Support for the Physician Scheduling Process at a German Hospital," Service Science, INFORMS, vol. 10(3), pages 215-229, September.
    8. Erhard, Melanie & Schoenfelder, Jan & Fügener, Andreas & Brunner, Jens O., 2018. "State of the art in physician scheduling," European Journal of Operational Research, Elsevier, vol. 265(1), pages 1-18.
    9. Farzad Zaerpour & Marco Bijvank & Huiyin Ouyang & Zhankun Sun, 2022. "Scheduling of Physicians with Time‐Varying Productivity Levels in Emergency Departments," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 645-667, February.
    10. Volland, Jonas & Fügener, Andreas & Brunner, Jens O., 2017. "A column generation approach for the integrated shift and task scheduling problem of logistics assistants in hospitals," European Journal of Operational Research, Elsevier, vol. 260(1), pages 316-334.
    11. Andreas Fügener & Jens O. Brunner, 2019. "Planning for Overtime: The Value of Shift Extensions in Physician Scheduling," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 732-744, October.
    12. Dina Bentayeb & Nadia Lahrichi & Louis-Martin Rousseau, 2023. "On integrating patient appointment grids and technologist schedules in a radiology center," Health Care Management Science, Springer, vol. 26(1), pages 62-78, March.
    13. Renata Mansini & Roberto Zanotti, 2020. "Optimizing the physician scheduling problem in a large hospital ward," Journal of Scheduling, Springer, vol. 23(3), pages 337-361, June.
    14. Xu, Shuling & Hall, Nicholas G., 2021. "Fatigue, personnel scheduling and operations: Review and research opportunities," European Journal of Operational Research, Elsevier, vol. 295(3), pages 807-822.
    15. Melissa R. Bowers & Charles E. Noon & Wei Wu & J. Kirk Bass, 2016. "Neonatal Physician Scheduling at the University of Tennessee Medical Center," Interfaces, INFORMS, vol. 46(2), pages 168-182, April.
    16. De Bruecker, Philippe & Van den Bergh, Jorne & Beliën, Jeroen & Demeulemeester, Erik, 2015. "Workforce planning incorporating skills: State of the art," European Journal of Operational Research, Elsevier, vol. 243(1), pages 1-16.
    17. 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.
    18. Safae Er-Rbib & Guy Desaulniers & Issmail Elhallaoui & Patrick Munroe, 2021. "Preference-based and cyclic bus driver rostering problem with fixed days off," Public Transport, Springer, vol. 13(2), pages 251-286, June.
    19. Lotfi Hidri & Achraf Gazdar & Mohammed M. Mabkhot, 2020. "Optimized Procedure to Schedule Physicians in an Intensive Care Unit: A Case Study," Mathematics, MDPI, vol. 8(11), pages 1-24, November.
    20. Wang, Fan & Zhang, Chao & Zhang, Hui & Xu, Liang, 2021. "Short-term physician rescheduling model with feature-driven demand for mental disorders outpatients," Omega, Elsevier, vol. 105(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:flsman:v:34:y:2022:i:4:d:10.1007_s10696-021-09426-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.