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Modified MAJ model for ranking decision making units in data envelopment analysis. (English) Zbl 1111.90323

Summary: Efficiency Data Envelopment Analysis (DEA) models assessing decision making units (DMUs) are unable to discriminate between efficient DMUs. From experience, we know that usually plural DMUs are efficient. To discriminate between these efficient DMUs is an interesting subject. To this aim, super-efficiency models are proposed.
In this paper we study a super-efficiency model, namely MAJ. Each time an efficient DMU is excluded from the set of the observed DMUs, a new production possibility set (PPS) is obtained. In this model, ranking is done based on the position of each excluded efficient DMU in relation to its corresponding new PPS. If the efficient DMUs and the new PPSs remain unchanged, it is expected that the ranking, also, remain unchanged. But, in this paper, we show that the technique used for rendering this model unit-invariant causes the ranking to change when some inputs of some inefficient DMUs change, without causing any change in the new PPS. In this paper, we modify this model so that this problem will not occur.

MSC:

90B50 Management decision making, including multiple objectives
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References:

[1] Alder, N.; Fridman, L.; Sinuany-Stern, Z., Review of ranking methods in data envelopment analysis context, European Journal of Operational Research, 140, 249-265 (2002) · Zbl 1001.90048
[2] Anderson, P.; Peterson, N. C., A procedure for ranking efficient units in data envelopment analysis, Management Science, 39, 10, 1261-1264 (1993) · Zbl 0800.90096
[3] Charnes, A.; Cooper, W. W.; Rhodes, E., Measuring the efficiency of decision making units, European Journal of Operational Research, 2, 6, 429-444 (1978) · Zbl 0416.90080
[4] 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
[5] Matrič, M.; Savič, G., An application of DEA for comparative analysis and ranking of regions in Serbia with regards to socio-economic development, European Journal of Operational Research, 132, 343-356 (2001) · Zbl 0994.90507
[6] Mehrabian, S.; Alirezaee, M. R.; 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
[7] Sexton, T. R.; Silkman, R. H.; Hogan, A. J., Data envelopment analysis: critique and extension, (Silkman, R. H., Measuring Efficiency: An Assessment of Data Envelopment Analysis (1986), Jossey-Bass: Jossey-Bass San Fransisco, CA), 73-105
[8] Thrall, R. M., Duality classification and slacks in data envelopment analysis, The Annal of Operation Research, 66, 109-138 (1996) · Zbl 0868.90003
[9] Tone, K., A slack-based measure of super-efficiency in data envelopment analysis, European Journal of Operational Research, 143, 32-41 (2002) · Zbl 1073.90520
[10] Torgersen, A. M.; Forsund, F. R.; Kittelsen, S. A.C., Slack-adjusted efficiency measures and ranking of efficient unit, The Journal of Productivity Analysis, 7, 379-398 (1996)
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