Discriminating Among Relatively Efficient Units in Data Envelopment Analysis: A Comparison of Alternative Methods and Some Extensions
Author(s)
Antreas D. Athanassopoulos
ABSTRACT
This paper concentrates on methods for comparing activity units found relatively efficient by data envelopment analysis (DEA). The use of the basic DEA models does not provide direct information regarding the performance of such units. The paper provides a systematic framework of alternative ways for ranking DEA-efficient units. The framework contains criteria derived as by-products of the basic DEA models and also criteria derived from complementary DEA analysis that needs to be carried out. The proposed framework is applied to rank a set of relatively efficient restaurants on the basis of their market efficiency.
This paper concentrates on methods for comparing activity units found relatively efficient by data envelopment analysis (DEA). The use of the basic DEA models does not provide direct information regarding the performance of such units. The paper provides a systematic framework of alternative ways for ranking DEA-efficient units. The framework contains criteria derived as by-products of the basic DEA models and also criteria derived from complementary DEA analysis that needs to be carried out. The proposed framework is applied to rank a set of relatively efficient restaurants on the basis of their market efficiency.
KEYWORDS
Data Envelopment Analysis; Cross-Efficiency; Super-Efficiency; Absolute Ranking; Linear Programming
Data Envelopment Analysis; Cross-Efficiency; Super-Efficiency; Absolute Ranking; Linear Programming
Cite this paper
A. Athanassopoulos, "Discriminating Among Relatively Efficient Units in Data Envelopment Analysis: A Comparison of Alternative Methods and Some Extensions," American Journal of Operations Research, Vol. 2 No. 1, 2012, pp. 1-9. doi: 10.4236/ajor.2012.21001.
A. Athanassopoulos, "Discriminating Among Relatively Efficient Units in Data Envelopment Analysis: A Comparison of Alternative Methods and Some Extensions," American Journal of Operations Research, Vol. 2 No. 1, 2012, pp. 1-9. doi: 10.4236/ajor.2012.21001.
References
[1] M. Farell, “The Measurement of Productive Efficiency,” Journal of Royal Statistical Society A, Vol. 120, Part III, 1957, pp. 253-281. doi:10.2307/2343100 [2] A. Charnes, W. Cooper and E. Rhodes, “Measuring the Efficiency of Decision Making Units,” European Journal of Operational Research, Vol. 2, No. 6, 1978, pp. 429- 444. doi:10.1016/0377-2217(78)90138-8 [3] R. Banker, Charnes and 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] R. Fare, S. Grosskopf and K. Lovell, “The Measurement of Efficiency of Production,” Kluwer-Nijhoff Publishing, Boston, 1985. [5] L. Seiford, “A Bibliography of Data Envelopment Analysis (1978-1995). Technical Report,” In: A. Charnes, W. Cooper, A. Lewin and L. Seiford, Eds., Data Envelopment Analysis: Theory, Method and Process, IC2 Management and Management Science Series, Quorum Books, New York, 1995. [6] H. Fried, K. Lovell and S. Schmidt, “The Measurement of Productive Efficiency: Techniques and Applications,” Oxford University Press, New York, 1993. [7] D. Adolphson, G. Cornia and L. Walters, “A Unified Framework for Classifying DEA Models,” In: H. Bradley, Ed., Operational Research’90, Pergamon Press, New York, 1990. [8] K. Lovell, L. Walters and L. Wood, “Stratified Models of Education Production Using DEA and Regression Analysis,” In: A. Charnes, W. Cooper, A. Lewin and L. Seiford, Eds., Data Envelopment Analysis: Theory, Method and Process, IC2 Management and Management Science Series, Quorum Books, New York, 1995. [9] P. Andersen and N. Petersen, “A Procedure for Ranking Efficient Units in Data Envelopment Analysis,” Management Science, Vol. 39, No. 10, 1994, pp. 1261-1264. doi:10.1287/mnsc.39.10.1261 [10] A. Athanassopoulos and J. Ballantine, “Ratio and Frontier Analysis for Assessing Corporate Performance: Evidence from the Grocery Industry in the UK,” Journal of the Operational Research Society, Vol. 46, No. 4, 1995, pp. 427-440. [11] T. Sexton, R. Silkman and A. Hogan, “Data Envelopment Analysis: Critique and Extensions,” New Directions for Program Evaluation, Vol. 1986, No. 32, 1986, pp. 73- 105. [12] J. Doyle and R. Green, “Efficiency and Cross-Efficiency in DEA,” Journal of Operational Research Society, Vol. 45, No. 4, 1994, pp. 567-578. doi:10.1057/jors.1994.84 [13] J. Doyle and R. Green, “Cross-Evaluation in DEA: Improving Discrimination among DMUs,” Infor, Vol. 32, No. 2, 1994, pp. 1-18. [14] A. Ali and L. Seiford, “Computational Accuracy and Infinitecimals in Data Envelopment Analysis,” Infor, Vol. 31, No. 4, 1993, pp. 290-297. [15] W. Cook, M. Kress and L. Seiford, “Prioritisation Models for Frontier Decision Making Units in DEA,” European Journal of Operational Research, Vol. 59, No. 2, 1992, pp. 319-323. doi:10.1016/0377-2217(92)90148-3 [16] B. Seaver, and K. Triantis, “The Implications of Using Messy Data to Estimate Production-Frontier-Based Technical Efficiency Measures,” Journal of Business and Economic Statistics, Vol. 7, No. 1, 1989, pp. 49-59. doi:10.2307/1391837 [17] B. Seaver, and K. Triantis, “The Impact of Outlier and Leverage Points for Technical Efficiency Measurement Using High Breakdown Procedures,” Management Science, Vol. 41, No. 6, 1995, pp. 937-956. doi:10.1287/mnsc.41.6.937 [18] P. Wilson, “Detecting Outliers in Deterministic Nonparametric Frontier Models with Multiple Outputs,” Journal of Business and Economic Statistics, Vol. 11, No. 3, 1993, pp. 319-323. doi:10.2307/1391956 [19] Y. Chen, “Ranking Efficient Units in DEA,” Omega, Vol. 32, No. 3, pp. 213-219. doi:10.1016/j.omega.2003.11.001 [20] L. Shanling, G. Jahanshahloo and M. Khodabakhshi, “A Super-Efficiency Model for Ranking Efficient Units in Data Envelopment Analysis,” European Journal of Operational Research, Vol. 184, No. 2, 2007, pp. 638-648. [21] J. Zhu, “Robustness of the Efficient DMUs in Data Envelopment Analysis,” European Journal of Operational Research, Vol. 90, No. 3, 1996, pp. 451-460. doi:10.1016/0377-2217(95)00054-2 [22] P. Bogetoft and J. L. Hougaard, “Super Efficiency Evaluations Based on Potential Slack,” European Journal of Operational Research, Vol. 152, No. 1, 2004, pp. 14- 21. doi:10.1016/S0377-2217(02)00642-2
[1] M. Farell, “The Measurement of Productive Efficiency,” Journal of Royal Statistical Society A, Vol. 120, Part III, 1957, pp. 253-281. doi:10.2307/2343100 [2] A. Charnes, W. Cooper and E. Rhodes, “Measuring the Efficiency of Decision Making Units,” European Journal of Operational Research, Vol. 2, No. 6, 1978, pp. 429- 444. doi:10.1016/0377-2217(78)90138-8 [3] R. Banker, Charnes and 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] R. Fare, S. Grosskopf and K. Lovell, “The Measurement of Efficiency of Production,” Kluwer-Nijhoff Publishing, Boston, 1985. [5] L. Seiford, “A Bibliography of Data Envelopment Analysis (1978-1995). Technical Report,” In: A. Charnes, W. Cooper, A. Lewin and L. Seiford, Eds., Data Envelopment Analysis: Theory, Method and Process, IC2 Management and Management Science Series, Quorum Books, New York, 1995. [6] H. Fried, K. Lovell and S. Schmidt, “The Measurement of Productive Efficiency: Techniques and Applications,” Oxford University Press, New York, 1993. [7] D. Adolphson, G. Cornia and L. Walters, “A Unified Framework for Classifying DEA Models,” In: H. Bradley, Ed., Operational Research’90, Pergamon Press, New York, 1990. [8] K. Lovell, L. Walters and L. Wood, “Stratified Models of Education Production Using DEA and Regression Analysis,” In: A. Charnes, W. Cooper, A. Lewin and L. Seiford, Eds., Data Envelopment Analysis: Theory, Method and Process, IC2 Management and Management Science Series, Quorum Books, New York, 1995. [9] P. Andersen and N. Petersen, “A Procedure for Ranking Efficient Units in Data Envelopment Analysis,” Management Science, Vol. 39, No. 10, 1994, pp. 1261-1264. doi:10.1287/mnsc.39.10.1261 [10] A. Athanassopoulos and J. Ballantine, “Ratio and Frontier Analysis for Assessing Corporate Performance: Evidence from the Grocery Industry in the UK,” Journal of the Operational Research Society, Vol. 46, No. 4, 1995, pp. 427-440. [11] T. Sexton, R. Silkman and A. Hogan, “Data Envelopment Analysis: Critique and Extensions,” New Directions for Program Evaluation, Vol. 1986, No. 32, 1986, pp. 73- 105. [12] J. Doyle and R. Green, “Efficiency and Cross-Efficiency in DEA,” Journal of Operational Research Society, Vol. 45, No. 4, 1994, pp. 567-578. doi:10.1057/jors.1994.84 [13] J. Doyle and R. Green, “Cross-Evaluation in DEA: Improving Discrimination among DMUs,” Infor, Vol. 32, No. 2, 1994, pp. 1-18. [14] A. Ali and L. Seiford, “Computational Accuracy and Infinitecimals in Data Envelopment Analysis,” Infor, Vol. 31, No. 4, 1993, pp. 290-297. [15] W. Cook, M. Kress and L. Seiford, “Prioritisation Models for Frontier Decision Making Units in DEA,” European Journal of Operational Research, Vol. 59, No. 2, 1992, pp. 319-323. doi:10.1016/0377-2217(92)90148-3 [16] B. Seaver, and K. Triantis, “The Implications of Using Messy Data to Estimate Production-Frontier-Based Technical Efficiency Measures,” Journal of Business and Economic Statistics, Vol. 7, No. 1, 1989, pp. 49-59. doi:10.2307/1391837 [17] B. Seaver, and K. Triantis, “The Impact of Outlier and Leverage Points for Technical Efficiency Measurement Using High Breakdown Procedures,” Management Science, Vol. 41, No. 6, 1995, pp. 937-956. doi:10.1287/mnsc.41.6.937 [18] P. Wilson, “Detecting Outliers in Deterministic Nonparametric Frontier Models with Multiple Outputs,” Journal of Business and Economic Statistics, Vol. 11, No. 3, 1993, pp. 319-323. doi:10.2307/1391956 [19] Y. Chen, “Ranking Efficient Units in DEA,” Omega, Vol. 32, No. 3, pp. 213-219. doi:10.1016/j.omega.2003.11.001 [20] L. Shanling, G. Jahanshahloo and M. Khodabakhshi, “A Super-Efficiency Model for Ranking Efficient Units in Data Envelopment Analysis,” European Journal of Operational Research, Vol. 184, No. 2, 2007, pp. 638-648. [21] J. Zhu, “Robustness of the Efficient DMUs in Data Envelopment Analysis,” European Journal of Operational Research, Vol. 90, No. 3, 1996, pp. 451-460. doi:10.1016/0377-2217(95)00054-2 [22] P. Bogetoft and J. L. Hougaard, “Super Efficiency Evaluations Based on Potential Slack,” European Journal of Operational Research, Vol. 152, No. 1, 2004, pp. 14- 21. doi:10.1016/S0377-2217(02)00642-2