IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v239y2016i1d10.1007_s10479-014-1594-6.html
   My bibliography  Save this article

Integer programming techniques for the nurse rostering problem

Author

Listed:
  • Haroldo G. Santos

    (Federal University of Ouro Preto)

  • Túlio A. M. Toffolo

    (Federal University of Ouro Preto
    KU Leuven)

  • Rafael A. M. Gomes

    (Federal University of Ouro Preto)

  • Sabir Ribas

    (Federal University of Minas Gerais)

Abstract

This work presents integer programming techniques to tackle the problem of the International Nurse Rostering Competition. Starting from a compact and monolithic formulation in which the current generation of solvers performs poorly, improved cut generation strategies and primal heuristics are proposed and evaluated. A large number of computational experiments with these techniques produced the following results: the optimality of the vast majority of instances was proved, the best known solutions were improved by up to 15 % and strong dual bounds were obtained. In the spirit of reproducible science, all code was implemented using the Computational Infrastructure for Operations Research.

Suggested Citation

  • Haroldo G. Santos & Túlio A. M. Toffolo & Rafael A. M. Gomes & Sabir Ribas, 2016. "Integer programming techniques for the nurse rostering problem," Annals of Operations Research, Springer, vol. 239(1), pages 225-251, April.
    • Handle: RePEc:spr:annopr:v:239:y:2016:i:1:d:10.1007_s10479-014-1594-6
    DOI: 10.1007/s10479-014-1594-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-014-1594-6
    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/s10479-014-1594-6?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. Nonobe, Koji & Ibaraki, Toshihide, 1998. "A tabu search approach to the constraint satisfaction problem as a general problem solver," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 599-623, April.
    2. Burke, Edmund K. & Li, Jingpeng & Qu, Rong, 2010. "A hybrid model of integer programming and variable neighbourhood search for highly-constrained nurse rostering problems," European Journal of Operational Research, Elsevier, vol. 203(2), pages 484-493, June.
    3. Kent Andersen & Gérard Cornuéjols & Yanjun Li, 2005. "Reduce-and-Split Cuts: Improving the Performance of Mixed-Integer Gomory Cuts," Management Science, INFORMS, vol. 51(11), pages 1720-1732, November.
    4. Cheang, B. & Li, H. & Lim, A. & Rodrigues, B., 2003. "Nurse rostering problems--a bibliographic survey," European Journal of Operational Research, Elsevier, vol. 151(3), pages 447-460, December.
    5. Giuseppe Andreello & Alberto Caprara & Matteo Fischetti, 2007. "Embedding {0, ½}-Cuts in a Branch-and-Cut Framework: A Computational Study," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 229-238, May.
    6. Atamturk, Alper & Nemhauser, George L. & Savelsbergh, Martin W. P., 2000. "Conflict graphs in solving integer programming problems," European Journal of Operational Research, Elsevier, vol. 121(1), pages 40-55, February.
    7. 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.
    8. Karla L. Hoffman & Manfred Padberg, 1993. "Solving Airline Crew Scheduling Problems by Branch-and-Cut," Management Science, INFORMS, vol. 39(6), pages 657-682, June.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Diego Pecin & Claudio Contardo & Guy Desaulniers & Eduardo Uchoa, 2017. "New Enhancements for the Exact Solution of the Vehicle Routing Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 489-502, August.
    6. 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).
    7. 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.
    8. 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.
    9. 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.
    10. Suk Ho Jin & Ho Yeong Yun & Suk Jae Jeong & Kyung Sup Kim, 2017. "Hybrid and Cooperative Strategies Using Harmony Search and Artificial Immune Systems for Solving the Nurse Rostering Problem," Sustainability, MDPI, vol. 9(7), pages 1-19, June.
    11. George H. G. Fonseca & Túlio A. M. Toffolo, 2022. "A fix-and-optimize heuristic for the ITC2021 sports timetabling problem," Journal of Scheduling, Springer, vol. 25(3), pages 273-286, June.
    12. 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.
    13. Reshma Chirayil Chandrasekharan & Pieter Smet & Tony Wauters, 2021. "An automatic constructive matheuristic for the shift minimization personnel task scheduling problem," Journal of Heuristics, Springer, vol. 27(1), pages 205-227, April.
    14. Jeffrey H. Kingston, 2021. "Modelling history in nurse rostering," Annals of Operations Research, Springer, vol. 302(2), pages 391-404, July.

    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. 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.
    2. 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.
    3. 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.
    4. David D. Cho & Kurt M. Bretthauer & Jan Schoenfelder, 2023. "Patient-to-nurse ratios: Balancing quality, nurse turnover, and cost," Health Care Management Science, Springer, vol. 26(4), pages 807-826, December.
    5. G Appa & D Magos & I Mourtos, 2004. "A Branch & Cut algorithm for a four-index assignment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(3), pages 298-307, March.
    6. Hadi W. Purnomo & Jonathan F. Bard, 2007. "Cyclic preference scheduling for nurses using branch and price," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(2), pages 200-220, March.
    7. Tuomas Sandholm & Subhash Suri & Andrew Gilpin & David Levine, 2005. "CABOB: A Fast Optimal Algorithm for Winner Determination in Combinatorial Auctions," Management Science, INFORMS, vol. 51(3), pages 374-390, March.
    8. Peyman Kiani Nahand & Mahdi Hamid & Mahdi Bastan & Ali Mollajan, 2019. "Human resource management: new approach to nurse scheduling by considering human error," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(6), pages 1429-1443, December.
    9. Jeff T. Linderoth & Eva K. Lee & Martin W. P. Savelsbergh, 2001. "A Parallel, Linear Programming-based Heuristic for Large-Scale Set Partitioning Problems," INFORMS Journal on Computing, INFORMS, vol. 13(3), pages 191-209, August.
    10. 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.
    11. 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.
    12. 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.
    13. Avella, Pasquale & D'Auria, Bernardo & Salerno, Saverio, 2006. "A LP-based heuristic for a time-constrained routing problem," European Journal of Operational Research, Elsevier, vol. 173(1), pages 120-124, August.
    14. Rajeswari Muniyan & Rajakumar Ramalingam & Sultan S. Alshamrani & Durgaprasad Gangodkar & Ankur Dumka & Rajesh Singh & Anita Gehlot & Mamoon Rashid, 2022. "Artificial Bee Colony Algorithm with Nelder–Mead Method to Solve Nurse Scheduling Problem," Mathematics, MDPI, vol. 10(15), pages 1-24, July.
    15. 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.
    16. Suk Ho Jin & Ho Yeong Yun & Suk Jae Jeong & Kyung Sup Kim, 2017. "Hybrid and Cooperative Strategies Using Harmony Search and Artificial Immune Systems for Solving the Nurse Rostering Problem," Sustainability, MDPI, vol. 9(7), pages 1-19, June.
    17. Deborah L. Kellogg & Steven Walczak, 2007. "Nurse Scheduling: From Academia to Implementation or Not?," Interfaces, INFORMS, vol. 37(4), pages 355-369, August.
    18. Burke, Edmund K. & McCollum, Barry & Meisels, Amnon & Petrovic, Sanja & Qu, Rong, 2007. "A graph-based hyper-heuristic for educational timetabling problems," European Journal of Operational Research, Elsevier, vol. 176(1), pages 177-192, January.
    19. 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.
    20. Rahimian, Erfan & Akartunalı, Kerem & Levine, John, 2017. "A hybrid Integer Programming and Variable Neighbourhood Search algorithm to solve Nurse Rostering Problems," European Journal of Operational Research, Elsevier, vol. 258(2), pages 411-423.

    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:annopr:v:239:y:2016:i:1:d:10.1007_s10479-014-1594-6. 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.