A UNIVERSAL SOLUTION FOR UNITS - INVARIANCE IN DATA ENVELOPMENT ANALYSIS

  • Jin XU China Center for Health Development Studies Peking University, Beijing, China
  • Panagiotis D. ZERVOPOULOS China Center for Health Development Studies Peking University, Beijing, China Department of Business Administration of Food and Agricultural Enterprises University of Ioannina, Agrinio, Greece
  • Zhenhua QIAN School of Social Science University of Science and Technology Beijing, China
  • Gang CHENG China Center for Health Development Studies Peking University, Beijing, China

Abstract

The directional distance function model is a generalization of the radial model in data envelopment analysis (DEA). The directional distance function model is appropriate for dealing with cases where undesirable outputs exist. However, it is not a units-invariant measure of efficiency, which limits its accuracy. In this paper, we develop a data normalization method for DEA, which is a universal solution for the problem of units-invariance in DEA. The efficiency scores remain unchanged when the original data are replaced with the normalized data in the existing units-invariant DEA models, including the radial and slack-based measure models, i.e., the data normalization method is compatible with the radial and slack-based measure models. Based on normalized data, a units-invariant efficiency measure for the directional distance function model is defined.

References

References
[1] Banker, R.D., Charnes, A. and Cooper, W.W. 1984. Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science 30: 1078-1092.
[2] Chambers, R.G., Chung, Y., and Färe, R. 1996. Benefit and distance functions, Journal of Economic Theory 70: 407-419.
[3] Chambers, R.G., Chung, Y. and Färe, R. 1998. Profit, directional distance functions, and nerlovian efficiency. Journal of Optimization Theory and Applications 98: 351-364.
[4] Charnes, A. 1994. Data envelopment analysis: theory, methodology and application, Kluwer Academic Publishers.
[5] Charnes, A., Cooper, W.W., and Rhodes, E. 1978. Measuring the efficiency of decision making units, European Journal of Operational Research 2: 429-444.
[6] Chung, Y., Färe, R., and Grosskopf, S. 1997. Productivity and undesirable outputs: a directional distance function approach, Journal of Environmental Management 51: 229-240.
[7] Cook, W.D., and Seiford, L.M. 2009. Data Envelopment Analysis (DEA) - Thirty Years On, European Journal of Operational Research 192: 1-17.
[8] Färe, R., and Knox Lovell, C. A. 1978. Measuring the Technical Efficiency of Production, Journal of Economic Theory 19: 150-162.
[9] Knox Lovell, C.A., and Pastor, J. T. 1995. “Units Invariant and Translation Invariant DEA Models”, Operations Research Letters 18: 147-151.
[10] Seiford, L.M. 1996. Data Envelopment Analysis: The Evolution of the State of the Art (1978–1995), The Journal of Productivity Analysis 6: 99-137.
[11] Tone, K. 2001. A Slacks - Based Measure of Efficiency in Data Envelopment Analysis, European Journal of Operational Research 130: 498-509.
Published
2012-12-31
How to Cite
XU, Jin et al. A UNIVERSAL SOLUTION FOR UNITS - INVARIANCE IN DATA ENVELOPMENT ANALYSIS. Theoretical and Practical Research in Economic Fields, [S.l.], v. 3, n. 2, p. 121-128, dec. 2012. ISSN 2068-7710. Available at: <https://journals.aserspublishing.eu/tpref/article/view/1173>. Date accessed: 27 dec. 2024.
Citation Formats
Issue
Vol 3 No 2 (2012): TPREF, Volume III, Issue 2(6), Winter 2012
Section
Articles

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