Operations research/management contributions to emergency department patient flow optimization: Review and research prospects

In recent years, Operations Research/Management (OR/OM) has had a significant impact on improving the performance of hospital Emergency Departments (EDs). This includes improving a wide range of processes involving patient flow from the initial call to the ED through disposition, discharge home, or admission to the hospital. We review approximately 350 related papers to (a) demonstrate the influence of OR/OM in EDs, and (b) assist both researchers and practitioners with the OR/OM techniques already available to optimize ED patient flow. In addition, we elaborate on some practical challenges yet to be addressed. By shedding light on some less studied aspects that can have significant impacts on ED operations, we also discuss important possibilities for future OR/OM researchers.

[1]  M. Cooke,et al.  The effect of a separate stream for minor injuries on accident and emergency department waiting times , 2002, Emergency medicine journal : EMJ.

[2]  L. Purnell.  A survey of emergency department triage in 185 hospitals: physical facilities, fast-track systems, patient-classification systems, waiting times, and qualification, training, and skills of triage personnel. , 1991, Journal of emergency nursing: JEN : official publication of the Emergency Department Nurses Association.

[3]  Robert Champion,et al.  Assessing the impact of streaming in a regional emergency department , 2008, Emergency medicine Australasia : EMA.

[4]  Lisa Cox,et al.  Improving emergency department efficiency by patient streaming to outcomes-based teams. , 2007, Australian health review : a publication of the Australian Hospital Association.

[5]  Alvin Karchere,et al.  Combat Problems, Weapon Systems, and the Theory of Allocation , 1953, Oper. Res..

[6]  Richard J Holden,et al.  Lean Thinking in emergency departments: a critical review. , 2011, Annals of emergency medicine.

[7]  A. K. Shahani,et al.  Capacity planning for intensive care units , 1998, Eur. J. Oper. Res..

[8]  H. Rubin,et al.  Discharging patients earlier in the day: a concept worth evaluating. , 2007, The health care manager.

[9]  R. Derlet,et al.  Prospective identification and triage of nonemergency patients out of an emergency department: a 5-year study. , 1995, Annals of emergency medicine.

[10]  Jeffrey W. Herrmann,et al.  A Survey of Queuing Theory Applications in Healthcare , 2007 .

[11]  James P. Jarvis,et al.  Modeling co-located servers and dispatch ties in the hypercube model , 1993, Comput. Oper. Res..

[12]  Sabi Singh,et al.  Application of lean manufacturing techniques in the Emergency Department. , 2009, The Journal of emergency medicine.

[13]  Marek Laskowski,et al.  Agent-Based Simulation of Emergency Departments with Patient Diversion , 2008, eHealth.

[14]  Elia El-Darzi,et al.  Length of Stay-Based Patient Flow Models: Recent Developments and Future Directions , 2005, Health care management science.

[15]  Christian Terwiesch,et al.  The financial consequences of lost demand and reducing boarding in hospital emergency departments. , 2011, Annals of emergency medicine.

[16]  P. Shekelle,et al.  Safely directing patients to appropriate levels of care: guideline-driven triage in the emergency service. , 2000, Annals of emergency medicine.

[17]  Steven Asch,et al.  Effects of hospital closures and hospital characteristics on emergency department ambulance diversion, Los Angeles County, 1998 to 2004. , 2006, Annals of emergency medicine.

[18]  L. Wallis,et al.  The cape triage score: a new triage system South Africa. Proposal from the cape triage group , 2006, Emergency Medicine Journal.

[19]  Richard C. Larson,et al.  Approximating the Performance of Urban Emergency Service Systems , 1975, Oper. Res..

[20]  Application of lean thinking in health care: a role in emergency departments globally , 2008, International journal of emergency medicine.

[21]  M. Lavieri,et al.  Predicting emergency department volume using forecasting methods to create a "surge response" for noncrisis events. , 2012, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[22]  E. S. Savas,et al.  Simulation and Cost-Effectiveness Analysis of New York's Emergency Ambulance Service , 1969 .

[23]  Manuel D. Rossetti,et al.  Emergency department simulation and determination of optimal attending physician staffing schedules , 1999, WSC '99.

[24]  Mark S. Daskin,et al.  APPLICATION OF AN EXPECTED COVERING MODEL TO EMERGENCY MEDICAL SERVICE SYSTEM DESIGN , 1982 .

[25]  L. Lind,et al.  A systematic review of triage-related interventions to improve patient flow in emergency departments , 2011, Scandinavian journal of trauma, resuscitation and emergency medicine.

[26]  Stephen K Epstein,et al.  Development of an emergency department work score to predict ambulance diversion. , 2006, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[27]  K. Rhodes,et al.  Access to emergency care: restricted by long waiting times and cost and coverage concerns. , 2004, Annals of emergency medicine.

[28]  Camilla Monefeldt,et al.  Client Involvement in Simulation Model Building: Hints and Insights from a Case Study in a London Hospital , 2003, Health care management science.

[29]  Pengyi Shi,et al.  Hospital Inpatient Operations : Mathematical Models and Managerial Insights , 2012 .

[30]  Joseph S. Pliskin,et al.  A geographic information system simulation model of EMS: reducing ambulance response time. , 2004, The American journal of emergency medicine.

[31]  P. Michelon,et al.  A mathematical programming approach for scheduling physicians in the emergency room , 2000, Health care management science.

[32]  F. Zwemer,et al.  Recently discharged inpatients as a source of emergency department overcrowding. , 2001, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[33]  Linda V. Green,et al.  Using Operations Research to Reduce Delays for Healthcare , 2008 .

[34]  Shari J. Welch.  Banner Results for Banner Health , 2009 .

[35]  S.J. Macdonald,et al.  Emergency department process improvement , 2005, 2005 IEEE Design Symposium, Systems and Information Engineering.

[36]  L. McCaig,et al.  National Hospital Ambulatory Medical Care Survey: 2001 emergency department summary. , 2003 .

[37]  Yariv N. Marmor,et al.  Emergency department operations: The basis for developing a simulation tool , 2005 .

[38]  Jeffery K. Cochran,et al.  A queuing-based decision support methodology to estimate hospital inpatient bed demand , 2008, J. Oper. Res. Soc..

[39]  M. Barry Dumas.  Simulation modeling for hospital bed planning , 1984 .

[40]  Gilles Reinhardt,et al.  Adding more beds to the emergency department or reducing admitted patient boarding times: which has a more significant influence on emergency department congestion? , 2009, Annals of emergency medicine.

[41]  R. A. Green,et al.  Using queueing theory to increase the effectiveness of emergency department provider staffing. , 2006, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[42]  M. Hauswald.  C AN P ARAMEDICS S AFELY D ECIDE W HICH P ATIENTS D O N OT N EED A MBULANCE T RANSPORT OR E MERGENCY D EPARTMENT C ARE ? , 2002, Prehospital emergency care : official journal of the National Association of EMS Physicians and the National Association of State EMS Directors.

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

[44]  Linda V. Green,et al.  OM Forum - The Vital Role of Operations Analysis in Improving Healthcare Delivery , 2012, Manuf. Serv. Oper. Manag..

[45]  G. Kelen,et al.  Effect of an emergency department (ED) managed acute care unit on ED overcrowding and emergency medical services diversion. , 2001, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[46]  Charles Simmons,et al.  Approach to decreasing emergency department ambulance diversion hours. , 2004, The Journal of emergency medicine.

[47]  R. Niska,et al.  National Hospital Ambulatory Medical Care Survey: 2006 emergency department summary. , 2008, National health statistics reports.

[48]  D. Magid,et al.  Emergency department crowding: consensus development of potential measures. , 2003, Annals of emergency medicine.

[49]  Tobias Andersson Granberg,et al.  Decision support tools for ambulance dispatch and relocation , 2007, J. Oper. Res. Soc..

[50]  Ward Whitt,et al.  Coping with Time‐Varying Demand When Setting Staffing Requirements for a Service System , 2007 .

[51]  Dominik Aronsky,et al.  The effect of emergency department expansion on emergency department overcrowding. , 2007, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[52]  Basheer M. Khumawala,et al.  An empirical comparison of tabu search, simulated annealing, and genetic algorithms for facilities location problems , 1997 .

[53]  Kurt M. Bretthauer,et al.  Blocking in Healthcare Operations: A New Heuristic and an Application , 2011 .

[54]  Peter G. Harrison,et al.  A Queueing Network Model of Patient Flow in an Accident and Emergency Department , 2006 .

[55]  David R Vinson,et al.  Team assignment system: expediting emergency department care. , 2004, Annals of emergency medicine.

[56]  Jonathan Karnon,et al.  Mathematical modelling in health care , 2009 .

[57]  C. Saunders,et al.  Time study of patient movement through the emergency department: sources of delay in relation to patient acuity. , 1987, Annals of emergency medicine.

[58]  Daoqin Tong,et al.  Enhancing Classic Coverage Location Models , 2010 .

[59]  Paul Robert Harper,et al.  Modelling for the planning and management of bed capacities in hospitals , 2002, J. Oper. Res. Soc..

[60]  R Davies,et al.  Modelling patient flows and resource provision in health systems , 1994 .

[61]  Gilbert Laporte,et al.  Ambulance location and relocation models , 2000, Eur. J. Oper. Res..

[62]  A. Kelly,et al.  Benchmarking ambulance call‐to‐needle times for thrombolysis after acute myocardial infarction in Australia: 
a pilot study , 2002, Internal medicine journal.

[63]  Gabriel Zayas-Cabán,et al.  Optimal Control of an Emergency Room Triage and Treatment Process , 2014 .

[64]  Wallace J. Hopp,et al.  PRINCIPLES OF HIGH EFFICIENCY HEALTH CARE , 2012 .

[65]  Solon Venâncio de Carvalho,et al.  Markov decision process applied to the control of hospital elective admissions , 2009, Artif. Intell. Medicine.

[66]  Mark S. Daskin,et al.  A Maximum Expected Covering Location Model: Formulation, Properties and Heuristic Solution , 1983 .

[67]  Timothy G Price,et al.  Prehospital provider prediction of emergency department disposition: implications for selective diversion. , 2005, Prehospital emergency care : official journal of the National Association of EMS Physicians and the National Association of State EMS Directors.

[68]  G. Jelinek,et al.  Impact of streaming "fast track" emergency department patients. , 2006, Australian health review : a publication of the Australian Hospital Association.

[69]  H. Simon,et al.  "Fast tracking" patients in an urban pediatric emergency department. , 1996, The American journal of emergency medicine.

[70]  Peter G. Taylor,et al.  A two-time-scale model for hospital patient flow , 2005 .

[71]  J. McNeil,et al.  Increasing utilisation of emergency ambulances. , 2011, Australian health review : a publication of the Australian Hospital Association.

[72]  K. Göransson,et al.  Swedish emergency department triage and interventions for improved patient flows: a national update , 2011, Scandinavian journal of trauma, resuscitation and emergency medicine.

[73]  J. Dale,et al.  On-scene alternatives for emergency ambulance crews attending patients who do not need to travel to the accident and emergency department: a review of the literature , 2004, Emergency Medicine Journal.

[74]  A. Bindman,et al.  Judging who needs emergency department care: a prerequisite for policy-making. , 1997, The American journal of emergency medicine.

[75]  Soroush Saghafian,et al.  Emergency Department Rotational Patient Assignment. , 2016, Annals of emergency medicine.

[76]  Jeffery K. Cochran,et al.  Developing nonlinear queuing regressions to increase emergency department patient safety: Approximating reneging with balking , 2010, Comput. Ind. Eng..

[77]  Arjun K Venkatesh,et al.  The growing role of emergency departments in hospital admissions. , 2012, The New England journal of medicine.

[78]  O. Djurdjev,et al.  How reliable is emergency department triage? , 1999, Annals of emergency medicine.

[79]  Reinaldo Morabito,et al.  Towards unified formulations and extensions of two classical probabilistic location models , 2005, Comput. Oper. Res..

[80]  Peter G. Harrison,et al.  Approximate queueing network analysis of patient treatment times , 2007, ValueTools '07.

[81]  E. Enguidanos,et al.  Guidelines for ambulance diversion , 2000 .

[82]  Edwin D Boudreaux,et al.  Patient satisfaction in the Emergency Department: a review of the literature and implications for practice. , 2004, The Journal of emergency medicine.

[83]  Lenworth M Jacobs,et al.  Effects of a fast-track area on emergency department performance. , 2006, The Journal of emergency medicine.

[84]  R. J. Vogel.  Health care finance: by Robert J. Buchanan. Heath, Lexington, MA, 1981. 174 pp. $23.95 , 1983 .

[85]  C. Palmer,et al.  Assessment of the effects and limitations of the 1998 to 2008 Abbreviated Injury Scale map using a large population-based dataset , 2011, Scandinavian journal of trauma, resuscitation and emergency medicine.

[86]  Sivakumar Appa Iyer,et al.  Application of queueing theory in health care: A literature review , 2013 .

[87]  Jan M. Chaiken,et al.  Response Areas for Two Emergency Units , 1972, Oper. Res..

[88]  Gabor D Kelen,et al.  Patients who leave without being seen: their characteristics and history of emergency department use. , 2006, Annals of emergency medicine.

[89]  D. Richardson,et al.  Reducing patient time in the emergency department , 2003, The Medical journal of Australia.

[90]  J. Goldberg.  Operations Research Models for the Deployment of Emergency Services Vehicles , 2004 .

[91]  Michael Pidd,et al.  Discrete event simulation for performance modelling in health care: a review of the literature , 2010, J. Simulation.

[92]  John R. Richards,et al.  Ten Solutions for Emergency Department Crowding , 2008, The western journal of emergency medicine.

[93]  M. Carter,et al.  Scheduling Emergency Room Physicians , 2001, Health care management science.

[94]  Donna Kelly,et al.  Impact of rapid entry and accelerated care at triage on reducing emergency department patient wait times, lengths of stay, and rate of left without being seen. , 2005, Annals of emergency medicine.

[95]  Alexander Kolker,et al.  Process Modeling of Emergency Department Patient Flow: Effect of Patient Length of Stay on ED Diversion , 2008, Journal of Medical Systems.

[96]  S. Peiró,et al.  Inappropriate use of an accident and emergency department: magnitude, associated factors, and reasons--an approach with explicit criteria. , 2001, Annals of emergency medicine.

[97]  Gabor D Kelen,et al.  Refining Surge Capacity: Conventional, Contingency, and Crisis Capacity , 2009, Disaster Medicine and Public Health Preparedness.

[98]  C. Lipinski,et al.  Emergency department rapid medical assessment: overall effect and mechanistic considerations. , 2015, The Journal of emergency medicine.

[99]  J. Barbera,et al.  EMS-initiated refusal and alternative methods of transport. , 1998, Prehospital emergency care : official journal of the National Association of EMS Physicians and the National Association of State EMS Directors.

[100]  Peter J. Kolesar,et al.  Improving the Sipp Approach for Staffing Service Systems That Have Cyclic Demands , 2001, Oper. Res..

[101]  T. Kirsch,et al.  The effects of ambulance diversion: a comprehensive review. , 2006, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[102]  S. Schneider,et al.  Rochester, New York: a decade of emergency department overcrowding. , 2001, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[103]  Gordon T. Vail,et al.  Applying the Lean principles of the Toyota Production System to reduce wait times in the emergency department. , 2010, CJEM.

[104]  Edbert B. Hsu,et al.  Inpatient disposition classification for the creation of hospital surge capacity: a multiphase study , 2006, The Lancet.

[105]  E Milne,et al.  Calculation of the need for paediatric intensive care beds. , 1995, Archives of disease in childhood.

[106]  A. Murphy,et al.  A national census of ambulance response times to emergency calls in Ireland , 2000, Journal of accident & emergency medicine.

[107]  David P Sklar,et al.  Emergency department crowding, part 2--barriers to reform and strategies to overcome them. , 2009, Annals of emergency medicine.

[108]  S. Leggat,et al.  Do triage systems in healthcare improve patient flow? A systematic review of the literature. , 2011, Australian health review : a publication of the Australian Hospital Association.

[109]  S. Grover,et al.  Use of the emergency department for nonurgent care during regular business hours. , 1996, CMAJ : Canadian Medical Association journal = journal de l'Association medicale canadienne.

[110]  J. Considine,et al.  Effect of emergency department fast track on emergency department length of stay: a case–control study , 2008, Emergency Medicine Journal.

[111]  Purnell Ld,et al.  A survey of emergency department triage in 185 hospitals: physical facilities, fast-track systems, patient-classification systems, waiting times, and qualification, training, and skills of triage personnel. , 1991 .

[112]  Ò. Miró,et al.  Analysis of patient flow in the emergency department and the effect of an extensive reorganisation , 2003, Emergency medicine journal : EMJ.

[113]  R. Beveridge,et al.  CAEP issues. The Canadian Triage and Acuity Scale: a new and critical element in health care reform. Canadian Association of Emergency Physicians. , 1998, The Journal of emergency medicine.

[114]  James R. Langabeer,et al.  Implementation of Lean and Six Sigma quality initiatives in hospitals: A goal theoretic perspective , 2009 .

[115]  B. Asplin,et al.  Does ambulance diversion matter? , 2003, Annals of emergency medicine.

[116]  Melissa L Dougherty,et al.  Redesigning care at the Flinders Medical Centre: clinical process redesign using “lean thinking” , 2008, The Medical journal of Australia.

[117]  Junfei Huang,et al.  Control of Patient Flow in Emergency Departments, or Multiclass Queues with Deadlines and Feedback , 2015, Oper. Res..

[118]  N. Mann,et al.  Evaluation of protocols allowing emergency medical technicians to determine need for treatment and transport. , 2000, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[119]  A. Ehrenberg,et al.  Triage in emergency departments: national survey. , 2005, Journal of clinical nursing.

[120]  W. Lovejoy,et al.  Little's law flow analysis of observation unit impact and sizing. , 2011, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[121]  Shahram Alamdari,et al.  Application of Queuing Analytic Theory to Decrease Waiting Times in Emergency Department: Does it Make Sense? , 2012, Archives of trauma research.

[122]  Matthew S. Maxwell,et al.  Approximate Dynamic Programming for Ambulance Redeployment , 2010, INFORMS J. Comput..

[123]  Martha A. Centeno,et al.  Reducing time in an emergency room via a fast-track , 1995, WSC '95.

[124]  Sema Elbeyli,et al.  IN-PATIENT FLOW ANALYSIS USING PROMODEL (TM) SIMULATION PACKAGE , 2000 .

[125]  R. Boaden,et al.  Developing bed managers: the why and the how. , 2007, Journal of nursing management.

[126]  L. McCaig,et al.  Staffing, capacity, and ambulance diversion in emergency departments: United States, 2003-04. , 2006, Advance data.

[127]  S. Rodi,et al.  Evaluation of a Fast Track Unit: Alignment of Resources and Demand Results in Improved Satisfaction and Decreased Length of Stay for Emergency Department Patients , 2006, Quality management in health care.

[128]  Timothy J Coats,et al.  Mathematical modelling of patient flow through an accident and emergency department , 2001 .

[129]  Belarmino Adenso-Díaz,et al.  A simple search heuristic for the MCLP: Application to the location of ambulance bases in a rural region , 1997 .

[130]  Wallace J. Hopp,et al.  Patient Streaming as a Mechanism for Improving Responsiveness in Emergency Departments , 2012, Oper. Res..

[131]  Ehsan Bolandifar,et al.  An emergency department patient flow model based on queueing theory principles. , 2013, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[132]  Jingshan Li,et al.  A system model of work flow in the patient room of hospital emergency department , 2013, Health care management science.

[133]  Ola Jabali,et al.  Staggered work shifts: a way to downsize and restructure an emergency department workforce yet maintain current operational performance , 2007, Health care management science.

[134]  Masood A. Badri,et al.  A Simulation Model for Scheduling in the Emergency Room , 1993 .

[135]  René Bekker,et al.  Time-dependent analysis for refused admissions in clinical wards , 2010, Ann. Oper. Res..

[136]  Madhu C. Reddy,et al.  A Systematic Review of Simulation Studies Investigating Emergency Department Overcrowding , 2010, Simul..

[137]  van der,et al.  Proceedings of the 2012 winter simulation conference , 2001, WSC 2008.

[138]  Eric Howell,et al.  Hospitalist bed management effecting throughput from the emergency department to the intensive care unit. , 2010, Journal of critical care.

[139]  S. Trzeciak,et al.  Emergency department overcrowding in the United States: an emerging threat to patient safety and public health , 2003, Emergency medicine journal : EMJ.

[140]  Michel Gendreau,et al.  The maximal expected coverage relocation problem for emergency vehicles , 2006, J. Oper. Res. Soc..

[141]  J. Brice,et al.  Use of an emergency department by nonurgent patients. , 2005, The American journal of emergency medicine.

[142]  Michael O. Ball,et al.  A Reliability Model Applied to Emergency Service Vehicle Location , 1993, Oper. Res..

[143]  Ieee Staff,et al.  Proceedings of the 2011 Winter Simulation Conference , 2011 .

[144]  T. Rea,et al.  A N E MERGENCY M EDICAL S ERVICES P ROGRAM OF A LTERNATE D ESTINATION OF P ATIENT C ARE , 2002, Prehospital emergency care : official journal of the National Association of EMS Physicians and the National Association of State EMS Directors.

[145]  Shari J. Welch.  Patient Segmentation: Redesigning Flow , 2009 .

[146]  Edbert B. Hsu,et al.  Creation of Surge Capacity by Early Discharge of Hospitalized Patients at Low Risk for Untoward Events , 2009, Disaster Medicine and Public Health Preparedness.

[147]  P. H. Millard,et al.  A simulation modelling approach to evaluating length of stay, occupancy, emptiness and bed blocking in a hospital geriatric department , 1998, Health care management science.

[148]  Avishai Mandelbaum,et al.  Routing and Staffing in Large-Scale Service Systems: The Case of Homogeneous Impatient Customers and Heterogeneous Servers , 2011, Oper. Res..

[149]  D J Worthington,et al.  Queueing Models for Hospital Waiting Lists , 1987, The Journal of the Operational Research Society.

[150]  S.C. Brailsford,et al.  Tutorial: Advances and challenges in healthcare simulation modeling , 2007, 2007 Winter Simulation Conference.

[151]  R. Scott Evans,et al.  An Agent Based Simulation Tool for Scheduling Emergency Department Physicians , 2008, AMIA.

[152]  D Richardson,et al.  No relationship between emergency department activity and triage categorization. , 1998, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[153]  D. Debehnke,et al.  The effects of a physician-nurse patient care team on patient satisfaction in an academic ED. , 2002, The American journal of emergency medicine.

[154]  Bin Hu,et al.  Partitioning of Servers in Queueing Systems During Rush Hour , 2009, Manuf. Serv. Oper. Manag..

[155]  Michel Gendreau,et al.  Physician Scheduling in Emergency Rooms , 2006, PATAT.

[156]  Mark Fackrell,et al.  Predicting overflow in an emergency department , 2007 .

[157]  Timothy G. Price,et al.  Prehospital Provider Prediction of Emergency Department Disposition: , 2005 .

[158]  Avishai Mandelbaum,et al.  ON PATIENT FLOW IN HOSPITALS: A DATA-BASED QUEUEING-SCIENCE PERSPECTIVE , 2015 .

[159]  S. Schneider,et al.  Emergency department crowding: a point in time. , 2003, Annals of emergency medicine.

[160]  R. Hall,et al.  Patient flow : reducing delay in healthcare delivery , 2006 .

[161]  Michel Gendreau,et al.  A dynamic model and parallel tabu search heuristic for real-time ambulance relocation , 2001, Parallel Comput..

[162]  Michael Williams,et al.  Hospitals and Clinical Facilities, Processes and Design for Patient Flow , 2013 .

[163]  Gül E. Okudan Kremer,et al.  Model comparison in Emergency Severity Index level prediction , 2013, Expert Syst. Appl..

[164]  Nobhojit Roy.  Attack on the Taj Mahal Palace Hotel: a proxy war on America? , 2009, Disaster medicine and public health preparedness.

[165]  Linda V. Green,et al.  Identifying Good Nursing Levels: A Queuing Approach , 2011, Oper. Res..

[166]  M. Brandeau,et al.  An overview of representative problems in location research , 1989 .

[167]  Asha Seth Kapadia,et al.  Predicting duration of stay in a pediatric intensive care unit: A Markovian approach , 2000, Eur. J. Oper. Res..

[168]  XiaoqingWang.  Emergency Department Staffing : A Separated Continuous Linear Programming Approach , 2015 .

[169]  David C. Lane,et al.  Looking in the wrong place for healthcare improvements: A system dynamics study of an accident and emergency department , 2000, J. Oper. Res. Soc..

[170]  R. G. Ingalls,et al.  PROCEEDINGS OF THE 2002 WINTER SIMULATION CONFERENCE , 2002 .

[171]  Durward K. Sobek,et al.  Reducing waste and errors: piloting lean principles at Intermountain Healthcare. , 2005, Joint Commission journal on quality and patient safety.

[172]  H M G Martins,et al.  Is Manchester (MTS) more than a triage system? A study of its association with mortality and admission to a large Portuguese hospital , 2009, Emergency Medicine Journal.

[173]  Ward Whitt,et al.  Engineering Solution of a Basic Call-Center Model , 2005, Manag. Sci..

[174]  P. Sprivulis.  Pilot study of metropolitan emergency department workload complexity. , 2004, Emergency medicine Australasia : EMA.

[175]  Noraida A. Ghani.  Multi-server Queuing Maximum Availability Location Problem with Stochastic Travel Times , .

[176]  Fatah Chetouane,et al.  Modeling and Improving Emergency Department Systems using Discrete Event Simulation , 2007, Simul..

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

[178]  Shari J. Welch,et al.  Emergency department performance measures and benchmarking summit. , 2006, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[179]  T. Falvo,et al.  The financial impact of ambulance diversions and patient elopements. , 2007, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[180]  M. V. van Baar,et al.  Reliability and validity of the Manchester Triage System in a general emergency department patient population in the Netherlands: results of a simulation study , 2008, Emergency Medicine Journal.

[181]  M Côté.  An Erlang-based stochastic model for patient flow , 2000 .

[182]  John W. Fowler,et al.  Comparison of ambulance diversion policies via simulation , 2012, Proceedings Title: Proceedings of the 2012 Winter Simulation Conference (WSC).

[183]  L Mayhew,et al.  Using queuing theory to analyse the Government’s 4-h completion time target in Accident and Emergency departments , 2008, Health care management science.

[184]  Vladimir Marianov,et al.  The Queueing Maximal availability location problem: A model for the siting of emergency vehicles , 1996 .

[185]  Edward P. C. Kao,et al.  Bed Allocation in a Public Health Care Delivery System , 1981 .

[186]  Renee Moilanen,et al.  When Emergency Rooms Close: Ambulance Diversion in the West San Fernando Valley , 2005 .

[187]  Richard C. Wuerz,et al.  Inconsistency of Emergency Department Triage , 1998 .

[188]  P R Yarnold,et al.  Effects of actual waiting time, perceived waiting time, information delivery, and expressive quality on patient satisfaction in the emergency department. , 1996, Annals of emergency medicine.

[189]  Ali Kokangul,et al.  A combination of deterministic and stochastic approaches to optimize bed capacity in a hospital unit , 2008, Comput. Methods Programs Biomed..

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

[191]  Gilbert Laporte,et al.  Scheduling ambulance crews for maximum coverage , 2010, J. Oper. Res. Soc..

[192]  J D Mayer,et al.  Emergency Medical Service: Delays, Response Time and Survival , 1979, Medical care.

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

[194]  Pierre Le Beux,et al.  A simple method to optimize hospital beds capacity , 2005, Int. J. Medical Informatics.

[195]  M. Levitt,et al.  Can paramedics using guidelines accurately triage patients? , 2001, Annals of emergency medicine.

[196]  E K Mensah,et al.  Distribution of variable vs fixed costs of hospital care. , 1999, JAMA.

[197]  Michel Gendreau,et al.  Parallel Tabu Search for Real-Time Vehicle Routing and Dispatching , 1999, Transp. Sci..

[198]  Yasar A. Ozcan.  Quantitative Methods in Health Care Management: Techniques and Applications , 2005 .

[199]  J. Cochran,et al.  Stochastic bed balancing of an obstetrics hospital , 2006, Health care management science.

[200]  Sangbok Lee,et al.  The role of preparedness in ambulance dispatching , 2011, J. Oper. Res. Soc..

[201]  John W. Fowler,et al.  Design of centralized Ambulance Diversion policies using Simulation-Optimization , 2011, Proceedings of the 2011 Winter Simulation Conference (WSC).

[202]  D. King,et al.  Redesigning emergency department patient flows: Application of Lean Thinking to health care , 2006, Emergency medicine Australasia : EMA.

[203]  Emilio Luque,et al.  Towards an Agent-Based Simulation of Hospital Emergency Departments , 2009, 2009 IEEE International Conference on Services Computing.

[204]  Kevin E McVaney,et al.  How well do paramedics predict admission to the hospital? A prospective study. , 2006, The Journal of emergency medicine.

[205]  David P Sklar,et al.  Emergency department crowding, part 1--concept, causes, and moral consequences. , 2009, Annals of emergency medicine.

[206]  Cem Saydam,et al.  Ambulance Deployment and Shift Scheduling: An Integrated Approach , 2011 .

[207]  Michael J. Magazine,et al.  Building Cyclic Schedules for Emergency Department Physicians , 2011, Interfaces.

[208]  Kathleen Nash,et al.  Evaluation of the fast track unit of a university emergency department. , 2007, Journal of emergency nursing: JEN : official publication of the Emergency Department Nurses Association.

[209]  A. Sama,et al.  Owning the cost of emergency medicine: beyond 2%. , 2013, Annals of emergency medicine.

[210]  Peter Sprivulis,et al.  Triage nurses validly and reliably estimate emergency department patient complexity , 2005, Emergency medicine Australasia : EMA.

[211]  Eric Howell,et al.  Active Bed Management by Hospitalists and Emergency Department Throughput , 2008, Annals of Internal Medicine.

[212]  P S Heckerling.  Time study of an emergency room. Identification of sources of patient delay. , 1984, IMJ. Illinois medical journal.

[213]  Frank McGuire.  Using simulation to reduce length of stay in emergency departments , 1994, Proceedings of Winter Simulation Conference.

[214]  J. Posnett,et al.  Dynamics of bed use in accommodating emergency admissions: stochastic simulation model , 1999, BMJ.

[215]  G B Hall,et al.  Assessment of ambulance response performance using a geographic information system. , 1999, Social science & medicine.

[216]  Charles S. ReVelle,et al.  The Maximum Availability Location Problem , 1989, Transp. Sci..

[217]  Robert J. Batt,et al.  Waiting Patiently: An Empirical Study of Queue Abandonment in an Emergency Department , 2015, Manag. Sci..

[218]  J Mantas,et al.  The intensive care units in greater Athens: needs and resources. , 1996, Intensive & critical care nursing.

[219]  Frank Zilm,et al.  New Directions in Emergency Service Operations and Planning , 2010, The Journal of ambulatory care management.

[220]  Dominik Aronsky,et al.  Forecasting emergency department crowding: a discrete event simulation. , 2008, Annals of emergency medicine.

[221]  Cem Saydam,et al.  A multiperiod set covering location model for dynamic redeployment of ambulances , 2008, Comput. Oper. Res..

[222]  John J. Bernardo,et al.  Developing and validating a decision support system for locating emergency medical vehicles in Louisville, Kentucky , 1994 .

[223]  J. Richards,et al.  Inappropriate use of emergency medical services transport: comparison of provider and patient perspectives. , 1999, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[224]  A. Pancioli,et al.  Can emergency department triage nurses predict patients' dispositions? , 2001, The American journal of emergency medicine.

[225]  G. Bevan,et al.  "Systematic" , 1966, Comput. J..

[226]  J. Wills,et al.  Ambulance diversion reduction: the Sacramento solution. , 2006, The American journal of emergency medicine.

[227]  H W Meislin,et al.  Fast Track: urgent care within a teaching hospital emergency department: can it work? , 1988, Annals of emergency medicine.

[228]  Alexander Komashie,et al.  Modeling emergency departments using discrete event simulation techniques , 2005, Proceedings of the Winter Simulation Conference, 2005..

[229]  Dominik Aronsky,et al.  The effect of physician triage on emergency department length of stay. , 2010, The Journal of emergency medicine.

[230]  N C Proudlove,et al.  Can good bed management solve the overcrowding in accident and emergency departments? , 2003, Emergency medicine journal : EMJ.

[231]  Richard L. Church,et al.  The maximal covering location problem , 1974 .

[232]  Rajan Batta,et al.  The Maximal Expected Covering Location Problem: Revisited , 1989, Transp. Sci..

[233]  C. Lipinski,et al.  Emergency department physician telemedical triage. , 2013, Telemedicine journal and e-health : the official journal of the American Telemedicine Association.

[234]  Gerard FitzGerald,et al.  Emergency department triage revisited , 2009, Emergency Medicine Journal.

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

[236]  S. Wright,et al.  Fast Track in the emergency department: a one-year experience with nurse practitioners. , 1992, The Journal of emergency medicine.

[237]  Junwen Wang,et al.  Reducing Length of Stay in Emergency Department: A Simulation Study at a Community Hospital , 2012, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[238]  Sarang Deo,et al.  The Impact of Size and Occupancy of Hospital on the Extent of Ambulance Diversion: Theory and Evidence , 2013, Oper. Res..

[239]  S. Samaha,et al.  The use of simulation to reduce the length of stay in an emergency department , 2003, Proceedings of the 2003 Winter Simulation Conference, 2003..

[240]  D. Eitel,et al.  Reliability and validity of a new five-level triage instrument. , 2000, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[241]  Jim Smith,et al.  Strategies to take hospitals off (revenue) diversion. , 2004, Healthcare financial management : journal of the Healthcare Financial Management Association.

[242]  Gilles Reinhardt,et al.  The relationship between inpatient discharge timing and emergency department boarding. , 2012, The Journal of emergency medicine.

[243]  M. Pearson,et al.  Average length of stay, delayed discharge, and hospital congestion , 2002, BMJ : British Medical Journal.

[244]  X. M. Huang,et al.  A planning model for requirement of emergency beds. , 1995, IMA journal of mathematics applied in medicine and biology.

[245]  Michel Bierlaire,et al.  An analytic finite capacity queueing network model capturing the propagation of congestion and blocking , 2009, Eur. J. Oper. Res..

[246]  L. Vertesi.  Does the Canadian Emergency Department Triage and Acuity Scale identify non-urgent patients who can be triaged away from the emergency department? , 2004, CJEM.

[247]  L. Cooper.  Location-Allocation Problems , 1963 .

[248]  C. Warden,et al.  T EMPORAL T RENDS IN A MBULANCE D IVERSION IN A M ID-SIZED M ETROPOLITAN A REA , 2003, Prehospital emergency care : official journal of the National Association of EMS Physicians and the National Association of State EMS Directors.

[249]  Reinaldo Morabito,et al.  Analysis of ambulance decentralization in an urban emergency medical service using the hypercube queueing model , 2007, Comput. Oper. Res..

[250]  T. Olsen,et al.  Review of modeling approaches for emergency department patient flow and crowding research. , 2011, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[251]  Dominik Aronsky,et al.  Placing physician orders at triage: the effect on length of stay. , 2010, Annals of emergency medicine.

[252]  Francis de Véricourt,et al.  Nurse Staffing in Medical Units: A Queueing Perspective , 2011, Oper. Res..

[253]  Mohamud Daya,et al.  Ambulance diversion and lost hospital revenues. , 2006, Annals of emergency medicine.

[254]  K. Preston White,et al.  A survey of data resources for simulating patient flows in healthcare delivery systems , 2005, Proceedings of the Winter Simulation Conference, 2005..

[255]  Pnina Vortman,et al.  Simulation-based models of emergency departments:: Operational, tactical, and strategic staffing , 2011, TOMC.

[256]  Renata Konrad,et al.  Modeling the impact of changing patient flow processes in an emergency department: Insights from a computer simulation study , 2013 .

[257]  R. P. Gregory,et al.  Ambulance emergency services for patients with coronary heart disease in Lancashire: achieving standards and improving performance , 2004, Emergency Medicine Journal.

[258]  RICHARD C. LARSON,et al.  A hypercube queuing model for facility location and redistricting in urban emergency services , 1974, Comput. Oper. Res..

[259]  Michael G.H. Bell,et al.  A game theory approach to measuring the performance reliability of transport networks , 2000 .

[260]  Ward Whitt,et al.  Partitioning Customers Into Service Groups , 1999 .

[261]  Jordan S. Peck,et al.  Improving Patient Flow Through Axiomatic Design of Hospital Emergency Departments , 2010 .

[262]  Ilan Vertinsky,et al.  Ambulance Location: A Probabilistic Enumeration Approach , 1973 .

[263]  Jordan S Peck,et al.  Predicting emergency department inpatient admissions to improve same-day patient flow. , 2012, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[264]  Gilbert Laporte,et al.  Solving an ambulance location model by tabu search , 1997 .

[265]  Erhan Erkut,et al.  Optimal ambulance location with random delays and travel times , 2008, Health care management science.

[266]  M. Domingues,et al.  Inappropriate use of emergency services : a systematic review of prevalence and associated factors , 2009 .

[267]  N. Rathlev,et al.  Emergency Department overcrowding and ambulance diversion: the impact and potential solutions of extended boarding of admitted patients in the Emergency Department. , 2006, The Journal of emergency medicine.

[268]  N. Koizumi,et al.  Modeling Patient Flows Using a Queuing Network with Blocking , 2005, Health Care Management Science.

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

[270]  Peter W. Glynn,et al.  Proceedings of the 2nd international conference on Performance evaluation methodologies and tools , 2007 .

[271]  Martin Pitt,et al.  An analysis of the academic literature on simulation and modelling in health care , 2009, J. Simulation.

[272]  Kenneth V Iserson,et al.  Triage in medicine, part I: Concept, history, and types. , 2007, Annals of emergency medicine.

[273]  Edward W. Davis,et al.  A Comparison of Heuristic and Optimum Solutions in Resource-Constrained Project Scheduling , 1975 .

[274]  Mark E. Ferguson,et al.  Cooperative strategies to reduce ambulance diversion , 2009, Proceedings of the 2009 Winter Simulation Conference (WSC).

[275]  A. Stack,et al.  Effective discharge communication in the emergency department. , 2012, Annals of emergency medicine.

[276]  C. Fullam.  Acuity-based ED nurse staffing: a successful 5-year experience. , 2002, Journal of emergency nursing: JEN : official publication of the Emergency Department Nurses Association.

[277]  Patricio Donoso,et al.  Assessing an ambulance service with queuing theory , 2008, Comput. Oper. Res..

[278]  P. Kolesar,et al.  Improving Emergency Responsiveness with Management Science , 2004 .

[279]  Byung Rae Cho,et al.  Industrial Engineering Research - Conference Proceedings , 1997 .

[280]  Peter J. Kolesar,et al.  ANNIVERSARY ARTICLE: Improving Emergency Responsiveness with Management Science , 2004, Manag. Sci..

[281]  H. Binns,et al.  Fast track and the pediatric emergency department: resource utilization and patients outcomes. , 1999, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[282]  Sadiq M. Sait,et al.  Evolutionary algorithms, simulated annealing, and Tabu search: a comparative study , 1998, Optics & Photonics.

[283]  Marian Vermeulen,et al.  Emergency department contributors to ambulance diversion: a quantitative analysis. , 2003, Annals of emergency medicine.

[284]  Celso C. Ribeiro,et al.  Tutorials in Operations Research , 2012, Int. Trans. Oper. Res..

[285]  James A. Fitzsimmons,et al.  A Methodology for Emergency Ambulance Deployment , 1973 .

[286]  Denise F. Blake,et al.  Fast track: Has it changed patient care in the emergency department? , 2008, Emergency medicine Australasia : EMA.

[287]  Avishai Mandelbaum,et al.  On Fair Routing from Emergency Departments to Hospital Wards: QED Queues with Heterogeneous Servers , 2012, Manag. Sci..

[288]  J. M. Moore,et al.  A Functional Equation and its Application to Resource Allocation and Sequencing Problems , 1969 .

[289]  Jeffery K. Cochran,et al.  A multi-class queuing network analysis methodology for improving hospital emergency department performance , 2009, Comput. Oper. Res..

[290]  H A Knappenberger,et al.  Evaluating bed allocation policy with computer simulation. , 1968, Health services research.

[291]  John W. Fowler,et al.  Analysis of ambulance diversion policies for a large-size hospital , 2009, Proceedings of the 2009 Winter Simulation Conference (WSC).

[292]  Amin H. Amershi,et al.  Studies in Resource Allocation Processes. , 1979 .

[293]  S. Kellermann,et al.  Ambulatory visits to hospital emergency departments: patterns and reasons for use: 24 hours in the E , 1996 .

[294]  Sheldon Howard Jacobson,et al.  Application of discrete-event simulation in health care clinics: A survey , 1999, J. Oper. Res. Soc..

[295]  Sally C. Brailsford,et al.  Advances and challenges in healthcare simulation modeling: tutorial , 2007, WSC.

[296]  Wen-Chen Tsai,et al.  Factors associated with frequent use of emergency services in a medical center. , 2003, Journal of the Formosan Medical Association = Taiwan yi zhi.

[297]  Eva K. Lee,et al.  Transforming Hospital Emergency Department Workflow and Patient Care , 2015, Interfaces.

[298]  Margaret Fry,et al.  Accuracy of triage nurses in predicting patient disposition. , 2007, Emergency medicine Australasia : EMA.

[299]  Junfei Huang,et al.  PATIENT FLOW MANAGEMENT IN EMERGENCY DEPARTMENTS , 2013 .

[300]  B. Nelson,et al.  Faculty triage shortens emergency department length of stay. , 2001, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[301]  Trevor Strome,et al.  Application of Lean principles to improve early cardiac care in the emergency department. , 2011, CJEM.

[302]  M. Schull,et al.  Disequilibrium between admitted and discharged hospitalized patients affects emergency department length of stay. , 2009, Annals of emergency medicine.

[303]  Martin Utley,et al.  Booked inpatient admissions and hospital capacity: mathematical modelling study , 2002, BMJ : British Medical Journal.

[304]  Andrew Eller,et al.  Rapid Assessment and Disposition: Applying LEAN in the Emergency Department , 2009, Journal for healthcare quality : official publication of the National Association for Healthcare Quality.

[305]  Wallace J. Hopp,et al.  Complexity-Augmented Triage: A Tool for Improving Patient Safety and Operational Efficiency , 2013, Manuf. Serv. Oper. Manag..

[306]  L. LeBlanc,et al.  Modeling emergency department operations using advanced computer simulation systems. , 1989, Annals of emergency medicine.

[307]  Shari J. Welch,et al.  Emergency department operational metrics, measures and definitions: results of the Second Performance Measures and Benchmarking Summit. , 2011, Annals of emergency medicine.

[308]  Qinan Wang,et al.  Modeling and analysis of high risk patient queues , 2004, Eur. J. Oper. Res..

[309]  David A Thompson,et al.  Five-level triage: a report from the ACEP/ENA Five-level Triage Task Force. , 2005, Journal of emergency nursing: JEN : official publication of the Emergency Department Nurses Association.

[310]  J. Koziol-Mclain,et al.  Seeking care for nonurgent medical conditions in the emergency department: through the eyes of the patient. , 2000, Journal of emergency nursing: JEN : official publication of the Emergency Department Nurses Association.

[311]  J. Christenson,et al.  Does reduced length of stay decrease the number of emergency department patients who leave without seeing a physician? , 1997, The Journal of emergency medicine.

[312]  Cem Saydam,et al.  Solving large-scale maximum expected covering location problems by genetic algorithms: A comparative study , 2002, Eur. J. Oper. Res..

[313]  Eric W Nawar,et al.  National Hospital Ambulatory Medical Care Survey: 2005 emergency department summary. , 2007, Advance data.

[314]  J. Wiler,et al.  Optimizing emergency department front-end operations. , 2010, Annals of emergency medicine.

[315]  Itay Gurvich,et al.  Centralized vs. Decentralized Ambulance Diversion: A Network Perspective , 2011, Manag. Sci..

[316]  Sarah Root,et al.  Scheduling Medical Residents at Boston University School of Medicine , 2009, Interfaces.

[317]  S. Ieraci,et al.  Streaming by case complexity: Evaluation of a model for emergency department Fast Track , 2008, Emergency medicine Australasia : EMA.

[318]  Robert J. Batt,et al.  Doctors Under Load : An Empirical Study of State-Dependent Service Times in Emergency Care , 2012 .

[319]  N. Dellaert,et al.  Reducing emergency department waiting times by adjusting work shifts considering patient visits to multiple care providers , 2012 .

[320]  Charles ReVelle,et al.  Concepts and applications of backup coverage , 1986 .

[321]  Fanwen Meng.  UNDERSTANDING PATIENT FLOWS AND CONSULTATION PATTERNS FOR CARE DELIVERY IN EMERGENCY DEPARTMENT , 2014 .

[322]  Arthur L Kellermann,et al.  Where Americans get acute care: increasingly, it's not at their doctor's office. , 2010, Health affairs.

[323]  D. Fatovich,et al.  Entry overload, emergency department overcrowding, and ambulance bypass , 2003, Emergency medicine journal : EMJ.

[324]  Margaret A. Draeger,et al.  An emergency department simulation model used to evaluate alternative nurse staffing and patient population scenarios , 1992, WSC '92.