Skip to main content
SpringerLink
Log in

A flexible mixed integer programming-based system for real-world nurse rostering

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

Abstract

Researchers have studied the nurse rostering problem for multiple decades. Initially, the formulations were rather primitive including only a few necessary restrictions, but down the road, the formulations have become more complex. Nonetheless, a fraction of the research reaches implementation in practice, and many wards still schedule nurses manually. In this article, we introduce a flexible nurse rostering system that employs mathematical optimization to automatically schedule nurses to shifts. We have developed this system in collaboration with practitioners to fully match their needs. The system consists of a comprehensive mixed integer programming (MIP) model along with a flexible framework. In addition to common constraints from the literature, the mathematical formulation includes three new constraints that further encourage healthy work schedules for each nurse. Additionally, we have reformulated some common constraints from the literature and allow for a complex shift structure that matches the needs of real hospital wards. This flexibility results in increased adaptability for different wards with different needs and is crucial to address the complex nurse rostering problem that practitioners face. We have successfully implemented this system in two wards at two Danish hospitals. We present the MIP model along with computational results for 12 real-world rostering instances. Furthermore, we discuss the practical impact of this system and provide general feedback from the practitioners using it. Overall, the results illustrate the capabilities of the system to tackle diverse nurse rostering instances and produce outstanding results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Agyei, W., Obeng-Denteh, W., & Andaam, E. A. (2015). Modeling nurse scheduling problem using 0–1 goal programming: A case study of tafo government hospital, kumasi-ghana. International Journal of Scientific & Technology Research, 4(3), 5–10.

    Google Scholar 

  • Azaiez, M. N., & Al Sharif, S. S. (2005). A 0–1 goal programming model for nurse scheduling. Computers and Operations Research, 32(3), 491–507. https://doi.org/10.1016/S0305-0548(03)00249-1

    Article  Google Scholar 

  • Baker, K. R. (1974). Scheduling a full-time workforce to meet cyclic staffing requirements. Management Science, 20(12), 1561–1568.

    Article  Google Scholar 

  • Bard, J. F., & Purnomo, H. W. (2005). Preference scheduling for nurses using column generation. European Journal of Operational Research, 164(2), 510–534. https://doi.org/10.1016/j.ejor.2003.06.046

    Article  Google Scholar 

  • Beddoe, G., Petrovic, S., & Li, J. (2009). A hybrid metaheuristic case-based reasoning system for nurse rostering. Journal of Scheduling, 12(2), 99–119. https://doi.org/10.1007/s10951-008-0082-8

    Article  Google Scholar 

  • Bilgin, B., De Causmaecker, P., Rossie, B., & Vanden Berghe, G. (2012). Local search neighbourhoods for dealing with a novel nurse rostering model. Annals of Operations Research, 194(1), 33–57. https://doi.org/10.1007/s10479-010-0804-0

    Article  Google Scholar 

  • Burke, E. K., & Curtois, T. (2014). New approaches to nurse rostering benchmark instances. European Journal of Operational Research, 237(1), 71–81. https://doi.org/10.1016/j.ejor.2014.01.039

    Article  Google Scholar 

  • Burke, E. K., Cowling, P., De Causmaecker, P., & Vanden Berghe, G. (2001). A memetic approach to the nurse rostering problem. Applied Intelligence, 15(3), 199–214. https://doi.org/10.1023/A:1011291030731

    Article  Google Scholar 

  • Burke, E. K., De Causmaecker, P., Vanden Berghe, G., & Van Landeghem, H. (2004). The state of the art of nurse rostering. Journal of Scheduling, 7(6), 441–449. https://doi.org/10.1023/B:JOSH.0000046076.75950.0b

    Article  Google Scholar 

  • Burke, E. K., De Causmaecker, P., Petrovic, S., & Vanden Berghe, G. (2006). Metaheuristics for handling time interval coverage constraints in nurse scheduling. Applied Artificial Intelligence, 20(9), 743–766. https://doi.org/10.1080/08839510600903841

    Article  Google Scholar 

  • Burke, E. K., Li, J., & Qu, R. (2010). A hybrid model of integer programming and variable neighbourhood search for highly-constrained nurse rostering problems. European Journal of Operational Research, 203(2), 484–493. https://doi.org/10.1016/j.ejor.2009.07.036

    Article  Google Scholar 

  • Burns, R., & Koop, G. (1987). A modular approach to optimal multiple-shift manpower scheduling. Operations Research, 35(1), 100–110.

    Article  Google Scholar 

  • Böòvarsdóttir, E. B., Bagger, N. C. F., Høffner, L. E., & Stidsen, T. (2019). Data for research on nurse rostering in Denmark [Data set]. https://doi.org/10.5281/zenodo.3966788.

  • Ceschia, S., Dang, N., De Causmaecker, P., Haspeslagh, S., & Schaerf, A. (2019). The second international nurse rostering competition. Annals of Operations Research, 274(1–2), 171–186.

    Article  Google Scholar 

  • Christiansen, M. L., Petersen, N. C., & Range, T. M. (2014). Automatiseret vagtplanlægning for sundhedspersonale [Automatic scheduling for healthcare personnel]. Fremtidens Hospital, Munksgaard, Chap, 25, 375–387.

    Google Scholar 

  • Curtois, T., & Qu, R. (2014). Computational results on new staff scheduling benchmark instances. Technical Report.

  • De Causmaecker, P., & Vanden Berghe, G. (2011). A categorisation of nurse rostering problems. Journal of Scheduling, 14(1), 3–16. https://doi.org/10.1007/s10951-010-0211-z

    Article  Google Scholar 

  • De Grano, M. L., Medeiros, D. J., & Eitel, D. (2009). Accommodating individual preferences in nurse scheduling via auctions and optimization. Health Care Management Science, 12(3), 228–242. https://doi.org/10.1007/s10729-008-9087-2

    Article  Google Scholar 

  • Dohn, A., & Mason, A. (2013). Branch-and-price for staff rostering: An efficient implementation using generic programming and nested column generation. European Journal of Operational Research, 230(1), 157–169. https://doi.org/10.1016/j.ejor.2013.03.018

    Article  Google Scholar 

  • Gärtner, J., Bohle, P., Arlinghaus, A., Schafhauser, W., Krennwallner, T., & Widl, M. (2018). Scheduling matters-some potential requirements for future rostering competitions from a practitioner’s view. In PATAT 2018 - Proceedings of the 12th international conference on the practice and theory of automated timetabling (pp. 33–42).

  • Glass, C. A., & Knight, R. A. (2010). The nurse rostering problem: A critical appraisal of the problem structure. European Journal of Operational Research, 202(2), 379–389. https://doi.org/10.1016/j.ejor.2009.05.046

    Article  Google Scholar 

  • Haspeslagh, S., De Causmaecker, P., Schaerf, A., & Stølevik, M. (2014). The first international nurse rostering competition 2010. Annals of Operations Research, 218(1), 221–236. https://doi.org/10.1007/s10479-012-1062-0

    Article  Google Scholar 

  • Jensen, L., Horsted, C. P., Lunde, A., & Hansen, M. B. (2008). Vagtplanlægning i det danske sygehusvæsen [Employee scheduling in the Danish healthcare sector].

  • Kellogg, D. L., & Walczak, S. (2007). Nurse scheduling: From academia to implementation or not? Interfaces, 37(4), 353–369. https://doi.org/10.1287/inte.1060.0247

    Article  Google Scholar 

  • Lin, C. C., Kang, J. R., Liu, W. Y., & Deng, D. J. (2014). Modelling a nurse shift schedule with multiple preference ranks for shifts and days-off. Mathematical Problems in Engineering, 2014, 10–13. https://doi.org/10.1155/2014/937842

    Article  Google Scholar 

  • Lin, C. C., Kang, J. R., Chiang, D. J., & Chen, C. L. (2015). Nurse scheduling with joint normalized shift and day-off preference satisfaction using a genetic algorithm with immigrant scheme. International Journal of Distributed Sensor Networks. https://doi.org/10.1155/2015/595419.

    Article  Google Scholar 

  • Maenhout, B., & Vanhoucke, M. (2010). Branching strategies in a branch-and-price approach for a multiple objective nurse scheduling problem. Journal of Scheduling, 13(1), 77–93. https://doi.org/10.1007/s10951-009-0108-x

    Article  Google Scholar 

  • Mihaylov, M., Smet, P., Van Den Noortgate, W., & Vanden Berghe, G. (2016). Facilitating the transition from manual to automated nurse rostering. Health Systems, 5(2), 120–131. https://doi.org/10.1057/hs.2015.12

    Article  Google Scholar 

  • Mischek, F., & Musliu, N. (2017). Integer programming model extensions for a multi-stage nurse rostering problem. Annals of Operations Research. https://doi.org/10.1007/s10479-017-2623-z

    Article  Google Scholar 

  • Petrovic, S. (2019). You have to get wet to learn how to swim applied to bridging the gap between research into personnel scheduling and its implementation in practice. Annals of Operations Research, 275(1), 161–179.

  • Rahimian, E., Akartunalı, K., & Levine, J. (2017). A hybrid integer programming and variable neighbourhood search algorithm to solve nurse rostering problems. European Journal of Operational Research, 258(2), 411–423. https://doi.org/10.1016/j.ejor.2016.09.030

    Article  Google Scholar 

  • Rigsrevisionen. (2015). Beretning til Statsrevisorerne om hospitalernes brug af personaleresurser [Report to the state auditors on the hospitals use of human resources].

  • Römer, M., & Mellouli, T. (2016). A direct milp approach based on state-expanded network flows and anticipation for multi-stage nurse rostering under uncertainty. In Proceedings of the 11th international conference on the practice and theory of automated timetabling (pp. 549–551).

  • Rönnberg, E., & Larsson, T. (2010). Automating the self-scheduling process of nurses in swedish healthcare: A pilot study. Health Care Management Science, 13(1), 35–53. https://doi.org/10.1007/s10729-009-9107-x

    Article  Google Scholar 

  • Rönnberg, E., Larsson, T., & Bertilsson, A. (2013). Automatic scheduling of nurses: What does it take in practice? Springer Optimization and Its Applications, 74, 151–178. https://doi.org/10.1007/978-1-4614-5094-8_8

    Article  Google Scholar 

  • Santos, H. G., Toffolo, T. A., Gomes, R. A., & Ribas, S. (2016). Integer programming techniques for the nurse rostering problem. Annals of Operations Research, 239(1), 225–251. https://doi.org/10.1007/s10479-014-1594-6

    Article  Google Scholar 

  • Smet, P., Brucker, P., De Causmaecker, P., & Vanden Berghe, G. (2016). Polynomially solvable personnel rostering problems. European Journal of Operational Research, 249(1), 67–75. https://doi.org/10.1016/j.ejor.2015.08.025

    Article  Google Scholar 

  • Smet, P., Salassa, F., & Vanden Berghe, G. (2017). Local and global constraint consistency in personnel rostering. International Transactions in Operational Research, 24(5), 1099–1117. https://doi.org/10.1111/itor.12357

    Article  Google Scholar 

  • Stølevik, M., Nordlander, T. E., Riise, A., & Frøyseth, H. (2011). A hybrid approach for solving real-world nurse rostering problems. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 6876, 85–99. https://doi.org/10.1007/978-3-642-23786-7_9

    Article  Google Scholar 

  • Turhan, A. M., & Bilgen, B. (2020). A hybrid fix-and-optimize and simulated annealing approaches for nurse rostering problem. Computers and Industrial Engineering, 145, 106531. https://doi.org/10.1016/j.cie.2020.106531

    Article  Google Scholar 

  • Valouxis, C., Gogos, C., Goulas, G., Alefragis, P., & Housos, E. (2012). A systematic two phase approach for the nurse rostering problem. European Journal of Operational Research, 219(2), 425–433.

    Article  Google Scholar 

  • Van Den Bergh, J., Beliën, J., De Bruecker, P., Demeulemeester, E., & De Boeck, L. (2013). Personnel scheduling: A literature review. European Journal of Operational Research, 226(3), 367–385. https://doi.org/10.1016/j.ejor.2012.11.029

    Article  Google Scholar 

  • Zanda, S., Zuddas, P., & Seatzu, C. (2018). Long term nurse scheduling via a decision support system based on linear integer programming: A case study at the university hospital in cagliari. Computers and Industrial Engineering, 126, 337–347. https://doi.org/10.1016/j.cie.2018.09.027

    Article  Google Scholar 

Download references

Acknowledgements

We thank the Department of Data and Development Support at Region Zealand (DU) for partnering with us on this project, along with the Danish Ministry of Health for providing with funds. We especially thank Lena Marie Fredholm Jensen, Allan Bo Hansen and Anne Bernth at DU, along with Joël Raucq at Raucq Consulting for their contribution to the project. Additionally, we thank the wards we have worked with for invaluable insight and feedback along with providing us with data. Finally, we thank Professor David Pisinger along with anonymous reviewers for their feedback that helped us improve this manuscript.

Author information

Authors and Affiliations

  1. Department of Technology, Management and Economics, Technical University of Denmark, Anker Engelundsvej 1, 2800, Kgs. Lyngby, Denmark

    Elín Björk Böðvarsdóttir, Niels-Christian Fink Bagger & Thomas J. R. Stidsen

  2. Fink Optimization ApS, Valdemarskrogen 44, 2860, Søborg, Denmark

    Niels-Christian Fink Bagger

  3. Department of Data and Development Support, Region Zealand, Alleen 15, 4180, Sorø, Denmark

    Laura Elise Høffner

Authors
  1. Elín Björk Böðvarsdóttir
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Niels-Christian Fink Bagger
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Laura Elise Høffner
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Thomas J. R. Stidsen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Elín Björk Böðvarsdóttir.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Böðvarsdóttir, E.B., Bagger, NC.F., Høffner, L.E. et al. A flexible mixed integer programming-based system for real-world nurse rostering. J Sched 25, 59–88 (2022). https://doi.org/10.1007/s10951-021-00705-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10951-021-00705-7

Keywords

Search

Navigation