Skip to main content
SpringerLink
Log in

Optimal control of ICU patient discharge: from theory to implementation

  • Published:
Health Care Management Science Aims and scope Submit manuscript

Abstract

This paper deals with the management of scarce health care resources. We consider a control problem in which the objective is to minimize the rate of patient rejection due to service saturation. The scope of decisions is limited, in terms both of the amount of resources to be used, which are supposed to be fixed, and of the patient arrival pattern, which is assumed to be uncontrollable. This means that the only potential areas of control are speed or completeness of service. By means of queuing theory and optimization techniques, we provide a theoretical solution expressed in terms of service rates. In order to make this theoretical analysis useful for the effective control of the healthcare system, however, further steps in the analysis of the solution are required: physicians need flexible and medically-meaningful operative rules for shortening patient length of service to the degree needed to give the service rates dictated by the theoretical analysis. The main contribution of this paper is to discuss how the theoretical solutions can be transformed into effective management rules to guide doctors’ decisions. The study examines three types of rules based on intuitive interpretations of the theoretical solution. Rules are evaluated through implementation in a simulation model. We compare the service rates provided by the different policies with those dictated by the theoretical solution. Probabilistic analysis is also included to support rule validity. An Intensive Care Unit is used to illustrate this control problem. The study focuses on the Markovian case before moving on to consider more realistic LoS distributions (Weibull, Lognormal and Phase-type distribution).

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
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Zenios SA (2004) Patient choice in kidney allocation: the role of the queueing discipline. Manuf Serv Oper Manag 6:280–301

    Google Scholar 

  2. Seshaiah CV, Thiagaraj HB (2011) A queueing network congestion model in hospitals. Eur J Oper Res 63:419–427

    Google Scholar 

  3. Solberg B, Asplin B, Weinick R, Magid D (2003) Emergency department crowding: consensus development of potential measures. Ann Emerg Med 42:824–834

    Article  Google Scholar 

  4. de Bruin AM, Bekker R, van Zanten L, Koole GM (2010) Dimensioning hospital wards using the Erlang loss model. Ann Oper Res 178:23–43

    Article  Google Scholar 

  5. Cochran JK, Barthi A (2006) Stochastic bed balancing of an obstetrics hospital. Health Care Manag Sci 9:31–45

    Article  Google Scholar 

  6. Griffiths JD, Price-Lloyd N, Smithies M, Williams JE (2005) Modelling the requirement for supplementary nurses in an intensive care unit. J Oper Res Soc 56:126–133

    Article  Google Scholar 

  7. Bekker R, Koeleman PM (2011) Scheduling admissions and reducing variability in bed demand. Health Care Manag Sci 14:237–249

    Article  Google Scholar 

  8. Harper P, Gamlin H (2003) Reduced outpatient waiting times with improved appointment scheduling: a simulation modelling approach. OR-Spectrum 25:207–222

    Article  Google Scholar 

  9. Vasilakis C, Sobolev BG, Kuramoto L, Levy AR (2007) A simulation study of scheduling clinic appointments in surgical care: individual surgeon versus pooled lists. J Oper Res Soc 58:202–211

    Google Scholar 

  10. Lakshmi C, Sivakumar A (2013) Application of queueing theory in health care: a literature review. Oper Res Health Care 2:25–39

    Article  Google Scholar 

  11. Gross D, Harris CM (2008) Fundamentals of queueing theory. Wiley

  12. Terekhov D, Beck JC (2008) A constraint programming approach for solving a queueing control problem. J Art Int Res 32:123–167

    Google Scholar 

  13. Stidham S (2002) Analysis, design and control of queueing systems. Oper Res 50:197–216

    Article  Google Scholar 

  14. Mallor F, Azcárate C (2014) Combining optimization with simulation to obtain credible models for intensive care units. Ann Oper Res 221:255–271

    Article  Google Scholar 

  15. Anderson D, Price C, Golden B, Jank G, Wasil E (2011) Examining the discharge practices of surgeons at a large medical center. Health Care Manag Sci 14:338–347

    Article  Google Scholar 

  16. Dobson G, Lee H, Pinker E (2010) A model of ICU bumping. Oper Res 58:1564–1576

    Article  Google Scholar 

  17. Shmueli A, Sprug CL, Kaplan E (2003) Optimizing admissions to an intensive care unit. Health Care Manag Sci 6:131–136

    Article  Google Scholar 

  18. Capuzzo M, Moreno RP, Alvisi R (2010) Admission and discharge of critically ill patients. Curr Opin Crit Care 16:499–504

    Article  Google Scholar 

  19. Kramer AA, Higgins TL, Zimmerman JE (2012) Intensive care unit readmissions in U.S. hospitals: patient characteristics, risk factors, and outcomes. Crit Care Med 40:3–10

    Article  Google Scholar 

  20. Marmor YN, Rohleder TR, Cook DJ, Huschka TD, Thompson JE (2013) Recovery bed planning in cardiovascular surgery: a simulation case study. Health Care Manag Sci. doi:10.1007/s10729-013-9231-5

    Google Scholar 

  21. Robert R, Reignier J, Tournoux-Facon C et al (2012) Refusal of intensive care unit admission due to a full unit: impact on mortality. Am J Respir Crit Care Med 185:1081–1087

    Article  Google Scholar 

  22. Sprung CL, Baras M, Iapichino G et al (2012) The Eldicus prospective, observational study of triage decision making in European intensive care units: part I–European intensive care admission triage scores. Crit Care Med 40:125–131

    Article  Google Scholar 

  23. Lin F, Chaboyer W, Wallis M (2009) A literature review of organisational, individual and teamwork factors contributing to the ICU discharge process. Aust Crit Care 22:29–43

    Article  Google Scholar 

  24. Sinuff T, Kahnamoui K, Cook DJ et al (2004) Rationing critical care beds: a systematic review. Crit Care Med 32:1588–1597

    Article  Google Scholar 

  25. Walter KL, Siegler M, Hall JB (2008) How decisions are made to admit patients to medical intensive care units (MICUs): a survey of MICU directors at academic medical centers across the United States. Crit Care Med 36:414–420

    Article  Google Scholar 

  26. Ridge JC, Jones SK, Nielsen MS, Shahani AK (1998) Capacity planning for intensive care units. Eur J Oper Res 105:346–355

    Article  Google Scholar 

  27. Costa AX, Ridley SA, Shahani AK, Harper PR, De Senna V, Nielsen MS (2003) Mathematical modelling and simulation for planning critical care capacity. Anaesthesia 58:320–327

    Article  Google Scholar 

  28. Sprung CL, Danis M, Iapichino G et al (2013) Triage of intensive care patients: identifying agreement and controversy. Int Care Med 39:1916–1924

    Article  Google Scholar 

  29. Task Force of the American College of Critical Care Medicine, Society of Critical Care Medicine (1999) Guidelines for intensive care unit admission, discharge, and triage. Crit Care Med 27:633–638

    Article  Google Scholar 

  30. Azcárate C, Mallor F, Barado J (2012) Calibration of a decision-making process in a simulation model by a bicriteria optimization problem, In Proceedings of the 2012 Winter Simulation Conference, 782–791

  31. Mallor F, Azcárate C, Barado J (2014) Control problems and management policies in health systems. Application to intensive care units. Flex Serv Manuf J. doi:10.1007/s10696-014-9209-8

    Google Scholar 

  32. Wolf RW (1982) Poisson arrivals see time average. Oper Res 30:223–231

    Article  Google Scholar 

  33. Heidegger CP, Treggiari MM, Romand JA (2005) A nationwide survey of intensive care unit discharge practices. Intensive Care Med 31:1676–1682

    Article  Google Scholar 

  34. Barlow RE, Proschan F (1981) Statistical theory of reliability and life testing. To begin with, silver spring, MD

  35. Steyrer J, Schiffinger M, Huber C et al (2013) Attitude is everything? The impact of workload, safety climate, and safety tools on medical errors: a study of intensive care units. Health Care Manage Rev 38:306–316

    Article  Google Scholar 

  36. Metcalfe MA, Sloggett A, McPherson K (1997) Mortality among appropriately referred patients refused admission to intensive-care units. Lancet 350:7–11

    Article  Google Scholar 

  37. Simchen E, Sprung CL, Galai N et al (2007) Survival of critically ill patients hospitalized in and out of intensive care. Crit Care Med 35:449–457

    Article  Google Scholar 

  38. Niven DJ, Bastos JF, Stelfox HT (2014) Critical care transition programs and the risk of readmission or death after discharge from an ICU: a systematic review and meta-analysis. Crit Care Med 42:179–187

    Article  Google Scholar 

  39. Lyons RA, Wareham K, Hutchings HA et al (2000) Population requirement for adult critical-care beds: a prospective quantitative and qualitative study. Lancet 355:595–598

    Article  Google Scholar 

  40. Rauner MS, Zeiles A, Schaffhauser-Linzattti MM, Hornik K (2003) Modelling the effects of the Austrian inpatient reimbursement system on length-of-stay distributions. OR-Spectrum 25:183–206

    Article  Google Scholar 

  41. Vasilakis C, Marshall AH (2005) Modelling nationwide hospital length of stay: opening the black box. J Oper Res Soc 56:862–869

    Article  Google Scholar 

Download references

Acknowledgments

This paper has been partially funded by grant MTM2012-36025. The authors would like to extend their gratitude to the reviewers and guest editor for their insightful comments, which have increased the quality of this paper.

Author information

Authors and Affiliations

  1. Department Statistics and Operational Research, ISC-Institute of Smart Cities, Public University of Navarre, Campus Arrosadía, 31006, Pamplona, Spain

    Fermín Mallor & Cristina Azcárate

  2. Hospital of Navarre, C/ Irunlarrea 3, 31008, Pamplona, Spain

    Julio Barado

Authors
  1. Fermín Mallor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cristina Azcárate
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Julio Barado
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fermín Mallor.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mallor, F., Azcárate, C. & Barado, J. Optimal control of ICU patient discharge: from theory to implementation. Health Care Manag Sci 18, 234–250 (2015). https://doi.org/10.1007/s10729-015-9320-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10729-015-9320-8

Keywords

MSC

Search

Navigation