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 journalArticle

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.
LanguageEnglish
Pages155-169
JournalHealth Care Management Science
Volume13
Issue number2
DOIs
Publication statusPublished - 2010

Fingerprint

Delivery of Health Care
Costs and Cost Analysis
Markov Chains
Resource Allocation
Administrative Personnel
Geriatrics
Datasets

Keywords

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

Cite this

@article{56ec0c77f9c14062aecf191c0696b200,
title = "A non-homogeneous discrete time Markov model for admission scheduling and resource planning in a cost or capacity constrained healthcare system",
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 . Stochasticoptimalcontrol",
author = "L Garg and S McClean and BJ Meenan and P Millard",
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",
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language = "English",
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journal = "Health Care Management Science",
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T1 - A non-homogeneous discrete time Markov model for admission scheduling and resource planning in a cost or capacity constrained healthcare system

AU - Garg, L

AU - McClean, S

AU - Meenan, BJ

AU - Millard, P

N1 - 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

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Resource management . Admission scheduling .

KW - Non-homogeneous Markov model . Stochasticoptimalcontrol

U2 - 10.1007/s10729-009-9120-0

DO - 10.1007/s10729-009-9120-0

M3 - Article

VL - 13

SP - 155

EP - 169

JO - Health Care Management Science

T2 - Health Care Management Science

JF - Health Care Management Science

SN - 1386-9620

IS - 2

ER -