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Slack-adjusted efficiency measures and ranking of efficient units

Abstract

In non-parametric methods many units are calculated as efficient. The article suggests a method for ranking efficient units, not by their efficiency, but by importance as benchmarks for the inefficient units, in contrast to earlier suggestions in the literature which rank units high if they are specialized. However, the total potentials for improvement frequently remain unrevealed by calculating radial efficiency measures of the Farrell type only. The article therefore first develops efficiency measures that explicitly extend the radial measures to include slacks. The new measures are applied to a typical multidimensional small-sample data set for Norwegian employment offices.

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References

  • Afriat, S. N. (1972). “Efficiency Estimation of Production Functions.” International Economic Review 13, 568–598.

    Google Scholar 

  • Andersen, P., and N. C. Petersen. (1993). “A Procedure for Ranking Efficient Units in Data Envelopment Analysis.” Management Science 39, 1261–1264.

    Google Scholar 

  • Banker, R. D., A. Charnes, and W. W. Cooper (1984). “Some Models for Estimating Technical and Scale Inefficiencies.” Management Science 30, 1078–1092.

    Google Scholar 

  • Bjurek, H., L. Hjalmarsson, and F. R. Førsund. (1990). “Deterministic Parametric and Nonparametric Estimation of Efficiency in Service Production: A Comparison.” Journal of Econometrics 46, 213–227.

    Google Scholar 

  • Bogetoft, P. (1994). “Incentive Efficient Production Frontiers: An Agency Perspective on DEA.” Management Science 40, 959–968.

    Google Scholar 

  • Burgess, J. F. Jr., and P. W. Wilson. (1995). “Decomposing Hospital Productivity Changes 1985–88: A Nonparametric Malmquist Approach.” Journal of Productivity Analysis 6, 343–363.

    Google Scholar 

  • Charnes, A., W. W. Cooper, and E. Rhodes. (1978). “Measuring the Efficiency of Decision Making Units.” European Journal of Operational Research 2 (6), 429–444.

    Google Scholar 

  • Charnes, A., C. T. Clark, W. W. Cooper, and B. Golany. (1985a). “A Developmental Study of Data Envelopment Analysis in Measuring the Efficiency of Maintenance Units in the U.S. Air Forces.” Annals of Operations Research 2, 95–112.

    Google Scholar 

  • Charnes, A., W. W. Cooper, B. Golany, L. Seiford, and J. Stutz. (1985b). “Foundations of Data Envelopment Analysis for Pareto-Koopmans Efficient Empirical Production Functions.” Journal of Econometrics 30, 91–107.

    Google Scholar 

  • Charnes, A., W. W. Cooper, A. Y. Lewin, R. C. Morey, and J. Rousseau. (1985c). “Sensitivity and Stability Analysis in DEA.” Annals of Operations Research 2, 139–156.

    Google Scholar 

  • Debreu G. (1951). “The Coefficient of Resource Utilization.” Econometrica 19 (3), 273–292.

    Google Scholar 

  • Farrell, M. J. (1957). “The Measurement of Productive Efficiency.” Journal of the Royal Statistical Society 120, 449–460.

    Google Scholar 

  • Fried, H. O., C. A. K. Lovell, and P. Vanden Eeckaut. (1993). “Evaluating the Performance of US Credit Unions.” Journal of Banking and Finance 17, 251–265.

    Google Scholar 

  • Frisch, R. (1965). Theory of Production. Dordrecht: D. Reidel.

    Google Scholar 

  • Färe, R., and C. A. K. Lovell. (1978). “Measuring the Technical Efficiency of Production.” Journal of Economic Theory 19, 150–162.

    Google Scholar 

  • Färe, R., S. Grosskopf, and C. A. K. Lovell. (1985). The Measurement of Efficiency of Production. Boston: Kluwer Academic Publishers.

    Google Scholar 

  • Førsund, F. R. (1993). “Productivity Growth in Norwegian Ferries.” In H. O. Fried, C. A. K. Lovell, and S. S. Schmidt (eds.), The Measurement of Productive Efficiency. New York: Oxford University Press, pp. 352–373.

    Google Scholar 

  • Førsund, F. R., and E. Hernæs. (1994). “A Comparative Analysis of Ferry Transport in Norway.” in A. Charnes, W. W. Cooper, A. Y. Lewin, and L. M. Seiford (eds.), Data Envelopment Analysis: Theory, Methodology and Applications. Dordrecht/Boston/London: Kluwer Academic Publishers, pp. 285–311.

    Google Scholar 

  • Førsund, F. R., and L. Hjalmarsson. (1974). “On the Measurement of Productive Efficiency.” Swedish Journal of Economics 76, 141–154.

    Google Scholar 

  • Førsund, F. R., and L. Hjalmarsson. (1979). “Generalised Farrell Measures on Efficiency: An Application to Milk Processing in Swedish Dairy Plants.” The Economic Journal 89, 294–315.

    Google Scholar 

  • Førsund, F. R., and L. Hjalmarsson. (1987). Analyses of Industrial Structure. A Putty-Clay Approach. Stockholm: Almqvist & Wiksell International.

    Google Scholar 

  • Kerstens and Vanden Eeckaut. (1993). “DEA and FDH Based Technical Efficiency Measurement: Comparing Radial and Nonradial Alternatives.” Paper presented at the Third European Workshop on Efficiency and Productivity Measurement, Center for Operations Research Econometrics, Université Catholique de Louvain, Louvain-La-Neuve, October 21–23, 1993.

    Google Scholar 

  • Kittelsen, S. A. C., and F. R. Førsund. (1992). “Efficiency Analysis of Norwegian District Courts.” Journal of Productivity Analysis 3, 277–306.

    Google Scholar 

  • Koopmans, T. C. (1951). “An Analysis of Production as an Efficient Combination of Activities.” in T. C. Koopmans (ed.), Activity Analysis of Production and Allocation. New York: John Wiley & Sons, Inc.

    Google Scholar 

  • Lewin, A. Y., and R. C. Morey. (1981). “Measuring the Relative Efficiency and Output Potential of Public Sector Organizations: An Application of Data Envelopment Analysis.” International Journal of Policy Analysis and Information Systems 5, 267–285.

    Google Scholar 

  • Lovell, C. A. K., L. C. Walters, and L. L. Wood. (1994). “Stratified Models of Education Production Using DEA and Regression Analysis.” in A. Charnes, W.W. Cooper, A.Y. Lewin, and L.M. Seiford (eds.), Data Envelopment Analysis: Theory, Methodology and Applications. Dordrecht/Boston/London: Kluwer Academic Publishers, pp. 329–351.

    Google Scholar 

  • Olesen, O. B., and N. C. Petersen. (1996). “Indicators of Ill-conditioned Data Sets and Model Misspecification in Data Envelopment Analysis: An Extended Facet Approach.” Management Science 42, 205–219.

    Google Scholar 

  • Russell, R. R. (1985). “Measures of Technical Efficiency.” Journal of Economic Theory 35, 109–126.

    Google Scholar 

  • Seiford, L. M. (1994). “A Bibliography of Data Envelopment Analysis (1978–1992).” In A. Charnes, W. W. Cooper, A. Y. Lewin, and L. M. Seiford (eds.), Data Envelopment Analysis: Theory, Methodology and Applications. Dordrecht/Boston/London: Kluwer Academic Publishers.

    Google Scholar 

  • Torgersen, A. M. (1992). “Produktivitetsanalyse av arbeidskontorene.” Report No. 43/92, SNF—Centre for Research in Economics and Business Administration, Oslo.

    Google Scholar 

  • Tulkens, H. (1993). “On FDH Efficiency Analyses: Some Methodological Issues and Applications to Retail Banking, Courts and Urban Transit.” Journal of Productivity Analysis 4, 183–210.

    Google Scholar 

  • Wilson, P. W. (1995). “Detecting Influential Observations in Data Envelopment Analysis.” Journal of Productivity Analysis 6, 27–45.

    Google Scholar 

  • Zieschang, K. (1984). “An Extended Farrell Efficiency Measure.” Journal of Economic Theory 33, 387–396.

    Google Scholar 

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Torgersen, A.M., Førsund, F.R. & Kittelsen, S.A.C. Slack-adjusted efficiency measures and ranking of efficient units. J Prod Anal 7, 379–398 (1996). https://doi.org/10.1007/BF00162048

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