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A hybrid model of integer programming and variable neighbourhood search for highly-constrained nurse rostering problems

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  • Burke, Edmund K.
  • Li, Jingpeng
  • Qu, Rong

Abstract

This paper presents a hybrid multi-objective model that combines integer programming (IP) and variable neighbourhood search (VNS) to deal with highly-constrained nurse rostering problems in modern hospital environments. An IP is first used to solve the subproblem which includes the full set of hard constraints and a subset of soft constrains. A basic VNS then follows as a postprocessing procedure to further improve the IP's resulting solutions. The satisfaction of the excluded constraints from the preceding IP model is the major focus of the VNS. Very promising results are reported compared with a commercial genetic algorithm and a hybrid VNS approach on real instances arising in a Dutch hospital. The comparison results demonstrate that our hybrid approach combines the advantages of both the IP and the VNS to beat other approaches in solving this type of problems. We also believe that the proposed methodology can be applied to other resource allocation problems with a large number of constraints.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:203:y:2010:i:2:p:484-493
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Li, Jingpeng & Bai, Ruibin & Shen, Yindong & Qu, Rong, 2015. "Search with evolutionary ruin and stochastic rebuild: A theoretic framework and a case study on exam timetabling," European Journal of Operational Research, Elsevier, vol. 242(3), pages 798-806.
    5. Scholl, Joachim & Boysen, Nils & Scholl, Armin, 2023. "E-platooning: Optimizing platoon formation for long-haul transportation with electric commercial vehicles," European Journal of Operational Research, Elsevier, vol. 304(2), pages 525-542.
    6. Lü, Zhipeng & Hao, Jin-Kao, 2012. "Adaptive neighborhood search for nurse rostering," European Journal of Operational Research, Elsevier, vol. 218(3), pages 865-876.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    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. 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.
    13. Burke, Edmund K. & Curtois, Tim, 2014. "New approaches to nurse rostering benchmark instances," European Journal of Operational Research, Elsevier, vol. 237(1), pages 71-81.
    14. Zhang, Junguang & Song, Xiwei & Díaz, Estrella, 2016. "Project buffer sizing of a critical chain based on comprehensive resource tightness," European Journal of Operational Research, Elsevier, vol. 248(1), pages 174-182.
    15. Edmund K. Burke & Timothy Curtois & Rong Qu & Greet Vanden Berghe, 2013. "A Time Predefined Variable Depth Search for Nurse Rostering," INFORMS Journal on Computing, INFORMS, vol. 25(3), pages 411-419, August.
    16. 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.
    17. Lin, Shih-Wei & Ying, Kuo-Ching, 2014. "Minimizing shifts for personnel task scheduling problems: A three-phase algorithm," European Journal of Operational Research, Elsevier, vol. 237(1), pages 323-334.
    18. Federico Della Croce & Fabio Salassa, 2014. "A variable neighborhood search based matheuristic for nurse rostering problems," Annals of Operations Research, Springer, vol. 218(1), pages 185-199, July.
    19. 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.
    20. W. Jaśkowski & M. Szubert & P. Gawron, 2016. "A hybrid MIP-based large neighborhood search heuristic for solving the machine reassignment problem," Annals of Operations Research, Springer, vol. 242(1), pages 33-62, July.
    21. Li, Jingpeng & Burke, Edmund K. & Curtois, Tim & Petrovic, Sanja & Qu, Rong, 2012. "The falling tide algorithm: A new multi-objective approach for complex workforce scheduling," Omega, Elsevier, vol. 40(3), pages 283-293.
    22. 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.
    23. Meignan, David & Knust, Sigrid, 2019. "A neutrality-based iterated local search for shift scheduling optimization and interactive reoptimization," European Journal of Operational Research, Elsevier, vol. 279(2), pages 320-334.

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