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Journal of Optimization
Volume 2015, Article ID 594727, 10 pages
http://dx.doi.org/10.1155/2015/594727
Research Article

Ranking All DEA-Efficient DMUs Based on Cross Efficiency and Analytic Hierarchy Process Methods

Department of Mathematics, Islamic Azad University, Arak Branch, Arak, Iran

Received 15 August 2014; Accepted 20 December 2014

Academic Editor: Farhad Hosseinzadeh Lotfi

Copyright © 2015 Dariush Akbarian. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Charnes, W. W. Cooper, and E. Rhodes, “Measuring the efficiency of decision making units,” European Journal of Operational Research, vol. 2, no. 6, pp. 429–444, 1978. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. R. D. Banker, A. Charnes, and W. W. Cooper, “Some mode ls for estimating technical and scale inefficiencies in data envelopment analysis,” Management Science, vol. 30, no. 9, pp. 1078–1092, 1984. View at Publisher · View at Google Scholar · View at Scopus
  3. D. D. Wu, “BiLevel programming data envelopment analysis with constrained resource,” European Journal of Operational Research, vol. 207, no. 2, pp. 856–864, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. D. D. Wu, “Performance evaluation: an integrated method using data envelopment analysis and fuzzy preference relations,” European Journal of Operational Research, vol. 194, no. 1, pp. 227–235, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. D. Wu and C.-G. Lee, “Stochastic DEA with ordinal data applied to a multi-attribute pricing problem,” European Journal of Operational Research, vol. 207, no. 3, pp. 1679–1688, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. D. Wu, O. Baron, and O. Berman, “Bargaining in competing supply chains with uncertainty,” European Journal of Operational Research, vol. 197, no. 2, pp. 548–556, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J.-X. Chen and M. Deng, “A cross-dependence based ranking system for efficient and inefficient units in DEA,” Expert Systems with Applications, vol. 38, no. 8, pp. 9648–9655, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. G. R. Jahanshahloo, H. V. Junior, F. H. Lotfi, and D. Akbarian, “A new DEA ranking system based on changing the reference set,” European Journal of Operational Research, vol. 181, no. 1, pp. 331–337, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. 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, pp. 638–648, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. F. H. Lotfi, A. A. Noora, G. R. Jahanshahloo, and M. Reshadi, “One DEA ranking method based on applying aggregate units,” Expert Systems with Applications, vol. 38, no. 10, pp. 13468–13471, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. 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, pp. 261–266, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. N. Adler, L. Friedman, and Z. Sinuany-Stern, “Review of ranking methods in the data envelopment analysis context,” European Journal of Operational Research, vol. 140, no. 2, pp. 249–265, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. P. Andersen and N. C. Petersen, “A procedure for ranking efficient units in data envelopment analysis,” Management Science, vol. 39, no. 10, pp. 1261–1264, 1993. View at Publisher · View at Google Scholar
  14. Y.-M. Wang, Y. Luo, and L. Liang, “Ranking decision making units by imposing a minimum weight restriction in the data envelopment analysis,” Journal of Computational and Applied Mathematics, vol. 223, no. 1, pp. 469–484, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. L. M. Seiford and J. Zhu, “Infeasibility of super-efficiency data envelopment analysis models,” INFOR Journal, vol. 37, no. 2, pp. 174–187, 1999. View at Google Scholar
  16. T. L. Saaty, The Analytic Hierarchy Process: Planning, Priority Setting and Resource Allocation, McGraw-Hill, New York, NY, USA, 1980. View at MathSciNet
  17. Z. Sinuany-Stern, A. Mehrez, and Y. Hadad, “An AHP/DEA methodology for ranking decision making units,” International Transactions in Operational Research, vol. 7, no. 2, pp. 109–124, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  18. J. Jablonsky, “Using analytic hierarchy process as a tool for ranking of efficient units in dea models,” in Proceedings of the International Symposium on the Analytic Hierarchy Process, 2011.
  19. J. Jablonsky, “Measuring the efficiency of production units by AHP models,” Mathematical and Computer Modelling, vol. 46, no. 7-8, pp. 1091–1098, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. M.-R. Alirezaee and M. R. Sani, “New analytical hierarchical process/data envelopment analysis methodology for ranking decision-making units,” International Transactions in Operational Research, vol. 18, no. 5, pp. 533–544, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, N. Shoja, G. Tohidi, and S. Razavian, “Ranking using l1-norm in data envelopment analysis,” Applied Mathematics and Computation, vol. 153, no. 1, pp. 215–224, 2004. View at Google Scholar
  22. A. Amirteimoori and S. Kordrostami, “Efficient surfaces and an efficiency index in DEA: a constant returns to scale,” Applied Mathematics and Computation, vol. 163, no. 2, pp. 683–691, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. F. Zahedi, “The analytic hierarchy process-a survey of t he method and its applications,” Interfaces, vol. 16, no. 4, pp. 96–108, 1986. View at Publisher · View at Google Scholar
  24. R. Ramanathan, “Data envelopment analysis for weight derivation and aggregation in the analytic hierarchy process,” Computers & Operations Research, vol. 33, no. 5, pp. 1289–1307, 2006. View at Publisher · View at Google Scholar · View at Scopus
  25. G. Crawford and C. Williams, “A note on the analysis of subjective judgment matrices,” Journal of Mathematical Psychology, vol. 29, no. 4, pp. 387–405, 1985. View at Publisher · View at Google Scholar · View at Scopus
  26. F. A. Lootsma, Multi-Criteria Decision Analysis via Ratio and Difference Judgement, vol. 29 of Applied Optimization, Kluwer Academic, Dordrecht, The Netherlands, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  27. N. K. M. Bryson and A. Joseph, “Generating consensus priority point vectors: a logarithmic goal programming approach,” Computers and Operations Research, vol. 26, no. 6, pp. 637–643, 1999. View at Publisher · View at Google Scholar · View at Scopus
  28. Y.-M. Wang, C. Parkan, and Y. Luo, “A linear programming method for generating the most favorable weights from a pairwise comparison matrix,” Computers & Operations Research, vol. 35, no. 12, pp. 3918–3930, 2008. View at Publisher · View at Google Scholar · View at Scopus
  29. Y.-M. Wang, K.-S. Chin, and G. K. K. Poon, “A data envelopment analysis method with assurance region for weight generation in the analytic hierarchy process,” Decision Support Systems, vol. 45, no. 4, pp. 913–921, 2008. View at Publisher · View at Google Scholar · View at Scopus
  30. T. R. Sexton, R. H. Silkman, and A. J. Hogan, “Data envelopment analysis: critique and extensions,” in Measuring Efficiency: An Assessment of Data Envelopment Analysis, R. H. Silkman, Ed., pp. 73–105, Jossey-Bass, San Francisco, Calif, USA, 1986. View at Google Scholar
  31. Y.-M. Wang and K.-S. Chin, “Some alternative models for DEA cross-efficiency evaluation,” International Journal of Production Economics, vol. 128, no. 1, pp. 332–338, 2010. View at Publisher · View at Google Scholar · View at Scopus
  32. Y.-M. Wang, K.-S. Chin, and Y. Luo, “Cross-efficiency evaluation based on ideal and anti-ideal decision making units,” Expert Systems with Applications, vol. 38, no. 8, pp. 10312–10319, 2011. View at Publisher · View at Google Scholar · View at Scopus
  33. H. H. Örkcü and H. Bal, “Goal programming approaches for data envelopment analysis cross efficiency evaluation,” Applied Mathematics and Computation, vol. 218, no. 2, pp. 346–356, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. J. Doyle and R. Green, “Efficiency and cross-efficiency in DEA: derivations, meanings and uses,” Journal of the Operational Research Society, vol. 45, no. 5, pp. 567–578, 1994. View at Publisher · View at Google Scholar · View at Scopus
  35. J. R. Doyle and R. Green, “Cross-evaluation in DEA: improving discrimination among DMUs,” INFOR: Information Systems and Operational Research, vol. 33, no. 3, pp. 205–222, 1995. View at Google Scholar
  36. G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, and D. Akbarian, “Finding weak defining hyperplanes of PPS of the BCC model,” Applied Mathematical Modelling, vol. 34, no. 11, pp. 3321–3332, 2010. View at Publisher · View at Google Scholar · View at Scopus