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

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## 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.

## Keywords

Resource management Admission scheduling Non-homogeneous Markov model Stochastic optimal control## Notes

### Acknowledgements

The authors acknowledge support for this work from the Engineering and Physical Sciences Research Council funded RIGHT and MATCH projects (Grant References EP/E019900/1 and GR/S29874/01). Any views or opinions presented herein are those of the authors and do not necessarily represent those of RIGHT or MATCH, their associates or their sponsors.

## References

- 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):863–878CrossRefGoogle Scholar
- 2.Milsum JH, Turban E, Vertinsky I (1973) Hospital admission systems: their evaluation and management. Manage Sci 19(6):646–666CrossRefGoogle Scholar
- 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 491–496Google Scholar
- 4.Buhaug H (2002) Long waiting lists in hospitals. BMJ 324(7332):252–253CrossRefGoogle Scholar
- 5.Worthington DJ (1987) Queueing models for hospital waiting lists. J Oper Res Soc 38(5):413–422Google Scholar
- 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):1–11Google Scholar
- 7.Murray M, Berwick DM (2003) Advanced access: reducing waiting and delays in primary care. J Am Med Assoc 289(8):1035–1040CrossRefGoogle Scholar
- 8.Groot PMA (1993) Decision support for admission planning under multiple resource constraints. Dissertation, Eindhoven University of TechnologyGoogle Scholar
- 9.Worthington DJ (1991) Hospital waiting list management models. J Oper Res Soc 42(10):833–843Google Scholar
- 10.Gorunescu F, McClean SI, Millard PH (2002) A queuing model for bed-occupancy management and planning of hospitals. J Oper Res Soc 53:19–24CrossRefGoogle Scholar
- 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 CrossRefGoogle Scholar
- 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 MarylandGoogle Scholar
- 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):163–171CrossRefGoogle Scholar
- 15.Vassilacopoulos G (1985) A simulation model for bed allocation to hospital inpatient departments. Simulation 45(5):233–241CrossRefGoogle Scholar
- 16.Lehaney B, Hlupic V (1995) Simulation modelling for resource allocation and planning in the health sector. J R Soc Health 115(6):382–385CrossRefGoogle Scholar
- 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):325–335CrossRefGoogle Scholar
- 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 211–252Google Scholar
- 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):1290–1301CrossRefGoogle Scholar
- 20.Williams SV (1983) How many intensive care beds are enough? Crit Care Med 11:412–416CrossRefGoogle Scholar
- 21.Jung AL, Streeter NS (1985) Total population estimate of newborn special-care bed needs. Pediatrics 75:993–996Google Scholar
- 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 12:340–345CrossRefGoogle Scholar
- 23.Parmanum J, Field D, Rennie J, Steer P (2000) National census of availability of neonatal intensive care. BMJ 321:727–729CrossRefGoogle Scholar
- 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 8:701–706CrossRefGoogle Scholar
- 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):39–49CrossRefGoogle Scholar
- 26.Mackay M, Lee M (2005) Choice of models for the analysis and forecasting of hospital beds. Health Care Manage Sci 8:221–230CrossRefGoogle Scholar
- 27.Ivatts S, Millard P (2002) Health care modelling-why should we try? Br J Health Care Manag 8(6):218–222Google Scholar
- 28.Plochg T, Klazinga NS (2002) Community-based integrated care: myth or must? Int J Qual Health Care 14(2):91–101Google Scholar
- 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 512–517Google Scholar
- 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):118–142CrossRefGoogle Scholar
- 31.McClean SI, Millard PH (1993) Patterns of length of stay after admission in geriatric medicine: an event history approach. Statistician 42(3):263–274CrossRefGoogle Scholar
- 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):213–220CrossRefGoogle Scholar
- 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):311–317CrossRefGoogle Scholar
- 34.Garg L, McClean SI, Meenan BJ, Millard PH (2008) Non-homogeneous Markov models for sequential pattern mining of healthcare data. IMA J Manag. Math. doi: 10.1093/imaman/dpn030 Google Scholar
- 35.Faddy MJ, McClean SI (2005) Markov chain modelling for geriatric patient care. Methods Inf. Med 44(3):369–373Google Scholar
- 36.Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7:308–313Google Scholar
- 37.MATLAB, The Language of Technical Computing, Version 7.7.0.471 (R2008b), September 17, 2008, The MathWorks, Inc., Natick, MassachussettsGoogle Scholar
- 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):255–261Google Scholar
- 39.Hauskrecht M, Fraser H (2000) Planning Treatment of ischemic heart disease with partially observable Markov decision processes. Artif Intell Med 18:221–244CrossRefGoogle Scholar
- 40.Stothers L (2007) Cost-Effectiveness Analyses. In: Penson DF, Wei JT (eds) Clinical research methods for surgeons. Humana, Totowa, pp 283–296CrossRefGoogle Scholar
- 41.Weinstein MC, Stason WB (1977) Foundations of cost-effectiveness analysis for health and medical practices. N Engl J Med 296:716–721CrossRefGoogle Scholar
- 42.Kocher MS, Henley MB (2003) It is money that matters: decision analysis and cost effectiveness analysis. Clin Orthop Relat Res 413:106–116CrossRefGoogle Scholar
- 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):191–202CrossRefGoogle Scholar
- 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 CrossRefGoogle Scholar
- 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):183–191Google Scholar
- 46.Sen A (1993) Capability and well-being. In: Nussbaum M, Sen A (eds) The quality of life. Clarendon, Oxford, pp 30–54CrossRefGoogle Scholar
- 47.Cookson R (2005) QALYs and the capability approach. Health Econ 14:817–829CrossRefGoogle Scholar