Advertisement

Journal of Medical Systems

, 40:32 | Cite as

Assessing the Queuing Process Using Data Envelopment Analysis: an Application in Health Centres

  • Komal A. Safdar
  • Ali Emrouznejad
  • Prasanta K. Dey
Systems-Level Quality Improvement
Part of the following topical collections:
  1. Systems-Level Quality Improvement

Abstract

Queuing is one of the very important criteria for assessing the performance and efficiency of any service industry, including healthcare. Data Envelopment Analysis (DEA) is one of the most widely-used techniques for performance measurement in healthcare. However, no queue management application has been reported in the health-related DEA literature. Most of the studies regarding patient flow systems had the objective of improving an already existing Appointment System. The current study presents a novel application of DEA for assessing the queuing process at an Outpatients’ department of a large public hospital in a developing country where appointment systems do not exist. The main aim of the current study is to demonstrate the usefulness of DEA modelling in the evaluation of a queue system. The patient flow pathway considered for this study consists of two stages; consultation with a doctor and pharmacy. The DEA results indicated that waiting times and other related queuing variables included need considerable minimisation at both stages.

Keywords

Data envelopment analysis Healthcare Queuing Patient flow Appointment scheduling system 

Notes

Acknowledgments

The authors would like to thank the editor of Journal of Medical Systems, Professor Jesse M Ehrenfeld, and three reviewers for their insightful comments and suggestions.

References

  1. 1.
    Adeleke, R. A., Ogunwale, O. D., and Halid, O. Y., Application of queuing theory to waiting time of out-patients in hospitals. Pac. J. Sci. Technol. 10(2):270–274, 2009.Google Scholar
  2. 2.
    Ramanathan, R., Operations assessment of hospitals in the Sultanate of Oman. Int. J. Prod. Oper. Manag. 25(1):39–54, 2005.CrossRefGoogle Scholar
  3. 3.
    Matta, M. E., and Patterson, S. S., Evaluating multiple performance measures across several dimensions at a multi-facility outpatient center. Healthc. Manag. Sci. 10(2):173–194, 2007.CrossRefGoogle Scholar
  4. 4.
    Mehandiritta, R., Applications of queuing theory in healthcare. Int. J. Comput. Bus. Res. 2(2):2229–6166, 2011.Google Scholar
  5. 5.
    Chuang, C. L., Chang, P. C., and Lin, R. H., An Efficiency data envelopment analysis model reinforced by classification and regression tree for hospital performance evaluation. J. Med. Syst. 35(5):1075–1083, 2011.PubMedCrossRefGoogle Scholar
  6. 6.
    Biju, M.K. and Naeema, K., Application of queuing theory in human resource management in healthcare, In: ICOQM-10, pp. 1019–1027, 2001.Google Scholar
  7. 7.
    Jun, J. B., Jacobson, S. H., and Swisher, J. R., Application of discrete-event simulation in healthcare clinics: A survey. J. Oper. Res. Soc. 50(2):109–123, 1999.CrossRefGoogle Scholar
  8. 8.
    Silva, F., and Serra, D., Locating emergency services with different priorities: The priority queuing covering location problem. J. Oper. Res. Soc. 59(9):1229–1238, 2008.CrossRefGoogle Scholar
  9. 9.
    Yeboah, E.K. and Thomas, M.E., A cost-effective way of reducing outpatient clinic waiting times: How we did it. Int. J. Healthc. Admin. 7(1), 2010.Google Scholar
  10. 10.
    Babes, M., and Sarma, G. V., Outpatient queues at the Ibn-Rochd health centre. J. Oper. Res. Soc. 42(10):845–855, 1991.CrossRefGoogle Scholar
  11. 11.
    Manzi, A, Magge H, Hedt-Gauthier, B.L., Michaelis, A.P., Cyamatare, F.R., Nyirazinyoye, L, Hirschhorn, L.R. and Ntaganira, J., Clinical mentorship to improve pediatric quality of care at the health centers of rural rwanda: A qualitative study of perceptions and acceptability of health workers. BMC Health Serv. Res. 14(275), 2014. Available at: http://www.biomedcentral.com/1472-6963/14/275 [Accessed: 27 Sept 2015].
  12. 12.
    Mensah, J., Asamoah, J., and Tawiah, A. A., Optimizing patient flow and resource utilization in outpatient clinic: A comparative study of Nkawie government hospital and Aniwaa health center. J. Appl. Bus. Econ. 16(3):181–188, 2015.Google Scholar
  13. 13.
    Bhattacharjee, P., and Ray, P. K., Patient flow modelling and performance analysis of healthcare delivery processes in hospitals: A review and reflections. Comput. Ind. Eng. 78:299–312, 2014.CrossRefGoogle Scholar
  14. 14.
    Proudlove, N. C., Black, S., and Fletcher, A., OR and the challenge to improve the NHS: Modeling for insight and improvement in in-patient flows. J. Oper. Res. Soc. 58(2):145–158, 2007.Google Scholar
  15. 15.
    Cayirli, T., and Veral, E., Outpatient scheduling in healthcare: A review of literature. J. Med. Syst. 35(5):1075–1083, 2003.Google Scholar
  16. 16.
    Gul, M., and Guneri, A. F., A comprehensive review of emergency department simulation applications for normal and disaster conditions. Comput. Ind. Eng. 83:327–344, 2015.CrossRefGoogle Scholar
  17. 17.
    May, J. H., Spangler, W. E., and Strum, D. P., The surgical scheduling problem: Current research and future opportunities. Prod. Oper. Manag. 20(3):392–405, 2011.CrossRefGoogle Scholar
  18. 18.
    Ashton, R., Hague, L., Brandreth, M., Worthington, D., and Cropper, S., A simulation-based study of a NHS walk-in centre. J. Oper. Res. Soc. 56(2):153–161, 2005.CrossRefGoogle Scholar
  19. 19.
    Cayirli, T., and Gunes, E. D., Outpatient appointment scheduling in presence of seasonal walk-ins. J. Oper. Res. Soc. 65:512–531, 2014.Google Scholar
  20. 20.
    Fetter, R. B., and Thompson, J. D., Patients’ waiting time and doctors’ idle time in the outpatient setting. Health Serv. Res. 1(1):66–90, 1966.PubMedPubMedCentralGoogle Scholar
  21. 21.
    Rising, E., Baron, R., and Averill, B., A system analysis of a university health service outpatient clinic. Oper. Res. 21(5):1030–1047, 1973.CrossRefGoogle Scholar
  22. 22.
    Fomundam, S., and Hermann, J.W., A survey of queuing theory applications in healthcare, Digital Repository at the University of Maryland, 2007. Available at: http://hdl.handle.net/1903/7222. [Accessed: 19 July 2013].
  23. 23.
    Lakshmi, C., and Sivakumar, A. I., Application of queuing theory in healthcare: A literature review. Oper. Res. Healthc. 2(1–2):25–39, 2013.Google Scholar
  24. 24.
    Mayhew, L., and Smith, D., Using queuing theory to analyse the government’s 4-h completion time target in accident and emergency departments. Healthc. Manag. Sci. 11(1):11–21, 2008.CrossRefGoogle Scholar
  25. 25.
    Gunal, M., and Pidd, M., Discrete-event simulation for performance modeling in healthcare: A review of the literature. J. Simul. 4:42–51, 2010.CrossRefGoogle Scholar
  26. 26.
    Konrad, R., DeSotto, K., Grocela, A., McAuley, P., Wang, J., Lyons, J., and Bruin, M., Modelling the impact of changing patient flow processes in an emergency department: insights from a computer simulation study. Oper. Res. Healthc. 2(4):66–74, 2013.Google Scholar
  27. 27.
    Brailsford, S. C., Lattimer, V. A., Tarnaras, P., and Turnbull, J. C., Emergency and on-demand healthcare: Modeling a large complex system. J. Oper. Res. Soc. 55:34–42, 2004. Case-Oriented Paper.CrossRefGoogle Scholar
  28. 28.
    Gunal, M. M., A guide for building hospital simulation models. Health Syst. 1:17–25, 2012.CrossRefGoogle Scholar
  29. 29.
    Lane, D. C., Monefeldt, C., and Rosenhead, J. V., Looking in the wrong place for healthcare improvements: A system dynamics study of an accident and emergency department. J. Oper. Res. Soc. 51(5):518–531, 2000.CrossRefGoogle Scholar
  30. 30.
    Pelone, F., Kringos, D.S., Romaniello, A., Archibugi, M., Salsiri, C., and Ricciardi, W., Primary care efficiency measurement using data envelopment analysis: A systematic review. J. Med. Syst. 39(1): 156, 2015.Google Scholar
  31. 31.
    O’Neill, L., Rauner, M., Heidenberger, K., and Kraus, M., A cross-national comparison and taxonomy of DEA-based hospital efficiency studies. Socio Econ. Plan. Sci. 42(3):158–189, 2008.CrossRefGoogle Scholar
  32. 32.
    Liu, J. S., Lu, L. Y. Y., Lu, W., and Lin, B. J. Y., A survey of DEA applications. Omega 41(5):893–902, 2013.CrossRefGoogle Scholar
  33. 33.
    Liu, J. S., Lu, L. Y. Y., Lu, W., and Lin, B. J. Y., Data envelopment analysis 1978–2010: A citation-based literature survey. Omega 41(1):3–15, 2013.CrossRefGoogle Scholar
  34. 34.
    Akazili, J., Adjuik, M., Appiah, C. J., and Zere, E., Using data envelopment analysis to measure the extent of technical efficiency of public health centers in Ghana. Bio. Med. Central Ltd. 20(2):232–248, 2008.Google Scholar
  35. 35.
    Flokou, A., Kontodimopoulos, N., and Niakas, D., Employing post-DEA cross-evaluation and cluster analysis in a sample of Greek NHS hospitals. J. Med. Syst. 35(5):1001–1014, 2011.PubMedCrossRefGoogle Scholar
  36. 36.
    Kawaguchi, H., Tone, K., and Tsutsui, M., Estimation of the efficiency of Japanese hospitals using a dynamic and network data envelopment analysis model. Healthc. Manag. Sci. 17:101–112, 2014.CrossRefGoogle Scholar
  37. 37.
    Nunamaker, T. R., Measuring routine nursing service efficiency: A comparison of cost per day and data envelopment analysis models. Health Serv. Res. 18(2):183–208, 1983.PubMedPubMedCentralGoogle Scholar
  38. 38.
    Ouellette, P., and Vierstraete, V., Technological change and efficiency in the presence of quasi- fixed inputs: A DEA application to the hospital sector. Eur. J. Oper. Res. 154(3):755–763, 2004.CrossRefGoogle Scholar
  39. 39.
    Parkin, D., and Hollingsworth, B., Measuring production efficiency of acute hospitals in Scotland, 1991–94: Validity issues in data envelopment analysis. Appl. Econ. 29(11):1425–1433, 1997.CrossRefGoogle Scholar
  40. 40.
    Hollingsworth, B., The measurement of efficiency and productivity of healthcare delivery. Health Econ. 17(10):1107–1128, 2008.PubMedCrossRefGoogle Scholar
  41. 41.
    Sherman, H. D., Improving the Productivity of Service Businesses. Sloan. Manage. Rev. 25(3):11–23, 1984.PubMedGoogle Scholar
  42. 42.
    Hollingsworth, B., Revolution, evolution or status-quo? Guidelines for efficiency measurement in healthcare. J. Prod. Anal. 37(1):1–5, 2012.CrossRefGoogle Scholar
  43. 43.
    Worthington, A. C., Frontier efficiency measurement in healthcare: A review of empirical techniques and selected applications. Med. Care Res. Rev. 61(2):135–170, 2004.PubMedCrossRefGoogle Scholar
  44. 44.
    Chang, H., Cheng, M. A., and Das, S., Hospital ownership and operating efficiency: Evidence from Taiwan. Eur. J. Oper. Res. 159(2):513–527, 2004.CrossRefGoogle Scholar
  45. 45.
    Jehu-Appiah, C., Sekidde, S., Adjuik, M., Akazili, J., Almeida, S.D., Nyonator, F., Baltussen, R., Asbu, E.Z. and Kirigia, J.M., Ownership and technical efficiency of hospitals: Evidence from Ghana using data envelopment analysis. Cost Effect. Res. Allocation, 12:9, 2015. Available at: http://www.resource-allocation.com/content/12/1/9 [Accessed: 8 June 2015].
  46. 46.
    Ramirez-Valdivia, M. T., Maturana, S., and Salvo-Garrido, S., A multiple-stage approach for performance improvement of primary healthcare practice. J. Med. Syst. 35(5):1015–1028, 2011.PubMedCrossRefGoogle Scholar
  47. 47.
    Ersoy, K., Kavuncubasi, S., Ozcan, Y. A., and Harris, J. M., II, Technical efficiencies of Turkish hospitals: DEA approach. J. Med. Syst. 21(2):67–74, 1997.PubMedCrossRefGoogle Scholar
  48. 48.
    Hollingsworth, B., and Parkin, D., The efficiency of Scottish acute hospitals: An application of data envelopment analysis. IMA J. Math. Appl. Med. Biol. 12(3–4):161–173, 1995.PubMedCrossRefGoogle Scholar
  49. 49.
    Puig-Junoy, J., Partitioning input cost efficiency into its allocative and technical components: An Empirical DEA application to hospitals. Socio Econ. Plan. Sci. 34(3):199–218, 2000.CrossRefGoogle Scholar
  50. 50.
    Tsai, P. F., and Molinero, C. M., A variable returns to scale data envelopment analysis model for the joint determination of efficiencies with an example of the UK health service. Eur. J. Oper. Res. 141(1):21–38, 2002.CrossRefGoogle Scholar
  51. 51.
    Salinas-Jimenez, J., and Smith, P., Data envelopment analysis applied to quality in primary healthcare. Ann. Oper. Res. 67(1):141–161, 1996.CrossRefGoogle Scholar
  52. 52.
    Thanassoulis, E., Boussofiane, A., and Dyson, R. G., A comparison of DEA and ratio analysis as tools for performance measurement. Omega 24(3):229–244, 1996.CrossRefGoogle Scholar
  53. 53.
    Chilingerian, J. A., and Sherman, H. D., DEA and primary care physician report cards: Deriving preferred practice cones from managed care service concepts and operating strategies. Ann. Oper. Res. 73:35–66, 1997.CrossRefGoogle Scholar
  54. 54.
    Wagner, J. M., Shimshak, D. G., and Novak, M. A., Advances in physician profiling: The use of DEA. Socio Econ. Plan. Sci. 37(2):141–163, 2003.CrossRefGoogle Scholar
  55. 55.
    Osman, I. H., Berbary, L. N., Sidani, Y., Al-Ayoubi, B., and Emrouznejad, A., Data envelopment analysis model for the appraisal and relative performance evaluation of nurses at an intensive care unit. J. Med. Syst. 35(5):1039–1062, 2011.PubMedCrossRefGoogle Scholar
  56. 56.
    Lewis, H. F., Sexton, T. R., and Dolan, M. A., An efficiency-based multicriteria strategic planning model for ambulatory surgery centers. J. Med. Syst. 35(5):1029–1037, 2011.PubMedCrossRefGoogle Scholar
  57. 57.
    Rouse, P., Harrison, J., and Turner, N., Cost and performance: Complements for improvement. J. Med. Syst. 35(5):1063–1074, 2011.PubMedCrossRefGoogle Scholar
  58. 58.
    Charnes, A., Cooper, W. W., and Rhodes, E., Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2(6):429–444, 1978.CrossRefGoogle Scholar
  59. 59.
    Banker, R. D., Charnes, A., and Cooper, W. W., Some models for estimating technical and scale efficiencies in data envelopment analysis. Manag. Sci. 30(9):1078–1092, 1984.CrossRefGoogle Scholar
  60. 60.
    Farrell, M. J., The measurement of productive efficiency. J. R. Stat. Soc. Ser. A (Gen.) 120(3):253–290, 1957.CrossRefGoogle Scholar
  61. 61.
    Lee, H., and Kim, C., Benchmarking of service quality with data envelopment analysis. Exp. Syst. Appl. 41(8):3761–3768, 2014.CrossRefGoogle Scholar
  62. 62.
    Charnes, A., and Cooper, W. W., Programming with linear fractional functionals. Nav. Res. Logist. Q. 9(3–4):181–185, 1962.CrossRefGoogle Scholar
  63. 63.
    Emrouznejad, A., and Cabanda, E., Managing service productivity: uses of frontier efficiency methodologies and MCDM for improving service performance. In: the series of “International Series in Operations Research & Management Science”, Springer-Verlag, ISBN 978-3-662-43436-9, 2014.Google Scholar
  64. 64.
    Cooper, W. W., Seiford, L. M., and Zhu, J., Data envelopment analysis: models and interpretations, chapter 1:1–39. In: Cooper, W. W., Seiford, L. M., and Zhu, J. (Eds.), Handbook on data envelopment analysis. Kluwer Academic Publisher, Boston, pp. 3–4, 2004.Google Scholar
  65. 65.
    Cooper, W. W., Seiford, L. M., and Tone, K., Data envelopment analysis: a comprehensive text with models, applications, references and DEA-solver software, 2nd edition. Springer, New York, 2007.Google Scholar
  66. 66.
    Ridge, J. C., Jones, S. K., Nielsen, M. S., and Shahani, A. K., Capacity planning for intensive care units. Eur. J. Oper. Res. 105(2):346–355, 1998.CrossRefGoogle Scholar
  67. 67.
    Thanassoulis, E., Introduction to the theory and application of data envelopment analysis: a foundation text with integrated software. Kluwer Academic Publishers, USA, 2001.CrossRefGoogle Scholar
  68. 68.
    Harrison, J. P., Coppola, M. N., and Wakefield, M., Efficiency of federal hospitals in the United States. J. Med. Syst. 28(5):411–422, 2004.PubMedCrossRefGoogle Scholar
  69. 69.
    Bwana, K. M., Measuring technical efficiency of faith based hospitals in Tanzania: An application of data envelopment analysis (DEA). Res. Appl. Econ. 7(1):1–12, 2015.CrossRefGoogle Scholar
  70. 70.
    Masiye, F., Kirigia, J. M., Emrouznejad, A., Sambo, L. G., Mounkaila, A., Chimfwembe, D., and Okello, D., Efficient management of health centres human resources in Zambia. J. Med. Syst. 30(6):473–481, 2006.PubMedCrossRefGoogle Scholar
  71. 71.
    Zuckerman, S., Hadley, J., and Iezzoni, L., Measuring hospital efficiency with frontier cost functions. J. Health Econ. 13(3):255–280, 1994.PubMedCrossRefGoogle Scholar
  72. 72.
    Al-Shammari, M., A multi-criteria data envelopment analysis model for measuring the productive efficiency of hospitals. Int. J. Oper. Prod. Manag. 19(9):879–891, 1999.CrossRefGoogle Scholar
  73. 73.
    Kose, T., Uckun, N., and Girginer, N., An efficiency analysis of the clinical departments of a public hospital in Eskisehir by using DEA. Glob. J. Adv. Pure Appl. Sci. 4:252–258, 2014.Google Scholar
  74. 74.
    Magnussen, J., Efficiency measurement and the operationalization of hospital production. Health Serv. Res. 31(1):21–37, 1996.PubMedPubMedCentralGoogle Scholar
  75. 75.
    Weng, S. J., Wu, T., Blackhurst, J., and Mackulak, G., An extended DEA model for hospital performance evaluation and improvement. Health Serv Outcome Res. Methodol. 9(1):39–53, 2009.CrossRefGoogle Scholar
  76. 76.
    Banker, R. D., Conrad, R.F. and Strauss, R.P., A comparative application of data envelopment analysis and translog methods: An illustrative study of hospital production. 1986.Google Scholar
  77. 77.
    Butler, T. W., and Li, L., The utility of returns to scale in DEA programming: An analysis of Michigan rural hospitals. Eur. J. Oper. Res. 161(2):469–477, 2005.CrossRefGoogle Scholar
  78. 78.
    Zere, E., McIntyre, D., and Addison, T., Technical efficiency and productivity of public sector hospitals in three South African provinces. S. Afr. J. Econ. 69(2):336–358, 2001.CrossRefGoogle Scholar
  79. 79.
    Dotoli, M., Epicoco, N., Falagario, M., and Sciancalepore, F., A cross-efficiency fuzzy data envelopment analysis technique for performance evaluation of decision making units under uncertainty. Comput. Ind. Eng. 79:103–114, 2015.CrossRefGoogle Scholar
  80. 80.
    Grosskopf, S., and Valdmanis, V., Measuring hospital performance: A nonparametric approach. J. Health Econ. 6(1):89–107, 1987.PubMedCrossRefGoogle Scholar
  81. 81.
    Huang, Y. G., and McLaughlin, C. P., Relative efficiency in rural primary health care: An application of data envelopment analysis. Health Serv. Res. 24(2):143–158, 1989.PubMedPubMedCentralGoogle Scholar
  82. 82.
    Kirigia, J. M., Emrouznejad, A., Cassoma, B., Asbu, E. Z., and Barry, S., A performance assessment method for hospitals: The case of municipal hospitals in Angola. J. Med. Syst. 32(6):509–519, 2008.PubMedCrossRefGoogle Scholar
  83. 83.
    Prior, D., Efficiency and total quality management in healthcare organizations: A dynamic frontier approach. Ann. Oper. Res. 145(1):281–299, 2006.CrossRefGoogle Scholar
  84. 84.
    Gerdtham, U. G., Löthgren, M., Tambour, M., and Rehnberg, M., Internal markets and health care efficiency: A multiple-output stochastic frontier analysis. Health Econ. 8(2):151–164, 1999.PubMedCrossRefGoogle Scholar
  85. 85.
    Parkin, D., and Hollingsworth, B., Measuring productivity efficiency of acute hospitals in Scotland, 1991-94: Validity issues in data envelopment analysis, Applied Economics, 29(11): 1425-1433, 1997.Google Scholar
  86. 86.
    Byrnes, P., and Valdmanis, V., Analyzing technical and allocative efficiency of hospitals. In: Charnes, A., Cooper, W. W., Lewin, A. Y., and Seiford, L. M. (Eds.), Data envelopment analysis: theory, methodology and applications. Kluwer, Boston, 1993.Google Scholar
  87. 87.
    Kang, H., Nembhard, H.B. and DeFlitch, C., identifying emergency department efficiency frontiers and the factors associated with their efficiency performance. In: Guan, Y., and Liao, H., (Eds), Proceedings of the 2014 Industrial and Systems Engineering Research Conference, 2014.Google Scholar
  88. 88.
    Linna, M., Measuring hospital cost efficiency with panel data models. Health Econ. 7(5):415–427, 1998.PubMedCrossRefGoogle Scholar
  89. 89.
    Kirigia, J. M., Emrouznejad, A., Sambo, L. G., Munguti, N., and Liambila, W., Using data envelopment analysis to measure the technical efficiency of public health centers in Kenya. J. Med. Syst. 28(2):155–166, 2004.PubMedCrossRefGoogle Scholar
  90. 90.
    Valdmanis, V., Sensitivity analysis for DEA models: An empirical example using public Vs NFP hospitals. J. Public Econ. 48(2):185–205, 1992.CrossRefGoogle Scholar
  91. 91.
    Blank, J. L. T., and Van Hurst, B. L., Governance and performance: The performance of dutch hospitals explained by governance characteristics. J. Med. Syst. 35(5):991–999, 2011.PubMedPubMedCentralCrossRefGoogle Scholar
  92. 92.
    Sorup, C.M., Estay, D.S., Jacobsen, P. and Anderson, P.D., Balancing patient flow and returning patients: A system dynamics study on emergency department crowding factors. Healthc. Manag. Sci. 2015. Available at: http://orbit.dtu.dk/ws/files/108550877/Balancing_patient.pdf [Accessed: 8 June 2015].
  93. 93.
    Harper, P. R., and Gamlin, H. M., Reduced outpatient waiting times with improved appointment scheduling: A simulation modeling approach. OR Spectr. 2(2):207–222, 2003.CrossRefGoogle Scholar
  94. 94.
    O’Keefe, R. M., Investigating outpatient departments: Implementable policies and qualitative approaches. J. Oper. Res. Soc. 36(8):705–712, 1998.CrossRefGoogle Scholar
  95. 95.
    Zhu, Z., Heng, B. H., and Teow, K. L., Analysis of factors causing long patient waiting time and clinic overtime in outpatient clinics. J. Med. Syst. 36(2):707–713, 2012.PubMedCrossRefGoogle Scholar
  96. 96.
    Aboueljinane, L., Sahin, E., and Jemai, Z., A review on simulation models applied to emergency medical service operations. Comput. Ind. Eng. 66(4):734–750, 2013.CrossRefGoogle Scholar
  97. 97.
    Brahimi, M., and Worthington, D. J., Queuing models for outpatient appointment systems: A case study. J. Oper. Res. Soc. 42(9):733–746, 1991.Google Scholar
  98. 98.
    Hill-Smith, I., Mathematical relationship between waiting times and appointment interval for doctors and patients. J. R. Coll. Gen. Pract. 39(329):492–494, 1989.PubMedPubMedCentralGoogle Scholar
  99. 99.
    Khori, V., Changizi, S., Biuckians, E., Keshtkar, A., Alizadeh, A. M., Mohaghgheghi, A. M., and Rabie, M. R., Relationship between consultation length and rational prescribing of drugs in Gorgan City, Islamic Republic of Iran. East Mediterr. Health J. 18(5):480–486, 2012.PubMedGoogle Scholar
  100. 100.
    Mankowska, D. S., Meisel, F., and Bierwirth, C., The home healthcare routing and scheduling problem with interdependent services. Healthc. Manag. Sci. 17:15–30, 2014.CrossRefGoogle Scholar
  101. 101.
    Welch, J. D., Appointment systems in hospitals and general practice: Appointment systems in hospital outpatient departments. J. Oper. Res. Soc. 15(3):224–232, 1964.CrossRefGoogle Scholar
  102. 102.
    Griffiths, J. D., Price-Lloyd, N., Smithies, M., and Williams, J. E., Modeling the requirement for supplementary nurses in an intensive care unit. J. Oper. Res. Soc. 56(2):126–133, 2005.CrossRefGoogle Scholar
  103. 103.
    Feldman, J., Liu, N., Topaloglu, H., and Ziya, S., Appointment scheduling under patient preference and No-show behavior. Oper. Res. 62(4):794–811, 2014.CrossRefGoogle Scholar
  104. 104.
    Hassin, R., and Mendel, S., Scheduling arrivals to queues: A single-server model with No- shows. Manag. Sci. 54(3):565–572, 2008.CrossRefGoogle Scholar
  105. 105.
    Klassen, K. J., and Yoogalingham, R., Improving performance in outpatient appointment services with a simulation optimization approach. Prod. Oper. Manag. 18(4):447–458, 2009.CrossRefGoogle Scholar
  106. 106.
    Huarng, F., and Lee, M. H., Using simulation in outpatient queues: A case study. Int. J. Healthc. Qual. Assur. 9(6):21–25, 1996.CrossRefGoogle Scholar
  107. 107.
    Cote, M. J., Patient flow and resource utilization in an outpatient clinic. Socio Econ. Plan. Sci. 33(3):231–245, 1999.CrossRefGoogle Scholar
  108. 108.
    Silvester, K., Lendon, R., Bevan, H., Steyn, R. and Walley, P., Reducing waiting times in the NHS: Is lack of capacity the problem? Clin. Manag. 12: Academic Paper, 1–7, 2004.Google Scholar
  109. 109.
    Klassen, K. J., and Rohleder, T. R., Scheduling outpatient appointments in a dynamic environment. J. Oper. Manag. 14(2):83–101, 1996.CrossRefGoogle Scholar
  110. 110.
    Cayirli, T., Veral, E., and Rosen, H., Assessment of patient classification in appointment system design. Prod. Oper. Manag. 17(3):338–353, 2008.Google Scholar
  111. 111.
    Halme, M., Joro, T., Korhonen, P., Salo, S., and Wallenius, J., A value efficiency approach to incorporating preference information in data envelopment analysis. Manag. Sci. 45(1):103–115, 1999.CrossRefGoogle Scholar
  112. 112.
    Golany, B., An interactive MOLP procedure for the extension of DEA to effectiveness analysis. J. Oper. Res. Soc. 39(8):725–734, 1988.CrossRefGoogle Scholar
  113. 113.
    Thanassoulis, E., and Dyson, R. G., Estimating preferred target input–output levels using data envelopment analysis. Eur. J. Oper. Res. 56(1):80–97, 1992.CrossRefGoogle Scholar
  114. 114.
    Zhu, J., Data envelopment analysis with preference structure. J. Oper. Res. Soc. 47(1):136–150, 1996.CrossRefGoogle Scholar
  115. 115.
    Athanassopoulos, A. D., Lambroukos, N., and Seiford, L., Data envelopment scenario analysis for setting targets to electricity generating plants. Eur. J. Oper. Res. 115(3):413–428, 1999.CrossRefGoogle Scholar
  116. 116.
    Thanassoulis, E., and Dunstan, P., Guiding schools to improved performance using data envelopment analysis: An illustration with data from a local education authority. J. Oper. Res. Soc. 45(11):1247–1262, 1994.CrossRefGoogle Scholar
  117. 117.
    Liu, J., Ding, F. F., and Lall, V., Using data envelopment analysis to compare suppliers for supplier selection and performance improvement. Supply Chain Manag. Int. J. 5(3):143–150, 2000.CrossRefGoogle Scholar
  118. 118.
    Martic, M., and Savic, G., An application of DEA for Comparative analysis and ranking of regions in Serbia with regards to social-economic development. Eur. J. Oper. Res. 132(2):343–356, 2001.CrossRefGoogle Scholar
  119. 119.
    Thanassoulis, E., Boussofiane, A., and Dyson, R. G., Exploring output quality targets in the provision of perinatal care in England using data envelopment analysis. Eur. J. Oper. Res. 80(3):588–607, 1995.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Komal A. Safdar
    • 1
  • Ali Emrouznejad
    • 1
  • Prasanta K. Dey
    • 1
  1. 1.Aston Business SchoolAston UniversityBirminghamUK

Personalised recommendations