A non-homogeneous discrete time Markov model for admission scheduling and resource planning in a cost or capacity constrained healthcare system

L Garg, S McClean, BJ Meenan, P Millard

Research output: Contribution to journalArticlepeer-review

Abstract

Healthcare resource planners need to develop policies that ensure optimal allocation of scarce healthcare resources. This goal can be achieved by forecasting daily resource requirements for a given admission policy. If resources are limited, admission should be scheduled according to the resource availability. Such resource availability or demand can change with time. We here model patient flow through the care system as a discrete time Markov chain. In order to have a more realistic representation, a non-homogeneous model is developed which incorporates time-dependent covariates, namely a patient’s present age and the present calendar year. The model presented in this paper can be used for admission scheduling, resource requirement forecasting and resource allocation, so as to satisfy the demand or resource constraints or to meet the expansion or contraction plans in a hospital and community based integrated care system. Such a model can be used with both fixed and variable numbers of admissions per day and should prove to be a useful tool for care managers and policy makers who require to make strategic management decisions. We also describe an application of the model to an elderly care system, using a historical dataset from the geriatric department of a London hospital.
Original languageEnglish
Pages (from-to)155-169
JournalHealth Care Management Science
Volume13
Issue number2
DOIs
Publication statusPublished - 2010

Bibliographical note

Reference text: 1. Gemmel P, van Dierdonck R (1999) Admission scheduling in
acute care hospitals: does the practice fit with the theory? Int J
Oper Prod Manage 19(9):863–878
2. Milsum JH, Turban E, Vertinsky I (1973) Hospital admission
systems: their evaluation and management. Manage Sci 19
(6):646–666
3. Shaw B, Marshall AH (2005) A Bayesian approach to modelling
inpatient expenditure. Proceedings of the 18th IEEE Symposium
on Computer-Based Medical Systems, pp 491–496
4. Buhaug H (2002) Long waiting lists in hospitals. BMJ 324
(7332):252–253
5. Worthington DJ (1987) Queueing models for hospital waiting
lists. J Oper Res Soc 38(5):413–422
6. Gupta D, Natarajan MK, Gafni A, Wang L, Shilton D, Holder D,
Yusuf S (2007) Capacity planning for cardiac catheterization: a
case study. Health Policy (Amsterdam) 82(1):1–11
7. Murray M, Berwick DM (2003) Advanced access: reducing waiting
and delays in primary care. J Am Med Assoc 289(8):1035–1040
8. Groot PMA (1993) Decision support for admission planning
under multiple resource constraints. Dissertation, Eindhoven
University of Technology
9. Worthington DJ (1991) Hospital waiting list management models.
J Oper Res Soc 42(10):833–843
10. Gorunescu F, McClean SI, Millard PH (2002) A queuing model for
bed-occupancy management and planning of hospitals. J Oper Res
Soc 53:19–24
11. Cochran J, Roche K (2007) A queuing-based decision support
methodology to estimate hospital inpatient bed demand. J Oper
Res Soc 59:1471–1482. doi:10.1057/palgrave.jors.2602499
12. Fomundam S, Herrmann JW (2007) A survey of queuing theory
applications in healthcare. ISR technical report, Technical Report
2007-24, College Park (MD): Institute for Systems Research,
University of Maryland
13. Fiems D, Koole G, Nain P (2005) Waiting times of scheduled
patients in the presence of emergency requests. Available online.
http://www.math.vu.nl/~koole/articles/report05a/art.pdf. title of
subordinate document. Accessed 12 Aug 2008
14. Kuzdrall PJ, Kwak NK, Schmitz HH (1981) Simulating space
requirements and scheduling policies in a hospital surgical suite.
Simulation 36(5):163–171
15. Vassilacopoulos G (1985) A simulation model for bed allocation
to hospital inpatient departments. Simulation 45(5):233–241
16. Lehaney B, Hlupic V (1995) Simulation modelling for resource
allocation and planning in the health sector. J R Soc Health 115
(6):382–385
17. Fone D, Hollinghurst S, Temple M, Round A, Lester N, Weightman
A, Roberts K, Coyle E, Bevan G, Palmer S (2003) Systematic
review of the use and value of computer simulation modelling in
population health and health care delivery. J Public Health Med 25
(4):325–335
18. Jacobson SH, Hall SN, Swisher James R (2006) Discrete-event
simulation of health care systems. In: Patient flow: reducing delay
in healthcare delivery. Springer, US, pp 211–252
19. Vissers JMH, Adan IJBF, Dellaert NP (2007) Developing a
platform for comparison of hospital admission systems: An
illustration. Eur J Oper Res 180(3):1290–1301
20. Williams SV (1983) How many intensive care beds are enough?
Crit Care Med 11:412–416
21. Jung AL, Streeter NS (1985) Total population estimate of
newborn special-care bed needs. Pediatrics 75:993–996
22. Plati C, Lemonidou C, Priami M, Baltopoulos G, Mantas J (1996)
The intensive care units in greater Athens: needs and resources.
Intensive Crit Care Nurs 12:340–345
23. Parmanum J, Field D, Rennie J, Steer P (2000) National census of
availability of neonatal intensive care. BMJ 321:727–729
24. Lampl C, Klingler D, Deisenhammer E, Hagenbichler E, Neuner
L, Pesec B (2001) Hospitalization of patients with neurological
disorders and estimation of the need of beds and of the related
costs in Austria's non-profit hospitals. Eur J Neurol 8:701–706
25. Nguyena JM, Sixc P, Antoniolib D, Glemaind P, Potele G,
Lombrailb P, Le Beuxf P (2005) A simple method to optimize
hospital beds capacity. Int J Med Inform 74(1):39–49
26. Mackay M, Lee M (2005) Choice of models for the analysis and
forecasting of hospital beds. Health Care Manage Sci 8:221–230
27. Ivatts S, Millard P (2002) Health care modelling-why should we
try? Br J Health Care Manag 8(6):218–222
28. Plochg T, Klazinga NS (2002) Community-based integrated care:
myth or must? Int J Qual Health Care 14(2):91–101
29. Garg L, McClean SI, Meenan B, Millard PH (2008) Optimal
control of patient admissions to satisfy resource restrictions.
Proceedings of the 21st IEEE Symposium on Computer-Based
Medical Systems, pp 512–517
30. Shonick W (1972) Understanding the nature of the random
fluctuations of the hospital daily census: an important health
planning tool. Med Care 10(2):118–142
31. McClean SI, Millard PH (1993) Patterns of length of stay after
admission in geriatric medicine: an event history approach.
Statistician 42(3):263–274
32. Marshall A, Vasilakis C, El-Darzi E (2005) Length of stay-based
patient flow models: recent developments and future directions.
Health Care Manage Sci 8(3):213–220
33. Faddy MJ, McClean SI (1999) Analysing data on lengths of stay
of hospital patients using phase-type distributions. Appl Stoch
Models Bus Ind 15(4):311–317
34. Garg L, McClean SI, Meenan BJ, Millard PH (2008) Nonhomogeneous
Markov models for sequential pattern mining of
healthcare data. IMA J Manag. Math. doi:10.1093/imaman/dpn030
35. Faddy MJ, McClean SI (2005) Markov chain modelling for
geriatric patient care. Methods Inf. Med 44(3):369–373
36. Nelder JA, Mead R (1965) A simplex method for function
minimization. Comput J 7:308–313
37. MATLAB, The Language of Technical Computing, Version
7.7.0.471 (R2008b), September 17, 2008, The MathWorks, Inc.,
Natick, Massachussetts
38. McClean SI, Millard PH (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
39. Hauskrecht M, Fraser H (2000) Planning Treatment of ischemic
heart disease with partially observable Markov decision processes.
Artif Intell Med 18:221–244
40. Stothers L (2007) Cost-Effectiveness Analyses. In: Penson DF,
Wei JT (eds) Clinical research methods for surgeons. Humana,
Totowa, pp 283–296
41. Weinstein MC, Stason WB (1977) Foundations of costeffectiveness
analysis for health and medical practices. N Engl J
Med 296:716–721
42. Kocher MS, Henley MB (2003) It is money that matters: decision
analysis and cost effectiveness analysis. Clin Orthop Relat Res
413:106–116
43. Romangnuolo J, Meier MA (2002) Medical or surgical therapy for
erosive reflux esophagitis: cost-utility analysis using a Markov
model. Ann Surg 236(2):191–202
44. Rowland DR, Pollock AM (2004) Choice and responsiveness for
older people in the "patient centred" NHS. BMJ 328:4–5.
doi:10.1136/bmj.328.7430.4
45. Robberstad B (2005) QALYs vs DALYs vs LYs gained: what are
the differences, and what difference do they make for health care
priority setting? Nor Epidemiol 15(2):183–191
46. Sen A (1993) Capability and well-being. In: Nussbaum M, Sen A
(eds) The quality of life. Clarendon, Oxford, pp 30–54
47. Cookson R (2005) QALYs and the capability approach. Health
Econ 14:817–829

Keywords

  • Resource management . Admission scheduling .
  • Non-homogeneous Markov model . Stochasticoptimalcontrol

Fingerprint

Dive into the research topics of 'A non-homogeneous discrete time Markov model for admission scheduling and resource planning in a cost or capacity constrained healthcare system'. Together they form a unique fingerprint.

Cite this