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A stochastic model for the patient-bed assignment problem with random arrivals and departures

Author

Listed:
  • Mojtaba Heydar

    (University of Tasmania
    Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers
    Curtin University)

  • Małgorzata M. O’Reilly

    (University of Tasmania
    Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers)

  • Erin Trainer

    (University of Tasmania)

  • Mark Fackrell

    (Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers
    The University of Melbourne)

  • Peter G. Taylor

    (Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers
    The University of Melbourne)

  • Ali Tirdad

    (Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers
    The University of Melbourne)

Abstract

We consider the patient-to-bed assignment problem that arises in hospitals. Both emergency patients who require hospital admission and elective patients who have had surgery need to be found a bed in the most appropriate ward. The patient-to-bed assignment problem arises when a bed request is made, but a bed in the most appropriate ward is unavailable. In this case, the next-best decision out of a many alternatives has to be made, according to some suitable decision making algorithm. We construct a Markov chain to model this problem in which we consider the effect on the length of stay of a patient whose treatment and recovery consists of several stages, and can be affected by stays in or transfers to less suitable wards. We formulate a dynamic program recursion to optimise an objective function and calculate the optimal decision variables, and discuss simulation techniques that are useful when the size of the problem is too large. We illustrate the theory with some numerical examples.

Suggested Citation

  • Mojtaba Heydar & Małgorzata M. O’Reilly & Erin Trainer & Mark Fackrell & Peter G. Taylor & Ali Tirdad, 2022. "A stochastic model for the patient-bed assignment problem with random arrivals and departures," Annals of Operations Research, Springer, vol. 315(2), pages 813-845, August.
    • Handle: RePEc:spr:annopr:v:315:y:2022:i:2:d:10.1007_s10479-021-03982-9
    DOI: 10.1007/s10479-021-03982-9
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    References listed on IDEAS

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    1. Warren B. Powell, 2016. "Perspectives of approximate dynamic programming," Annals of Operations Research, Springer, vol. 241(1), pages 319-356, June.
    2. Mark Fackrell, 2009. "Modelling healthcare systems with phase-type distributions," Health Care Management Science, Springer, vol. 12(1), pages 11-26, March.
    3. Warren B. Powell, 2009. "What you should know about approximate dynamic programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(3), pages 239-249, April.
    4. Peter J. H. Hulshof & Martijn R. K. Mes & Richard J. Boucherie & Erwin W. Hans, 2016. "Patient admission planning using Approximate Dynamic Programming," Flexible Services and Manufacturing Journal, Springer, vol. 28(1), pages 30-61, June.
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