Advertisement

Journal of Productivity Analysis

, Volume 23, Issue 2, pp 203–221 | Cite as

Visualizing Efficiency and Reference Relations in Data Envelopment Analysis with an Application to the Branches of a German Bank

  • Marcus Porembski
  • Kristina Breitenstein
  • Paul Alpar
Article

Abstract

The interest in Data Envelopment Analysis (DEA) as a method for analyzing the productivity of homogeneous Decision Making Units (DMUs) has significantly increased in recent years. One of the main goals of DEA is to measure for each DMU its production efficiency relative to the other DMUs under analysis. Apart from a relative efficiency score, DEA also provides reference DMUs for inefficient DMUs. An inefficient DMU has, in general, more than one reference DMU, and an efficient DMU may be a reference unit for a large number of inefficient DMUs. These reference and efficiency relations describe a net which connects efficient and inefficient DMUs. We visualize this net by applying Sammon’s mapping. Such a visualization provides a very compact representation of the respective reference and efficiency relations and it helps to identify for an inefficient DMU efficient DMUs respectively DMUs with a high efficiency score which have a similar structure and can therefore be used as models. Furthermore, it can also be applied to visualize potential outliers in a very efficient way.

Keywords

data envelopment analysis Sammon’s mapping visualization outlier 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andersen, P., Petersen, N.C. 1993“A Procedure for Ranking Efficient Units in Data Envelopment Analysis”Management Science3912611264Google Scholar
  2. Athanassopoulos, A., Triantis, K. 1998“Assessing Aggregate Cost Efficiency and the Related Policy Implications for Greek Local Municipalities”Information Systems and Operational Research366683Google Scholar
  3. Banker, R., Charnes, A., Cooper, W.W. 1984“Some Models for Estimating Technical and Scale Inefficiency in Data Envelopment Analysis”Management Science3010781092Google Scholar
  4. Berger, A.N., Humphrey, D.B. 1992Measurement and Efficiency Issues in Commercial BankingGriliches, Z. eds. Output Measurement in the Service SectorsUniversity of Chicago PressChicagoGoogle Scholar
  5. Chambers, J.M., Cleveland, W.S., Kleiner, B., Tukey, P.A. 1983Graphical Methods for Data AnalysisWadsworthBelmont CaliforniaGoogle Scholar
  6. Charnes, A., Cooper, W.W., LewinA.Y. Morey, R.C., Rousseau, J.J. 1985“Sensitivity and Stability Analysis in DEA”Annals of Operations Research2139156Google Scholar
  7. Charnes, A., Cooper, W.W., Rhodes, E. 1978“Measuring the Efficiency of Decision Making Units”European Journal of Operations Research2429444Google Scholar
  8. Charnes, A., Neralic, L. 1992“Sensitivity Analysis of the Proportionate Change of Inputs (or Outputs) in Data Envelopment Analysis”Glasnik Matematicki27393405Google Scholar
  9. Charnes, , A., , Rousseau, J.J., Semple, J.H. 1996“Sensitivity and Stability of Efficiency Classifications in Data Envelopment Analysis”.Journal of Productivity Analysis7518Google Scholar
  10. Cooper, W.W., Seiford, L.M., Tone, K. 2000Data Envelopment AnalysisKluwer Academic PublishersDordrechtGoogle Scholar
  11. Dzwinel, W. 1994“How to make Sammon’s Mapping useful for Multidimensional Data Structure Analysis”Pattern Recognition27949959Google Scholar
  12. Farrell, M.J. 1957“The Measurement of Productive Efficiency”.Journal of the Royal Statistic Society120253290Google Scholar
  13. Färe, R., Grosskopf, S., Lovell, C.A.K. 1985The Measurement of Efficiency of ProductionKluwer-NijhoffBostonGoogle Scholar
  14. König A. (1998) “A Survey of Methods for Multivariate Data Projection, Visualization and Interactive Analysis”. In Proceedings of the 5th International Conference on Soft Computing and Information/Intelligent Systems IIZUKA’98, Iizuka, Fukuoka, Japan, October 16–20, 1998, pp. 55–59Google Scholar
  15. König, A., M. Eberhardt, and R. Wenzel (1999) “Advances in Dimensionality Reduction Techniques for Interactive Visualization, Exploratory Data Analysis, Classification, and Rapid Pattern Recognition Design”. In Proceedings of the 4th International Conference on Advances in Pattern Recognition and Digital Techniques ICAPRDT’99, Calcutta, India, December 27–29, 1999Google Scholar
  16. Lovell, C.A.K. 1996Production Frontiers and Productive EfficienyFried, H.O.Lovell, C.A.K.Schmidt, S.S. eds. The Measurement of Productive EfficiencyOxford University PressNew York, Oxford367Google Scholar
  17. Minoux, M. 1986Mathematical ProgrammingChichester, New York, Brisbane, Toronto, SingaporeJohn Wiley and SonsGoogle Scholar
  18. Neralic, L. 1997“Sensitivity Analysis in Data Envelopment Analysis for Arbitrary Perturbations of Data”Glasnik Matematicki32315335Google Scholar
  19. Sammon, J.W.,Jr. 1969“A Nonlinear Mapping for Data Structure Analysis”IEEE Transactions on ComputersC-18401409Google Scholar
  20. Seaver, B., Triantis, K. 1992“A Fuzzy Clustering Approach Used in Evaluating Technical Efficiency Measures in Manufacturing”.Journal of Productivity Analysis3337363Google Scholar
  21. Seaver, B., Triantis, K. 1995“The Impact of Outliers and Leverage Points for Technical Efficiency Measurement Using High Breakdown Procedures”Management Science41937956Google Scholar
  22. Seaver, B., Triantis, K., Reeves, C. 1999“The Identification of Influential Subsets in Regression Using a Fuzzy Clustering Strategy”Technometrics41340351Google Scholar
  23. Shephard, R.W. 1970Theory of Cost and Production FunctionPrinceton University PressPrinceton, NJGoogle Scholar
  24. Simar, L., Wilson, P.W. 1998“Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models”Management Science444961Google Scholar
  25. Thompson, R.G., Dharmapala, P.S., Diaz, J., Gonzales-Lima, M.D., Thrall, R.M. 1996“DEA Multiplier Analytic Center Sensitivity Analysis with an Illustrative Application to Independent Oil Companies”Annals of Operations Research66163180Google Scholar
  26. Wilson, P.W. 1993“Detecting Outliers in Deterministic Nonparametric Frontier Models with Multiple Outputs”Journal of Business and Economic Statistics11319323Google Scholar
  27. Wilson, P.W. 1995“Detecting Influential Observations in Data Envelopment Analysis”The Journal of Productivity Analysis62745Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Marcus Porembski
    • 1
  • Kristina Breitenstein
    • 2
  • Paul Alpar
    • 3
  1. 1.School for Economics and Business AdministrationUniversity of MarburgMarburgGermany
  2. 2.School for Economics and Business AdministrationUniversity of MarburgMarburgGermany
  3. 3.School for Economics and Business AdministrationUniversity of MarburgMarburgGermany

Personalised recommendations