Journal of Medical Systems

, Volume 35, Issue 5, pp 1001–1014 | Cite as

Employing post-DEA Cross-evaluation and Cluster Analysis in a Sample of Greek NHS Hospitals

  • Angeliki Flokou
  • Nick KontodimopoulosEmail author
  • Dimitris Niakas
Original Paper


To increase Data Envelopment Analysis (DEA) discrimination of efficient Decision Making Units (DMUs), by complementing “self-evaluated” efficiencies with “peer-evaluated” cross-efficiencies and, based on these results, to classify the DMUs using cluster analysis. Healthcare, which is deprived of such studies, was chosen as the study area. The sample consisted of 27 small- to medium-sized (70–500 beds) NHS general hospitals distributed throughout Greece, in areas where they are the sole NHS representatives. DEA was performed on 2005 data collected from the Ministry of Health and the General Secretariat of the National Statistical Service. Three inputs -hospital beds, physicians and other health professionals- and three outputs -case-mix adjusted hospitalized cases, surgeries and outpatient visits- were included in input-oriented, constant-returns-to-scale (CRS) and variable-returns-to-scale (VRS) models. In a second stage (post-DEA), aggressive and benevolent cross-efficiency formulations and clustering were employed, to validate (or not) the initial DEA scores. The “maverick index” was used to sort the peer-appraised hospitals. All analyses were performed using custom-made software. Ten benchmark hospitals were identified by DEA, but using the aggressive and benevolent formulations showed that two and four of them respectively were at the lower end of the maverick index list. On the other hand, only one 100% efficient (self-appraised) hospital was at the higher end of the list, using either formulation. Cluster analysis produced a hierarchical “tree” structure which dichotomized the hospitals in accordance to the cross-evaluation results, and provided insight on the two-dimensional path to improving efficiency. This is, to our awareness, the first study in the healthcare domain to employ both of these post-DEA techniques (cross efficiency and clustering) at the hospital (i.e. micro) level. The potential benefit for decision-makers is the capability to examine high and low “all-round” performers and maverick hospitals more closely, and identify and address problems typically overlooked by first-stage DEA.


Data envelopment analysis Cross-efficiency Cluster analysis Benchmarking Hospital 


  1. 1.
    Nunamaker, T. R., Measuring routine nursing service efficiency: a comparison of cost per patient day and data envelopment analysis models. Health Serv. Res. 18:183–205, 1983.Google Scholar
  2. 2.
    Sherman, H. D., Hospital efficiency measurement and evaluation. Med. Care 22:922–938, 1984.CrossRefGoogle Scholar
  3. 3.
    Baker, R. C., and Talluri, S., A closer look at the use of data envelopment analysis for technology selection. Comput. Ind. Eng. 32:101–108, 1997.CrossRefGoogle Scholar
  4. 4.
    Boussofiane, A., Dyson, R. G., and Thanassoulis, E., Applied data envelopment analysis. Eur. J. Oper. Res. 52:1–15, 1991.CrossRefGoogle Scholar
  5. 5.
    Doyle, J., and Green, R H., Efficiency and cross efficiency in DEA: derivations, meanings and uses. J. Oper. Res. Soc. 45:567–578, 1994.Google Scholar
  6. 6.
    Sexton, T.R., Silkman, R.H., and Hogan, A.J., Data envelopment analysis: critique and extensions, in: R.H. Silkman (eds.) Measuring Efficiency: An Assessment of Data Envelopment Analysis, Jossey-Bass, San Francisco, CA. pp. 73–105, 1986.Google Scholar
  7. 7.
    Hollingsworth, B., and Wildman, J., Efficiency and Cross Efficiency Measures: A Validation Using OECD Data. Working paper 132, Centre for Health Program Evaluation (CHPE), 2002.Google Scholar
  8. 8.
    Adler, N., Friedman, L., and Sinuany-Stern, Z., Review of ranking methods in the data envelopment analysis context. Eur. J. Oper. Res. 140:249–265, 2002.zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Anderson, T. R., Hollingsworth, K. B., and Inmam, L., The fixed weighting nature of a cross-evaluation model. J. Prod. Anal. 17:249–255, 2002.CrossRefGoogle Scholar
  10. 10.
    Mukherjee, A., Nath, P., and Pal, M., Performance benchmarking and strategic homogeneity of Indian banks. Int. J. Bank Market. 20:122–139, 2002.CrossRefGoogle Scholar
  11. 11.
    Braglia, M., and Petroni, A., A quality assurance-oriented methodology for handling trade-offs in supplier selection. Int. J. Phys. Distrib. Logist. Manag. 30:96–111, 2000.CrossRefGoogle Scholar
  12. 12.
    Shang, J., and Sueyoshi, T., A unified framework for the selection of a flexible manufacturing system. Eur. J. Oper. Res. 85:297–315, 1995.zbMATHCrossRefGoogle Scholar
  13. 13.
    Sarkis, J., Evaluating flexible manufacturing systems alternatives using data envelopment analysis. Eng. Economist 43:25–48, 1997.CrossRefGoogle Scholar
  14. 14.
    Sarkis, J., and Talluri, S., Performance based clustering for benchmarking of US airports. Transport. Res. Part A 38:329–346, 2004.CrossRefGoogle Scholar
  15. 15.
    Martin, J. C., and Roman, C., A benchmarking analysis of Spanish commercial airports: a comparison between SMOP and DEA ranking methods. Networks Spatial Econ. 6:111–134, 2006.zbMATHCrossRefGoogle Scholar
  16. 16.
    Wu, J., Liang, L., and Chen, Y., DEA game cross-efficiency approach to Olympic rankings. Omega 37:909–918, 2009.CrossRefGoogle Scholar
  17. 17.
    Wu, J., Liang, L., and Yang, F., Achievement and benchmarking of countries at the Summer Olympics using cross efficiency evaluation method. Eur. J. Oper. Res. 197:722–730, 2009.zbMATHCrossRefGoogle Scholar
  18. 18.
    Sarkis, J., and Talluri, S., Eco-efficiency measurement using DEA: research and practitioner issues. J. Environ. Assess. Pol. Manag. 6:91–123, 2004.CrossRefGoogle Scholar
  19. 19.
    Sarkis, J., and Weinrach, J., Using data envelopment analysis to evaluate environmentally conscious waste treatment technology. J. Cleaner Prod. 9:417–427, 2001.CrossRefGoogle Scholar
  20. 20.
    Chen, T. Y., An assessment of technical efficiency and cross-efficiency in Taiwan’s electricity distribution sector. Eur. J. Oper. Res. 137:421–43, 2002.zbMATHCrossRefGoogle Scholar
  21. 21.
    Sajeev, A. G., and Narayan, R., A performance benchmarking study of Indian railway zones. Benchmark. Int. J. 15:599–617, 2008.CrossRefGoogle Scholar
  22. 22.
    Basso, A., and Funari, S., A Quantitative approach to evaluate the relative efficiency of museums. J. Cult. Econ. 28:195–216, 2004.CrossRefGoogle Scholar
  23. 23.
    Banker, R. D., Charnes, A., and Cooper, W. W., Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manag. Sci. 30:1078–1092, 1984.zbMATHCrossRefGoogle Scholar
  24. 24.
    Charnes, A., Cooper, W., and Rhodes, E., Measuring the efficiency of decision-making units. Eur. J. Oper. Res. 3:429–444, 1978.MathSciNetCrossRefGoogle Scholar
  25. 25.
    Emrouznejad, A., Ali Emrouznejad’s data envelopment analysis homepage, 1995–2003,
  26. 26.
    Emrouznejad, A., Parker, B. R., and Tavares, G., Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA. Soc. Econ. Plann. Sci. 42:151–157, 2008.CrossRefGoogle Scholar
  27. 27.
    Lam, K. F., In the determination of weight sets to compute cross-efficiency ratios in DEA. J. Oper. Res. Soc. 61:134–143, 2010.zbMATHCrossRefGoogle Scholar
  28. 28.
    Despotis, D. K., Improving the discriminating power of DEA: Focus on globally efficient units. J. Oper. Res. Soc. 53:314–323, 2002.zbMATHCrossRefGoogle Scholar
  29. 29.
    Liang, L., Wu, J., Cook, W. D., and Zhu, J., Alternative secondary goals in DEA cross efficiency evaluation. Int. J. Prod. Econ. 113:1025–1030, 2008.CrossRefGoogle Scholar
  30. 30.
    Talluri, S., and Sarkis, J., Extensions in efficiency measurement of alternate machine component grouping solutions via data envelopment analysis. IEEE Trans. Eng. Manag. 44:299–304, 1997.CrossRefGoogle Scholar
  31. 31.
    Doyle, J. R., Multiple correlation clustering. Int. J. Man-Machine Studies 37:751–765, 1992.MathSciNetCrossRefGoogle Scholar
  32. 32.
    Aletras, V., Kontodimopoulos, N., Zagouldoudis, A., and Niakas, D., The short-term effect on technical and scale efficiency of establishing Regional Health Systems and General Management in Greek NHS hospitals. Health Policy 83:236–245, 2007.CrossRefGoogle Scholar
  33. 33.
    Magnussen, J., Efficiency measurement and the operationalization of hospital production. Health Serv. Res. 31:21–37, 1996.Google Scholar
  34. 34.
    Dyson, R. G., Allen, R., Camanho, A. S., Podinovski, V. V., Sarrico, C. S., and Shale, E. A., Pitfalls and protocols in DEA. Eur. J. Oper. Res. 132:245–259, 2001.zbMATHCrossRefGoogle Scholar
  35. 35.
    Ozcan, Y. A., and Luke, R. D., A national study of the efficiency of hospitals in urban markets. Health Serv. Res. 27:719–739, 1993.Google Scholar
  36. 36.
    Harrison, J., Coppola, N., and Wakefield, M., Efficiency of federal hospitals in the United States. J. Med. Sys. 28:411–422, 2004.CrossRefGoogle Scholar
  37. 37.
    Helmig, B., and Lapsley, I., On the efficiency of public, welfare and private hospitals in Germany over time—A sectoral DEA-Study. Health Serv. Manag. Res. 14:263–274, 2001.CrossRefGoogle Scholar
  38. 38.
    Renner, A., Kirigia, J., Zere, E., Barry, S., Kirigia, D., Kamara, C., and Muthuri, L., Technical efficiency of peripheral health units in Pujehun district of Sierra Leone: a DEA application. BMC Health Serv. Res. 5:77, 2005.CrossRefGoogle Scholar
  39. 39.
    Osei, D., d'Almeida, S., George, M.O., Kirigia, J.M., Mensah, A.O., and Kainyu, L.H., Technical efficiency of public district hospitals and health centers in Ghana: a pilot study. Cost Eff. Resour. Alloc. 3:9, 2005.Google Scholar
  40. 40.
    Chilingerian, J., and Sherman H.D., Health care applications: from hospitals to physicians, from productive efficiency to quality frontiers. In: Cooper, W., Seiford W., Lawrence M., and Zhu J., (Eds.) Handbook on Data Envelopment Analysis, Springer US, 495, 2004Google Scholar
  41. 41.
    Rovithis, D., Health economic evaluation in Greece. Int. J. Techno. Assess. Health Care. 22:388–395, 2006.Google Scholar
  42. 42.
    Mossialos, E., Allin, S., and Davaki, K., Analyzing the Greek health system: A tale of fragmentation and inertia. Health Econ. 14:151–168, 2005.CrossRefGoogle Scholar
  43. 43.
    Mersha, T., Output performance measurement in outpatient care. OMEGA Int. J. Manag. Sci. 17:159–167, 1989.CrossRefGoogle Scholar
  44. 44.
    Roemer, M. I., Moustafa, A. T., and Hopkins, C. E., A Proposed hospital quality index: Hospital Death Rates Adjusted for Case Severity. Health Serv. Res. 3:96–118, 1968.Google Scholar
  45. 45.
    O'Neill, L., Rauner, M., Heidenberger, K., and Krau, M., A cross-national comparison and taxonomy of DEA-based hospital efficiency studies. Soc. Econ. Plann. Sci. 42:158–189, 2008.CrossRefGoogle Scholar
  46. 46.
    Kontodimopoulos, N., Nanos, P., and Niakas, D., Balancing efficiency of health services and equity of access in remote areas in Greece. Health Policy 76:49–57, 2006.CrossRefGoogle Scholar
  47. 47.
    Giokas, D. I., Greek hospitals: how well their resources are used. Omega 29:73–83, 2001.CrossRefGoogle Scholar
  48. 48.
  49. 49.
    Angulo-Meza, L., and Lins, M. P. E., Review of methods for increasing discrimination in data envelopment analysis. Ann. Oper. Res. 116:225–242, 2002.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Angeliki Flokou
    • 1
  • Nick Kontodimopoulos
    • 1
    Email author
  • Dimitris Niakas
    • 1
  1. 1.Faculty of Social SciencesHellenic Open UniversityPatrasGreece

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