×

A super-efficiency model for ranking efficient units in data envelopment analysis. (English) Zbl 1149.90079

Summary: Data envelopment analysis (DEA) is a body of research methodologies to evaluate overall efficiencies and identify the sources and estimate the amounts of inefficiencies in inputs and outputs. In DEA, the best performers are called DEA efficient and the efficiency score of a DEA efficient unit is denoted by an unity. In the last decade, ranking DEA efficient units has become the interests of many DEA researchers and a variety of models (called super-efficiency models) were developed to rank DEA efficient units. While the models developed in the past are interesting and meaningful, they have the disadvantages of being infeasible or instable occasionally. In this research, we develop a super-efficiency model to overcome some deficiencies in the earlier models. Both theoretical results and numerical examples are provided.

MSC:

90B50 Management decision making, including multiple objectives
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Adler, N.; Friedman, L.; Sinuany-Stern, Z., Review of ranking methods in the data envelopment analysis context, European Journal of Operational Research, 140, 249-265 (2002) · Zbl 1001.90048
[2] Andersen, P.; Petersen, N. C., A procedure for ranking efficient units in data envelopment analysis, Management Science, 39, 10, 1261-1264 (1993) · Zbl 0800.90096
[3] Banker, R. D.; Charnes, A.; Cooper, W. W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 30, 1078-1092 (1984) · Zbl 0552.90055
[4] Bardhan, I.; Bowlin, W. F.; Cooper, W. W.; Sueyoshi, T., Model for efficiency dominance in data envelopment analysis. Part I: Additive models and MED measures, Journal of the Operations Research Society of Japan, 39, 322-332 (1996) · Zbl 0873.90001
[5] Bazaraa, M. S.; Jarvis, J. J.; Sherali, H. D., Linear Programming and Networks Flows (1990), John Wiley & Sons · Zbl 0722.90042
[6] Bogetoft, P., Incentive efficient production frontiers: an agency perspective on DEA, Management Science, 40, 959-968 (1994) · Zbl 0816.90017
[7] Charnes, A.; Cooper, W. W.; Rhodes, E., Measuring the efficiencies of DMUs, European Journal of Operational Research, 2, 6, 429-444 (1978) · Zbl 0416.90080
[8] Charnes, A.; Haag, S.; Jaska, P.; Semple, J., Sensitivity of efficiency classifications in the additive model of data envelopment analysis, International Journal of System Science, 23, 789-798 (1992) · Zbl 0749.90002
[9] Jahanshahloo, G. R.; Khodabakhshi, M., Suitable combination of inputs for improving outputs in DEA with determining input congestion—Considering textile industry of China, Applied Mathematics and Computation, 151, 1, 263-273 (2004) · Zbl 1043.90538
[10] Dula, J. H.; Hickman, B. L., Effects of excluding the column being scored from the DEA envelopment LP technology matrix, The Journal of the Operational Research Society, 48, 1001-1012 (1997) · Zbl 0901.90001
[11] M.L. Durchholz, Large-scale data envelopment analysis models and related applications, Ph.D. Thesis, Department of Computer Science and Engineering, Southern Methodist University, Dallas, TX 75275, 1994.; M.L. Durchholz, Large-scale data envelopment analysis models and related applications, Ph.D. Thesis, Department of Computer Science and Engineering, Southern Methodist University, Dallas, TX 75275, 1994.
[12] Fridman, L.; Sinuany-Stern, Z., Scaling units via the canonical correlation analysis and the data envelopment analysis, European Journal of Operational Research, 100, 3, 629-637 (1997) · Zbl 0918.90003
[13] Jahanshahloo, G. R.; Khodabakhshi, M., Determining assurance interval for non-Archimedean element in the improving outputs model in DEA, Applied Mathematics and Computation, 151, 2, 501-506 (2004) · Zbl 1049.90030
[14] Mehrabian, S.; Alirezaee, A.; Jahanshahloo, G. R., A complete efficiency ranking of decision making units in DEA, Computational Optimization and Applications (COAP), 14, 261-266 (1999) · Zbl 0963.91021
[15] Seiford, L. M.; Zhu, J., Infeasibility of super-efficiency data envelopment analysis, INFOR, 37, 2, 174-187 (1999) · Zbl 07677588
[16] Sexton, T. R.; Silkman, R. H.; Hogan, A. J., Data envelopment analysis: critique and extensions, (Silkman, R. H., Measuring Efficiency: An Assessment of Data Envelopment Analysis (1986), Jossey-Bass: Jossey-Bass San Fransisco, CA), 73-105
[17] Thompson, R. G.; Darmapalah, P. S.; Thrall, R. M., Importance for DEA of zeros in data, multipliers, and solutions, The Journal of Productivity Analysis, 4, 379-390 (1993)
[18] Thrall, R. M., Duality, classification and slacks in data envelopment analysis, The Annals of Operations Research, 66, 109-138 (1996) · Zbl 0868.90003
[19] Tone, K., A slakes-based measure of efficiency in data envelopment analysis, European Journal of Operational Research, 130, 498-509 (2001) · Zbl 0990.90523
[20] K. Tone, A slackes-based measure of super-efficiency in data envelopment analysis, European Journal of Operational Research, in press.; K. Tone, A slackes-based measure of super-efficiency in data envelopment analysis, European Journal of Operational Research, in press. · Zbl 1073.90520
[21] Torgersen, A. M.; Forsund, F. R.; Kittelsen, S. A.C., Slack-adjusted efficiency measures and ranking of efficient units, The Journal of Productivity Analysis, 7, 379-398 (1996)
[22] Xue, M.; Harker, P. T., Note: Ranking DMUs with infeasible super-efficiency DEA models, Management Sciences, 48, 5, 705-710 (2002) · Zbl 1232.90306
[23] Zhu, J., Robustness of the efficient decision making units in data envelopment analysis, European Journal of Operational Research, 90, 451-460 (1996) · Zbl 0907.90007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.