Bed Blocking in Hospitals Due to Scarce Capacity in Geriatric Institutions—Cost Minimization via Fluid Models

References

• Afèche P, Araghi M, Baron O (2017) Customer acquisition, retention, and queueing-related service quality: Optimal advertising, staffing, and priorities for a call center. Manufacturing Service Oper. Management 19(4):509–712.Link, Google Scholar
• Akcali E, Coté MJ, Lin C (2006) A network flow approach to optimizing hospital bed capacity decisions. Health Care Management Sci. 9(4):391–404.Crossref, Google Scholar
• Armony M, Israelit S, Mandelbaum A, Marmor YN, Tseytlin Y, Yom-Tov GB (2015) On patient flow in hospitals: A data-based queueing-science perspective. Stochastic Systems 5(1):146–194.Link, Google Scholar
• Arrow KJ, Harris T, Marschak J (1951) Optimal inventory policy. Econometrica J. Econometric Soc. 19(3):250–272.Crossref, Google Scholar
• Ata B, Killaly BL, Olsen TL, Parker RP (2013) On hospice operations under medicare reimbursement policies. Management Sci. 59(5):1027–1044.Link, Google Scholar
• Balsamo S, de Nitto Personé V, Onvural R (2001) Analysis of Queueing Networks with Blocking (Springer, New York).Crossref, Google Scholar
• Bassamboo A, Harrison JM, Zeevi A (2006) Design and control of a large call center: Asymptotic analysis of an lp-based method. Oper. Res. 54(3):419–435.Link, Google Scholar
• BBC News (2016) Hospital bed-blocking costs NHS England £900m a year. Accessed February 5, 2016, http://www.bbc.com/news/health-35481849.Google Scholar
• Bekker R, de Bruin AM (2010) Time-dependent analysis for refused admissions in clinical wards. Ann. Oper. Res. 178(1):45–65.Crossref, Google Scholar
• Bretthauer KM, Heese HS, Pun H, Coe E (2011) Blocking in healthcare operations: A new heuristic and an application. Production Oper. Management 20(3):375–391.Crossref, Google Scholar
• Caplan GA, Sulaiman NS, Mangin DA, Ricauda NA, Wilson AD, Barclay L (2012) A meta-analysis of “hospital in the home.” Medical J. Australia 197(9):512–519.Crossref, Google Scholar
• Cheah JY, Smith JM (1994) Generalized M/G/C/C state dependent queueing models and pedestrian traffic flows. Queueing Systems 15(1–4):365–386.Crossref, Google Scholar
• Cochran JK, Bharti A (2006) Stochastic bed balancing of an obstetrics hospital. Health Care Management Sci. 9(1):31–45.Crossref, Google Scholar
• Cohen I, Mandelbaum A, Zychlinski N (2014) Minimizing mortality in a mass casualty event: Fluid networks in support of modeling and staffing. IIE Trans. 46(7):728–741.Crossref, Google Scholar
• De Vries T, Beekman RE (1998) Applying simple dynamic modelling for decision support in planning regional health care. Eur. J. Oper. Res. 105(2):277–284.Crossref, Google Scholar
• Desai MS, Penn ML, Brailsford S, Chipulu M (2008) Modelling of hampshire adult services—gearing up for future demands. Health Care Management Sci. 11(2):167–176.Crossref, Google Scholar
• Donoghue WF (1969) Distributions and Fourier Transforms (Elsevier, Amsterdam).Google Scholar
• El-Darzi E, Vasilakis C, Chaussalet T, Millard PH (1998) A simulation modelling approach to evaluating length of stay, occupancy, emptiness and bed blocking in a hospital geriatric department. Health Care Management Sci. 1(2):143–149.Crossref, Google Scholar
• Faddy M, Graves N, Pettitt A (2009) Modeling length of stay in hospital and other right skewed data: Comparison of phase-type, gamma and log-normal distributions. Value Health 12(2):309–314.Crossref, Google Scholar
• Faddy MJ, McClean SI (2005) Markov chain modelling for geriatric patient care. Methods Inform. Medicine 44(3):369–373.Crossref, Google Scholar
• Garnett O, Mandelbaum A, Reiman M (2002) Designing a call center with impatient customers. Manufacturing Service Oper. Management 4(3):208–227.Link, Google Scholar
• Gershwin SB (1987) An efficient decomposition method for the approximate evaluation of tandem queues with finite storage space and blocking. Oper. Res. 35(2):291–305.Link, Google Scholar
• Gray LC, Broe GA, Duckett SJ, Gibson DM, Travers C, McDonnell G (2006) Developing a policy simulator at the acute-aged care interface. Australian Health Rev. 30(4):450–457.Crossref, Google Scholar
• Green LV (2004) Capacity planning and management in hospitals. Operations Research and Health Care (Springer, New York), 15–41.Google Scholar
• Green LV, Kolesar PJ, Whitt W (2007) Coping with time-varying demand when setting staffing requirements for a service system. Production Oper. Management 16(1):13–39.Crossref, Google Scholar
• Hardy GH, Littlewood JE, Pólya G (1952) Inequalities (Cambridge University Press, Cambridge, UK).Google Scholar
• Hare WL, Alimadad A, Dodd H, Ferguson R, Rutherford A (2009) A deterministic model of home and community care client counts in British Columbia. Health Care Management Sci. 12(1):80–98.Crossref, Google Scholar
• Harrison GW, Millard PH (1991) Balancing acute and long-term care: The mathematics of throughput in departments of geriatric medicine. Methods Inform. Medicine 30(3):221–228.Crossref, Google Scholar
• Harrison JM, Zeevi A (2005) A method for staffing large call centers based on stochastic fluid models. Manufacturing Service Oper. Management 7(1):20–36.Link, Google Scholar
• Hillier FS, Boling RW (1967) Finite queues in series with exponential or erlang service times—a numerical approach. Oper. Res. 15(2):286–303.Link, Google Scholar
• Jennings OB, Massey WA, McCalla C (1997) Optimal profit for leased lines services. Proc. 15th Internat. Teletraffic Congress, Washington, DC, vol. 15, 803–814.Google Scholar
• Kao EPC, Tung GG (1981) Bed allocation in a public health care delivery system. Management Sci. 27(5):507–520.Link, Google Scholar
• Katsaliaki K, Brailsford S, Browning D, Knight P (2005) Mapping care pathways for the elderly. J. Health Organ. Management 19(1):57–72.Crossref, Google Scholar
• Kerbache L, MacGregor Smith J (1987) The generalized expansion method for open finite queueing networks. Eur. J. Oper. Res. 32(3):448–461.Crossref, Google Scholar
• Kerbache L, MacGregor Smith J (1988) Asymptotic behavior of the expansion method for open finite queueing networks. Comput. Oper. Res. 15(2):157–169.Crossref, Google Scholar
• Koizumi N, Kuno E, Smith TE (2005) Modeling patient flows using a queuing network with blocking. Health Care Management Sci. 8(1):49–60.Crossref, Google Scholar
• Li A, Whitt W, Zhao J (2015) Staffing to stabilize blocking in loss models with time-varying arrival rates. Probab. Engrg. Inform. Sci. 30(2):185–211.Crossref, Google Scholar
• Liu Y, Whitt W (2011a) Large-time asymptotics for theGt/Mt/st+GItmany-server fluid queue with abandonment. Queueing Systems 67(2):145–182.Crossref, Google Scholar
• Liu Y, Whitt W (2011b) A network of time-varying many-server fluid queues with customer abandonment. Oper. Res. 59(4):835–846.Link, Google Scholar
• Liu Y, Whitt W (2012) TheGt/GI/st+GImany-server fluid queue. Queueing Systems 71(4):405–444.Crossref, Google Scholar
• Liu Y, Whitt W (2014) Many-server heavy-traffic limit for queues with time-varying parameters. Ann. Appl. Probab. 24(1):378–421.Crossref, Google Scholar
• Mandelbaum A, Massey WA, Reiman MI (1998) Strong approximations for Markovian service networks. Queueing Systems 30(1–2):149–201.Crossref, Google Scholar
• Mandelbaum A, Massey WA, Reiman MI, Rider B (1999) Time varying multiserver queues with abandonment and retrials. Proc. 16th Internat. Teletraffic Conf., Edinburgh, Scotland, vol. 4, 4–7.Google Scholar
• Marazzi A, Paccaud F, Ruffieux C, Beguin C (1998) Fitting the distributions of length of stay by parametric models. Medical Care 36(6):915–927.Crossref, Google Scholar
• McCalla C, Whitt W (2002) A time-dependent queueing-network model to describe the life-cycle dynamics of private-line telecommunication services. Telecomm. Systems 19(1):9–38.Crossref, Google Scholar
• McClean S, Millard P (1993) Patterns of length of stay after admission in geriatric medicine: An event history approach. Statistician 42(3):263–274.Crossref, Google Scholar
• McClean S, Millard P (2006) Where to treat the older patient? Can Markov models help us better understand the relationship between hospital and community care? J. Oper. Res. Soc. 58(2):255–261.Crossref, Google Scholar
• Nahmias S, Cheng Y (2009) Production and Operations Analysis (McGraw-Hill, New York).Google Scholar
• Namdaran F, Burnet C, Munroe S (1992) Bed blocking in Edinburgh hospitals. Health Bull. 50(3):223–227.Google Scholar
• NHS England (2015) Bed availability and occupancy data. Accessed August 20, 2015, https://www.england.nhs.uk/statistics/statistical-work-areas/bed-availability-and-occupancy/bed-data-overnight/.Google Scholar
• OECD iLibrary (2013) Health at a glance. Accessed November 21, 2013, http://dx.doi.org/10.1787/health_glance-2013-en.Google Scholar
• Olivares M, Terwiesch C, Cassorla L (2008) Structural estimation of the newsvendor model: An application to reserving operating room time. Management Sci. 54(1):41–55.Link, Google Scholar
• Osorio C, Bierlaire M (2009) An analytic finite capacity queueing network model capturing the propagation of congestion and blocking. Eur. J. Oper. Res. 196(3):996–1007.Crossref, Google Scholar
• Perros HG (1994) Queueing Networks with Blocking (Oxford University Press, Oxford, UK).Google Scholar
• Porteus EL (2002) Foundations of Stochastic Inventory Theory (Stanford University Press, Stanford, CA).Crossref, Google Scholar
• Rohleder TR, Cooke D, Rogers P, Egginton J (2013) Coordinating health services: An operations management perspective. Handbook of Healthcare Operations Management (Springer, Bring), 421–445.Crossref, Google Scholar
• Rubin SG, Davies GH (1975) Bed blocking by elderly patients in general-hospital wards. Age Ageing 4(3):142–147.Crossref, Google Scholar
• Shepperd S, Doll H, Angus RM, Clarke MJ, Iliffe S, Kalra L, Ricauda NA, Wilson AD (2008) Admission avoidance hospital at home. Cochrane Database Syst Rev. 4:CD007491.Crossref, Google Scholar
• Shi P, Chou MC, Dai JG, Ding D, Sim J (2015) Models and insights for hospital inpatient operations: Time-dependent ED boarding time. Management Sci. 62(1):1–28.Google Scholar
• Takahashi Y, Miyahara H, Hasegawa T (1980) An approximation method for open restricted queueing networks. Oper. Res. 28(3 Part I):594–602.Link, Google Scholar
• Taylor G, McClean S, Millard P (1997) Continuous-time Markov models for geriatric patient behaviour. Appl. Stochastic Models Data Anal. 13(3–4):315–323.Crossref, Google Scholar
• Taylor GJ, McClean SI, Millard PH (2000) Stochastic models of geriatric patient bed occupancy behaviour. J. Royal Statist. Soc. Ser. A 163(1):39–48.Crossref, Google Scholar
• Ticona L, Schulman KA (2016) Extreme home makeover—the role of intensive home health care. New England J. Medicine 375(18):1707–1709.Crossref, Google Scholar
• Travers CM, McDonnell GD, Broe GA, Anderson P, Karmel R, Duckett SJ, Gray LC (2008) The acute-aged care interface: Exploring the dynamics of bed blocking. Australasian J. Ageing 27(3):116–120.Crossref, Google Scholar
• United Nations Population Fund (2014) News of ageing 2014. Accessed October 13, 2015, http://www.unfpa.org/ageing.Google Scholar
• Whitt W (2002) Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues (Springer, New York).Crossref, Google Scholar
• Whitt W (2007) What you should know about queueing models to set staffing requirements in service systems. Naval Res. Logist. 54(5):476–484.Crossref, Google Scholar
• Whitt W (2013) OM forum—offered load analysis for staffing. Manufacturing Service Oper. Management 15(2):166–169.Link, Google Scholar
• Wolstenholme E (1999) A patient flow perspective of UK health services: Exploring the case for new intermediate care initiatives. System Dynam. Rev. 15(3):253–271.Crossref, Google Scholar
• World Health Organization (2014) Innovation for ageing populations – Addressing the challenges of frailty and disability. Accessed June 24, 2014, http://www.who.int/kobe_centre/ageing/en/.Google Scholar
• Xie H, Chaussalet TJ, Millard PH (2005) A continuous time Markov model for the length of stay of elderly people in institutional long-term care. J. Royal Statist. Soc. Ser. A 168(1):51–61.Crossref, Google Scholar
• Yom-Tov GB, Mandelbaum A (2014) Erlang-r: A time-varying queue with reentrant customers, in support of healthcare staffing. Manufacturing Service Oper. Management 16(2):283–299.Link, Google Scholar
• Zhang Y, Puterman ML, Nelson M, Atkins D (2012) A simulation optimization approach to long-term care capacity planning. Oper. Res. 60(2):249–261.Link, Google Scholar
• Zohar E, Mandelbaum A, Shimkin N (2002) Adaptive behavior of impatient customers in tele-queues: Theory and empirical support. Management Sci. 48(4):566–583.Link, Google Scholar