A New Approach for Ranking Efficient Units in Data Envelopment Analysis and Application to a Sample of Vietnamese Agricultural Bank Branches

Affiliation(s)

Water Resources University, Hanoi, Vietnam.

Military Technical Academy, Hanoi, Vietnam.

Air Defence-Air Force Academy, Hanoi, Vietnam.

Water Resources University, Hanoi, Vietnam.

Military Technical Academy, Hanoi, Vietnam.

Air Defence-Air Force Academy, Hanoi, Vietnam.

ABSTRACT

This paper proposes a new approach for ranking efficiency units in data envelopment analysis as a modification of the super-efficiency models developed by Tone [1]. The new approach based on slacks-based measure of efficiency (SBM) for dealing with objective function used to classify all of the decision-making units allows the ranking of all inefficient DMUs and overcomes the disadvantages of infeasibility. This method also is applied to rank super-efficient scores for the sample of 145 agricultural bank branches in Viet Nam during 2007-2010. We then compare the estimated results from the new SCI model and the exsisting SBM model by using some statistical tests.

This paper proposes a new approach for ranking efficiency units in data envelopment analysis as a modification of the super-efficiency models developed by Tone [1]. The new approach based on slacks-based measure of efficiency (SBM) for dealing with objective function used to classify all of the decision-making units allows the ranking of all inefficient DMUs and overcomes the disadvantages of infeasibility. This method also is applied to rank super-efficient scores for the sample of 145 agricultural bank branches in Viet Nam during 2007-2010. We then compare the estimated results from the new SCI model and the exsisting SBM model by using some statistical tests.

KEYWORDS

Data Envelopment Analysis (DEA); Slacks-Based Measure of Efficiency (SBM); SCI Super-Efficient

Data Envelopment Analysis (DEA); Slacks-Based Measure of Efficiency (SBM); SCI Super-Efficient

Cite this paper

N. Minh, P. Khanh and P. Tuan, "A New Approach for Ranking Efficient Units in Data Envelopment Analysis and Application to a Sample of Vietnamese Agricultural Bank Branches,"*American Journal of Operations Research*, Vol. 2 No. 1, 2012, pp. 126-136. doi: 10.4236/ajor.2012.21015.

N. Minh, P. Khanh and P. Tuan, "A New Approach for Ranking Efficient Units in Data Envelopment Analysis and Application to a Sample of Vietnamese Agricultural Bank Branches,"

References

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[2] A. Charnes, W. W. Cooper and E. Rhodes, “Measuring the Efficiency of Decision-marking Units,” European Journal of Operational Research, Vol. 2, No. 4, 1978, pp. 429-444. doi:10.1016/0377-2217(78)90138-8

[3] R. D. Banker, A. Charnes and W. W. Cooper, “Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis,” Management Science, Vol. 30, No. 9, 1984, pp. 1078-1092. doi:10.1287/mnsc.30.9.1078

[4] N. Adler, L. Friedman and Z. Sinuany-Stern, “Review of Ranking Methods in Data Envelopment Analysis Context,” European Journal of Operation Research, Vol. 140, No. 2, 2002, pp. 249-265. doi:10.1016/S0377-2217(02)00068-1

[5] P. Andersen and N. C. Petersen, “A Procedure for Ranking Efficient Units in Data Envelopment,” Analysis Management Science, Vol. 39, No. 10, 1993, pp. 1261- 1294.

[6] F. H. Liu and L. C. Tsai, “Ranking of DEA Units with a Set of Weights to Performance Indices,” Paper was prepared for The Fourth International Symposium on DEA, 4-6 September, 2004, at Aston University.

[7] F. H. Lotfi, M. Navabakhs, A. Tehranian, M. Rostamy- Malkhalifeh and R. Shahverdi, “Ranking Bank Branches with Interval Data-The Application of DEA,” International Mathematical Forum, Vol. 2, No. 9, 2007, pp. 429- 440.

[8] S. Li, G. R. Jahanshahloo and M. Khodabakhshi, “A Super-Efficiency Model for Ranking Efficient Units in Data Envelopment Analysis,” Applied Mathematics and Computation, Vol. 184, No. 2, 2007, pp. 638-648. doi:10.1016/j.amc.2006.06.063

[9] S. Mehrabian, M. R. Alirezaee and G. R. Jahanshahloo, “A Complete Efficiency Ranking of Decision Making Units in Data Envelopment Analysis,” Computational Optimization and Applications, Vol. 14, No. 2, 1999, pp. 261-266. doi:10.1023/A:1008703501682

[10] K. Tone, “A Slacks-Based Measure of Efficiency in Data Envelopment Analysis,” European Journal of Operational Research, Vol. 130, 2001, pp. 489-509. doi:10.1016/S0377-2217(99)00407-5

[11] C. A. Favero and L. Papi, “Technical Efficiency and Scale Efficiency in the Italian Banking Sector: A Non-Parametric Approach,” Applied Economics, Vol. 27, No. 4, 1995, pp. 385-395. doi:10.1080/00036849500000123

[12] D. C. Wheelock and P. W. Wilson, “Technical Progress, Inefficiency, and Productivity Change in U.S. Banking, 1984-1993,” Journal of Money, Credit and Banking, Vol. 31, No. 2, 1999, pp. 212-234. doi:10.2307/2601230

[13] G. Lang and P. Welzel, “Technology and Cost Efficiency in Universal Banking A ‘Thick Frontier’-Analysis of the German Banking Industry,” Journal of Productivity Analysis, Vol. 10, No. 1, 1998, pp. 63-84. doi:10.1023/A:1018346332447

[14] M. Asmild, J. C. Paradi, V. Aggarwall and C. Schaffnit, “Combining DEA Window Analysis with the Malmquist Index Approach in a Study of the Canadian Banking Industry”, Journal of Productivity Analysis, Vol. 21, No. 1, 2004, pp. 67-89. doi:10.1023/B:PROD.0000012453.91326.ec

[15] A. S. Camanho and R. G. Dyson, “Efficiency, Size, Benchmark and Targets for Bank Branches: An Application of Data Envelopment Analysis’,” Journal of Operation Research Society, Vol. 50, No. 9, 1999, pp. 903-915. doi:10.1057/palgrave.jors.2600792

[16] D. Hauner and S. Peiris, “Banking Efficiency and Competition in Low Income Countries: The Case of Uganda,” Applied Economics, Vol. 40, No. 21, 2008, pp. 2703-2720. doi:10.1080/00036840600972456

[17] D. C. Wheelock and P. W. Wilson, “New Evidence on Returns to Scale and Product Mix among U.S. Commercial Banks,” Journal of Money, Credit and Banking, Vol. 47, No. 3, 2001, pp. 653-674.

[18] T.-Y. Chen, “A Measurement of Taiwan’s Bank Efficiency and Productivity Change during the Asian Financial Crisis,” International Journal of Services Technology and Management, Vol. 6, No. 6, 2005, pp. 485-503. doi:10.1504/IJSTM.2005.007510

[19] N. K. Minh and G. T. Long, “Ranking Efficiency of Commercial Banks in Vietnam with Supper Slack-Based Model of Data Envelopment Analysis,” Proceeding of DEA Symposium, Seikei University, Tokyo, 2008.

[20] W. W. Cooper and K. Tone, “Measures of Inefficiency in Data Envelopment Analysis and Stochastic Frontier Estimation,” European Journal of Operational Research, Vol. 99, No. 1, 1997, pp. 72-78. doi:10.1016/S0377-2217(96)00384-0

[21] W. W. Cooper, L. M. Seiford and K. Tone, “Introduction to Data Envelopment Analysis and Its Use—With DEA- Solver Software and References,” Springer, New York, 2007.

[22] E. Fiorentino, A. Karmann and M. Koetter, “The Cost Efficiency of German Banks: A Comparison of SFA and DEA,” Discussion Paper Series 2: Banking Financial Studies, No. 10, Deutsche Bundesbank, 2006.

[23] L. Friedman, and Z. Sinuany-Stern, “Scaling Units via the Canonical Correlation Analysis and the Data Envelopment Analysis,” European Journal of Operation Research, Vol. 100, No. 3, 1997, pp. 629-637. doi:10.1016/S0377-2217(97)84108-2

[24] G. R. Jahanshahloo, L. F. Hosseinzadeh and M. Moradi, “Sensitivity and Stability Analysis in DEA with Interval Data,” Applied Mathematics and Computation, Vol. 156, No. 2, 2004, pp. 463-477. doi:10.1016/j.amc.2003.08.005

[25] L. M. Seiford and J. Zhu, “Infeasiblity of Super-Efficiency Data Envelopment Analysis Models,” Infor, Vol. 37, No. 2, 1999, pp. 174-187.

[26] T. R. Sexton, R. H Silkman and A. J. Hogan, “Data Envelopment Analysis: Critique and Extensions,” Measuring Efficiency: An Assessment of Data Envelopment Analysis, Vol. 1986, No. 32, 1986, pp. 73-105.

[27] Z. Sinuany-Stern, A. Mehrez and A. Barboy, “Academic Departments Efficiency via Data Envelopment Analysis,” Computers and Operations Research, Vol. 21, No. 5, 1994, pp. 543-556. doi:10.1016/0305-0548(94)90103-1

[28] Z. Sinuany-Stern and L. Friedman, “Data Envelopment Analysis and the Discriminant Analysis of Ratios for Raking Units,” European Journal of Operational Research, Vol. 111, No. 3, 1998, pp. 470-478. doi:10.1016/S0377-2217(97)00313-5

[29] A. M. Torgersen, F. R. Forsund and S. A. C. Kittelsen, “Slack-Adjusted Efficiency Measures and Ranking of Efficient Units,” Journal of Productivity Analysis, Vol. 7, No. 4, 1986, pp. 379-398. doi:10.1007/BF00162048

[1] K. Tone, “A Slacks-Based Measure of Efficiency in Data Envelopment Analysis,” European Journal of Operational Research, Vol. 143, No. 1, 2002, pp. 32-41. doi:10.1016/S0377-2217(01)00324-1

[2] A. Charnes, W. W. Cooper and E. Rhodes, “Measuring the Efficiency of Decision-marking Units,” European Journal of Operational Research, Vol. 2, No. 4, 1978, pp. 429-444. doi:10.1016/0377-2217(78)90138-8

[3] R. D. Banker, A. Charnes and W. W. Cooper, “Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis,” Management Science, Vol. 30, No. 9, 1984, pp. 1078-1092. doi:10.1287/mnsc.30.9.1078

[4] N. Adler, L. Friedman and Z. Sinuany-Stern, “Review of Ranking Methods in Data Envelopment Analysis Context,” European Journal of Operation Research, Vol. 140, No. 2, 2002, pp. 249-265. doi:10.1016/S0377-2217(02)00068-1

[5] P. Andersen and N. C. Petersen, “A Procedure for Ranking Efficient Units in Data Envelopment,” Analysis Management Science, Vol. 39, No. 10, 1993, pp. 1261- 1294.

[6] F. H. Liu and L. C. Tsai, “Ranking of DEA Units with a Set of Weights to Performance Indices,” Paper was prepared for The Fourth International Symposium on DEA, 4-6 September, 2004, at Aston University.

[7] F. H. Lotfi, M. Navabakhs, A. Tehranian, M. Rostamy- Malkhalifeh and R. Shahverdi, “Ranking Bank Branches with Interval Data-The Application of DEA,” International Mathematical Forum, Vol. 2, No. 9, 2007, pp. 429- 440.

[8] S. Li, G. R. Jahanshahloo and M. Khodabakhshi, “A Super-Efficiency Model for Ranking Efficient Units in Data Envelopment Analysis,” Applied Mathematics and Computation, Vol. 184, No. 2, 2007, pp. 638-648. doi:10.1016/j.amc.2006.06.063

[9] S. Mehrabian, M. R. Alirezaee and G. R. Jahanshahloo, “A Complete Efficiency Ranking of Decision Making Units in Data Envelopment Analysis,” Computational Optimization and Applications, Vol. 14, No. 2, 1999, pp. 261-266. doi:10.1023/A:1008703501682

[10] K. Tone, “A Slacks-Based Measure of Efficiency in Data Envelopment Analysis,” European Journal of Operational Research, Vol. 130, 2001, pp. 489-509. doi:10.1016/S0377-2217(99)00407-5

[11] C. A. Favero and L. Papi, “Technical Efficiency and Scale Efficiency in the Italian Banking Sector: A Non-Parametric Approach,” Applied Economics, Vol. 27, No. 4, 1995, pp. 385-395. doi:10.1080/00036849500000123

[12] D. C. Wheelock and P. W. Wilson, “Technical Progress, Inefficiency, and Productivity Change in U.S. Banking, 1984-1993,” Journal of Money, Credit and Banking, Vol. 31, No. 2, 1999, pp. 212-234. doi:10.2307/2601230

[13] G. Lang and P. Welzel, “Technology and Cost Efficiency in Universal Banking A ‘Thick Frontier’-Analysis of the German Banking Industry,” Journal of Productivity Analysis, Vol. 10, No. 1, 1998, pp. 63-84. doi:10.1023/A:1018346332447

[14] M. Asmild, J. C. Paradi, V. Aggarwall and C. Schaffnit, “Combining DEA Window Analysis with the Malmquist Index Approach in a Study of the Canadian Banking Industry”, Journal of Productivity Analysis, Vol. 21, No. 1, 2004, pp. 67-89. doi:10.1023/B:PROD.0000012453.91326.ec

[15] A. S. Camanho and R. G. Dyson, “Efficiency, Size, Benchmark and Targets for Bank Branches: An Application of Data Envelopment Analysis’,” Journal of Operation Research Society, Vol. 50, No. 9, 1999, pp. 903-915. doi:10.1057/palgrave.jors.2600792

[16] D. Hauner and S. Peiris, “Banking Efficiency and Competition in Low Income Countries: The Case of Uganda,” Applied Economics, Vol. 40, No. 21, 2008, pp. 2703-2720. doi:10.1080/00036840600972456

[17] D. C. Wheelock and P. W. Wilson, “New Evidence on Returns to Scale and Product Mix among U.S. Commercial Banks,” Journal of Money, Credit and Banking, Vol. 47, No. 3, 2001, pp. 653-674.

[18] T.-Y. Chen, “A Measurement of Taiwan’s Bank Efficiency and Productivity Change during the Asian Financial Crisis,” International Journal of Services Technology and Management, Vol. 6, No. 6, 2005, pp. 485-503. doi:10.1504/IJSTM.2005.007510

[19] N. K. Minh and G. T. Long, “Ranking Efficiency of Commercial Banks in Vietnam with Supper Slack-Based Model of Data Envelopment Analysis,” Proceeding of DEA Symposium, Seikei University, Tokyo, 2008.

[20] W. W. Cooper and K. Tone, “Measures of Inefficiency in Data Envelopment Analysis and Stochastic Frontier Estimation,” European Journal of Operational Research, Vol. 99, No. 1, 1997, pp. 72-78. doi:10.1016/S0377-2217(96)00384-0

[21] W. W. Cooper, L. M. Seiford and K. Tone, “Introduction to Data Envelopment Analysis and Its Use—With DEA- Solver Software and References,” Springer, New York, 2007.

[22] E. Fiorentino, A. Karmann and M. Koetter, “The Cost Efficiency of German Banks: A Comparison of SFA and DEA,” Discussion Paper Series 2: Banking Financial Studies, No. 10, Deutsche Bundesbank, 2006.

[23] L. Friedman, and Z. Sinuany-Stern, “Scaling Units via the Canonical Correlation Analysis and the Data Envelopment Analysis,” European Journal of Operation Research, Vol. 100, No. 3, 1997, pp. 629-637. doi:10.1016/S0377-2217(97)84108-2

[24] G. R. Jahanshahloo, L. F. Hosseinzadeh and M. Moradi, “Sensitivity and Stability Analysis in DEA with Interval Data,” Applied Mathematics and Computation, Vol. 156, No. 2, 2004, pp. 463-477. doi:10.1016/j.amc.2003.08.005

[25] L. M. Seiford and J. Zhu, “Infeasiblity of Super-Efficiency Data Envelopment Analysis Models,” Infor, Vol. 37, No. 2, 1999, pp. 174-187.

[26] T. R. Sexton, R. H Silkman and A. J. Hogan, “Data Envelopment Analysis: Critique and Extensions,” Measuring Efficiency: An Assessment of Data Envelopment Analysis, Vol. 1986, No. 32, 1986, pp. 73-105.

[27] Z. Sinuany-Stern, A. Mehrez and A. Barboy, “Academic Departments Efficiency via Data Envelopment Analysis,” Computers and Operations Research, Vol. 21, No. 5, 1994, pp. 543-556. doi:10.1016/0305-0548(94)90103-1

[28] Z. Sinuany-Stern and L. Friedman, “Data Envelopment Analysis and the Discriminant Analysis of Ratios for Raking Units,” European Journal of Operational Research, Vol. 111, No. 3, 1998, pp. 470-478. doi:10.1016/S0377-2217(97)00313-5

[29] A. M. Torgersen, F. R. Forsund and S. A. C. Kittelsen, “Slack-Adjusted Efficiency Measures and Ranking of Efficient Units,” Journal of Productivity Analysis, Vol. 7, No. 4, 1986, pp. 379-398. doi:10.1007/BF00162048