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A Mathematical Programming Model for Scheduling Nursing Personnel in a Hospital

Author

Listed:
  • D. Michael Warner

    (University of Michigan)

  • Juan Prawda

    (Tulane University)

Abstract

The Nursing Personnel Scheduling Problem is defined as the identification of that staffing pattern which (1) specifies the number of nursing personnel of each skill class to be scheduled among the wards and nursing shifts of a scheduling period, (2) satisfies total nursing personnel capacity, integral assignment, and other relevant constraints, and (3) minimizes a "shortage cost" of nursing care services provided for the scheduling period. The problem is posed as a mixed-integer quadratic programming problem, which is decomposed by a primal resource-directive approach into a multiple-choice programming master problem, with quadratic programming sub-problems. Initial results suggest that a linear programming formulation, with a post-optimal feasibility search scheme, may be substituted for the multiple-choice master problem. The model is tested on six wards of a 600-bed general hospital, and results are presented.

Suggested Citation

  • D. Michael Warner & Juan Prawda, 1972. "A Mathematical Programming Model for Scheduling Nursing Personnel in a Hospital," Management Science, INFORMS, vol. 19(4-Part-1), pages 411-422, December.
    • Handle: RePEc:inm:ormnsc:v:19:y:1972:i:4-part-1:p:411-422
    DOI: 10.1287/mnsc.19.4.411
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    Cited by:

    1. Edmund Burke & Jingpeng Li & Rong Qu, 2012. "A Pareto-based search methodology for multi-objective nurse scheduling," Annals of Operations Research, Springer, vol. 196(1), pages 91-109, July.
    2. U Aickelin & E K Burke & J Li, 2007. "An estimation of distribution algorithm with intelligent local search for rule-based nurse rostering," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(12), pages 1574-1585, December.
    3. Li, Ling & Benton, W. C., 2003. "Hospital capacity management decisions: Emphasis on cost control and quality enhancement," European Journal of Operational Research, Elsevier, vol. 146(3), pages 596-614, May.
    4. Gergely Mincsovics & Nico Dellaert, 2010. "Stochastic dynamic nursing service budgeting," Annals of Operations Research, Springer, vol. 178(1), pages 5-21, July.
    5. 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.
    6. Gerard M. Campbell, 1999. "Cross-Utilization of Workers Whose Capabilities Differ," Management Science, INFORMS, vol. 45(5), pages 722-732, May.
    7. Jingpeng Li & Uwe Aickelin & Edmund K. Burke, 2009. "A Component-Based Heuristic Search Method with Evolutionary Eliminations for Hospital Personnel Scheduling," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 468-479, August.
    8. Wright, P. Daniel & Mahar, Stephen, 2013. "Centralized nurse scheduling to simultaneously improve schedule cost and nurse satisfaction," Omega, Elsevier, vol. 41(6), pages 1042-1052.
    9. Frederick M Howard & Catherine A Gao & Christopher Sankey, 2020. "Implementation of an automated scheduling tool improves schedule quality and resident satisfaction," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-9, August.
    10. 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.
    11. 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.
    12. Campbell, Gerard M. & Diaby, Moustapha, 2002. "Development and evaluation of an assignment heuristic for allocating cross-trained workers," European Journal of Operational Research, Elsevier, vol. 138(1), pages 9-20, April.
    13. Ali Janati & Djavad Nejad & Mehdi Ariafar & Seyyedeh Roghayyeh Mirshojaee & Mohammad Mahdavi Moghaddam & Saaied Ghodousi Nejad & Majid Ghodousi Nejad & Morteza Arab Zozani & Ali Vafaee & Elham Baghban, 2016. "Optimization of Nurse Numbers in Emergency Department of a District Hospital in a Developing Country Iran, 2014," Modern Applied Science, Canadian Center of Science and Education, vol. 10(5), pages 1-41, May.
    14. Venkataraman, R. & Brusco, M. J., 1996. "An integrated analysis of nurse staffing and scheduling policies," Omega, Elsevier, vol. 24(1), pages 57-71, February.
    15. Sabah M. Al-Najjar & Samir Hussain Ali, 2011. "Staffing and Scheduling Emergency Rooms in Two Public Hospitals: A Case Study," International Journal of Business Administration, International Journal of Business Administration, Sciedu Press, vol. 2(2), pages 137-148, May.
    16. Li, L. X. & Benton, W. C., 1996. "Performance measurement criteria in health care organizations: Review and future research directions," European Journal of Operational Research, Elsevier, vol. 93(3), pages 449-468, September.
    17. 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.
    18. 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.
    19. repec:dau:papers:123456789/4010 is not listed on IDEAS
    20. Chiaramonte Michael & Cochran Jeffery & Caswell David, 2015. "Nurse preference rostering using agents and iterated local search," Annals of Operations Research, Springer, vol. 226(1), pages 443-461, March.
    21. 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.
    22. Andrés Miniguano-Trujillo & Fernanda Salazar & Ramiro Torres & Patricio Arias & Koraima Sotomayor, 2021. "An integer programming model to assign patients based on mental health impact for tele-psychotherapy intervention during the Covid–19 emergency," Health Care Management Science, Springer, vol. 24(2), pages 286-304, June.
    23. Brusco, Michael J., 2015. "A bicriterion algorithm for the allocation of cross-trained workers based on operational and human resource objectives," European Journal of Operational Research, Elsevier, vol. 247(1), pages 46-59.
    24. Gang Li & Joy M. Field & Hongxun Jiang & Tian He & Youming Pang, 2019. "Decision Models for Workforce and Technology Planning in Services," Papers 1909.12829, arXiv.org.
    25. Dellaert, Nico & Jeunet, Jully & Mincsovics, Gergely, 2011. "Budget allocation for permanent and contingent capacity under stochastic demand," International Journal of Production Economics, Elsevier, vol. 131(1), pages 128-138, May.

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