Ranking of DMUs Based on Efficiency Intervals

Tomoe Entani

doi:10.20965/jaciii.2011.p0063

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JACIII Vol.15 No.1 pp. 63-67

doi: 10.20965/jaciii.2011.p0063

(2011)

Paper:

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Ranking of DMUs Based on Efficiency Intervals

Tomoe Entani

Kochi University, 2-5-1 Akebono, Kochi, Japan

Received:

February 15, 2010

Accepted:

April 22, 2010

Published:

January 20, 2011

Keywords:

interval DEA, efficiency interval, pessimistic viewpoint, ranking

Abstract

The efficiency of the Interval Data Envelopment Analysis (Interval DEA), we proposed, obtains its bounds from optimistic and pessimistic viewpoints. Intervals represent the uncertainty of given input-output data and the intuitive evaluation of decision makers. The partial order relation that intervals give elements may be complex, especially when elements are numerous. The efficiency measurement we propose combining optimistic and pessimistic efficiency in Interval DEA is comparable because both represent the difference of the analyzed Decision Making Unit (DMU) from the most efficient one. The efficiency measurement is defined as their minimum and determined mainly by pessimistic efficiency. Optimistic efficiency is considered if it is inadequate compared to pessimistic efficiency. Pessimistic efficiency based evaluation resembles natural evaluation and DMUs are arranged linearly.

Cite this article as:

Tomoe Entani, “Ranking of DMUs Based on Efficiency Intervals,” J. Adv. Comput. Intell. Intell. Inform., Vol.15, No.1, pp. 63-67, 2011.

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References

[1] A. Charnes, W. W. Cooper, and E. Rhodes, “Measuring the efficiency of decision making Unit,” European J. of Operational Research, Vol.2, pp. 429-444, 1978.
[2] T. Entani, Y. Maeda, and H. Tanaka, “Dual models of interval DEA and its extension to interval data,” European J. of Operational Research, Vol.136, pp. 32-45, 2002.
[3] D. Dubois and H. Prade, “Systems of linear fuzzy constraints,” Fuzzy Sets and Systems, Vol.3, pp. 37-48, 1980.
[4] N. Adler, L. Friedman, and Z. Sinuany-Stern, “Review of ranking methods in the data envelopment analysis context,” European J. of Operational Research, Vol.140, pp. 249-265, 2002.
[5] J. Doyle and R. Green, “Efficiency and cross-efficiency in data envelopment analysis: Derivatives, meanings and uses,” J. of the Operational Research Society, Vol.45, pp. 567-578, 1994.
[6] A. Charnes, C. T. Clark, W. W. Cooper, and B. Golany, “A developmental study of data envelopment analysis in measuring the efficiency of maintenance units in the US air forces,” Annals of Operations Research, Vol.2, pp. 95-112, 1985.
[7] A. M. Torgersen, F. R. Forsund, and S. A. C. Kittelsen, “Slackadjusted efficiency measures and ranking of efficient units,” J. of Productivity Analysis, Vol.7, pp. 379-398, 1996.
[8] P. Andersen and N. C. Petersen, “A procedure for ranking efficient units in data envelopment analysis,” Management Science, Vol.39, pp. 1261-1264, 1993.
[9] K. Tone, “A slacks-based measure of super-efficiency in data envelopment analysis,” European J. of Operational Research, Vol.143 pp. 32-41, 2002.
[10] J. Zhu, “Supper-efficiency and DEA sensitivity analysis,” European J. of Operational Research, Vol.129, pp. 443-455, 2001.
[11] W. D. Cook and M. Kress, “A data envelopment model for aggregating preference rankings,” Management Science, Vol.36, pp. 1302-1310, 1990.
[12] T. Obata and H. Ishii, “A method for discriminating efficient candidates with ranked voting data,” European J. of Operational Research, Vol.151, pp. 233-237, 2003.
[13] R. Ramanathan, “An Introduction to data envelopment analysis context: A tool for performance measurement,” Saga Publications, New Delhi-Thousand Oaks-London, 2003.

[1] [1] A. Charnes, W. W. Cooper, and E. Rhodes, “Measuring the efficiency of decision making Unit,” European J. of Operational Research, Vol.2, pp. 429-444, 1978.

[2] [2] T. Entani, Y. Maeda, and H. Tanaka, “Dual models of interval DEA and its extension to interval data,” European J. of Operational Research, Vol.136, pp. 32-45, 2002.

[3] [3] D. Dubois and H. Prade, “Systems of linear fuzzy constraints,” Fuzzy Sets and Systems, Vol.3, pp. 37-48, 1980.

[4] [4] N. Adler, L. Friedman, and Z. Sinuany-Stern, “Review of ranking methods in the data envelopment analysis context,” European J. of Operational Research, Vol.140, pp. 249-265, 2002.

[5] [5] J. Doyle and R. Green, “Efficiency and cross-efficiency in data envelopment analysis: Derivatives, meanings and uses,” J. of the Operational Research Society, Vol.45, pp. 567-578, 1994.

[6] [6] A. Charnes, C. T. Clark, W. W. Cooper, and B. Golany, “A developmental study of data envelopment analysis in measuring the efficiency of maintenance units in the US air forces,” Annals of Operations Research, Vol.2, pp. 95-112, 1985.

[7] [7] A. M. Torgersen, F. R. Forsund, and S. A. C. Kittelsen, “Slackadjusted efficiency measures and ranking of efficient units,” J. of Productivity Analysis, Vol.7, pp. 379-398, 1996.

[8] [8] P. Andersen and N. C. Petersen, “A procedure for ranking efficient units in data envelopment analysis,” Management Science, Vol.39, pp. 1261-1264, 1993.

[9] [9] K. Tone, “A slacks-based measure of super-efficiency in data envelopment analysis,” European J. of Operational Research, Vol.143 pp. 32-41, 2002.

[10] [10] J. Zhu, “Supper-efficiency and DEA sensitivity analysis,” European J. of Operational Research, Vol.129, pp. 443-455, 2001.

[11] [11] W. D. Cook and M. Kress, “A data envelopment model for aggregating preference rankings,” Management Science, Vol.36, pp. 1302-1310, 1990.

[12] [12] T. Obata and H. Ishii, “A method for discriminating efficient candidates with ranked voting data,” European J. of Operational Research, Vol.151, pp. 233-237, 2003.

[13] [13] R. Ramanathan, “An Introduction to data envelopment analysis context: A tool for performance measurement,” Saga Publications, New Delhi-Thousand Oaks-London, 2003.