A Model of ICU Bumping

Many intensive care units (ICUs) face overcrowding. One response to this overcrowding is to bump ICU patients to other departments of the hospital to make room for new patient arrivals. Such bumping clearly has the potential to reduce quality of care. In this paper we develop a stochastic model of a single ICU with patient bumping. The purpose of this model is to enable planners to predict performance, in terms of bumping, under differing arrival patterns and capacity. We develop a Markov chain model and a new aggregation-disaggregation algorithm for this problem that enables us to keep track of the time in system for each patient despite the high dimensionality of the problem. Our approach allows for more accurate modeling of the system than previous work that assumed an exponential distribution for length of stay (LOS). We also demonstrate the superior computational efficiency of our approach over the Gauss-Seidel iterative method for solving the Markov chain. Finally, we use the model to explore how different surgery schedules influence bumping rates.

[1]  K. Kirchhoff,et al.  American Association of Critical-Care Nurses' national survey of facilities and units providing critical care. , 2006, American journal of critical care : an official publication, American Association of Critical-Care Nurses.

[2]  Susannah L Rose,et al.  Factors influencing length of stay in the intensive care unit. , 2006, American journal of critical care : an official publication, American Association of Critical-Care Nurses.

[3]  G. M. Koole,et al.  Modeling the emergency cardiac in-patient flow: an application of queuing theory , 2007, Health care management science.

[4]  C. Steiner,et al.  Does managed care affect the supply and use of ICU services? , 1999, Inquiry : a journal of medical care organization, provision and financing.

[5]  C Weissman,et al.  Analyzing intensive care unit length of stay data: problems and possible solutions. , 1997, Critical care medicine.

[6]  Elif Akcali,et al.  A network flow approach to optimizing hospital bed capacity decisions , 2006, Health care management science.

[7]  Otis B. Jennings,et al.  Nurse-to-Patient Ratios in Hospital Staffing: A Queueing Perspective , 2008 .

[8]  Luciano Gattinoni,et al.  Volume of activity and occupancy rate in intensive care units. Association with mortality , 2004, Intensive Care Medicine.

[9]  T. Clemmer,et al.  Descriptive analysis of critical care units in the United States , 1992, Critical care medicine.

[10]  J. Tu,et al.  Can clinicians predict ICU length of stay following cardiac surgery? , 1996, Canadian journal of anaesthesia = Journal canadien d'anesthesie.

[11]  M. Mackay,et al.  Modelling Variability in Hospital Bed Occupancy , 2005, Health care management science.

[12]  L. Green,et al.  A Queueing Model for Nurse Staffing , 2007 .

[13]  L. Green,et al.  Strategies for cutting hospital beds: the impact on patient service. , 2001, Health services research.

[14]  Sarah M. Ryan,et al.  Capacity Expansion for Random Exponential Demand Growth with Lead Times , 2004, Manag. Sci..

[15]  Ira Horowitz,et al.  Analysis of capacity management of the intensive care unit in a hospital , 1999, Eur. J. Oper. Res..

[16]  Gunter Bolch,et al.  Queueing Networks and Markov Chains , 2005 .

[17]  Peter J Pronovost,et al.  Intensive care unit physician staffing: financial modeling of the Leapfrog standard. , 2004, Critical care medicine.

[18]  Julie C. Lowery,et al.  Simulation of a hospital's surgical suite and critical care area , 1992, WSC '92.

[19]  C. David.  Can clinicians predict ICU length of stay following cardiac surgery , 1996 .

[20]  J. Vincent,et al.  Can the experienced ICU physician predict ICU length of stay and outcome better than less experienced colleagues? , 2004, Intensive Care Medicine.

[21]  E. Litvak,et al.  Queuing Theory Accurately Models the Need for Critical Care Resources , 2004, Anesthesiology.

[22]  L. Green.  How Many Hospital Beds? , 2002, Inquiry : a journal of medical care organization, provision and financing.

[23]  Julie C. Lowery,et al.  Multi-Hospital Validation of Critical Care Simulation Model , 1993, Proceedings of 1993 Winter Simulation Conference - (WSC '93).

[24]  Mohamud Daya,et al.  Effect of increased ICU capacity on emergency department length of stay and ambulance diversion. , 2005, Annals of emergency medicine.

[25]  W. Knaus,et al.  Variations in Mortality and Length of Stay in Intensive Care Units , 1993, Annals of Internal Medicine.

[26]  P. Marik,et al.  What’s in a day? Determining intensive care unit length of stay , 2000, Critical care medicine.