Table of Contents Author Guidelines Submit a Manuscript
Advances in Operations Research
Volume 2014, Article ID 431749, 9 pages
http://dx.doi.org/10.1155/2014/431749
Research Article

Benchmarking in Data Envelopment Analysis: An Approach Based on Genetic Algorithms and Parallel Programming

Center of Operations Research (CIO), University Miguel Hernandez of Elche, Avenida de la Universidad s/n, 03202 Elche (Alicante), Spain

Received 20 October 2013; Accepted 28 December 2013; Published 13 February 2014

Academic Editor: Shangyao Yan

Copyright © 2014 Juan Aparicio et al. 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. T. Coelli, D. S. P. Rao, and G. E. Battese, An Introduction to EffiCiency and Productivity Analysis, Kluwer Academic, 1998.
  2. W. W. Cooper, L. M. Seiford, and K. Tone, Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver software, Kluwer Academic, Boston, Mass, USA, 2000.
  3. J. Aparicio, J. L. Ruiz, and I. Sirvent, “Closest targets and minimum distance to the Pareto-efficient frontier in DEA,” Journal of Productivity Analysis, vol. 28, pp. 209–218, 2007. View at Google Scholar
  4. M. C. A. S. Portela, P. C. Borges, and E. Thanassoulis, “Finding xlosest targets in non-oriented DEA models: the case of convex and non-convex technologies,” Journal of Productivity Analysis, vol. 19, pp. 251–269, 2003. View at Google Scholar
  5. A. Amirteimoori and S. Kordrostami, “A Euclidean distance-based measure of efficiency in data envelopment analysis,” Optimization, vol. 59, no. 7, pp. 985–996, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  6. J. Aparicio and J. T. Pastor, “On how to properly calculate the Euclidean distance-based measure in DEA,” Optimization, 2012. View at Publisher · View at Google Scholar
  7. J. T. Pastor and J. Aparicio, “The relevance of DEA benchmarking information and the least-distance measure: comment,” Mathematical and Computer Modelling, vol. 52, no. 1-2, pp. 397–399, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  8. F. X. Frei and P. T. Harker, “Projections onto efficient frontiers: theoretical and computational extensions to DEA,” Journal of Productivity Analysis, vol. 11, pp. 275–300, 1999. View at Google Scholar
  9. E. Gonzalez and A. Alvarez, “From efficiency measurement to efficiency improvement: the choice of a relevant benchmark,” European Journal of Operational Research, vol. 133, pp. 512–520, 2001. View at Google Scholar
  10. C. Baek and J.-d. Lee, “The relevance of DEA benchmarking information and the least-distance measure,” Mathematical and Computer Modelling, vol. 49, no. 1-2, pp. 265–275, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  11. G. R. Jahanshahloo, J. Vakili, and S. M. Mirdehghan, “Using the minimum distance of DMUs from the frontier of the PPS for evaluating group performance of DMUs in DEA,” Asia-Pacific Journal of Operational Research, vol. 29, no. 2, Article ID 1250010, 25 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. W. Briec, “Hölder distance functions and measurement of technical efficiency,” Journal of Productivity Analysis, vol. 11, pp. 111–131, 1998. View at Google Scholar
  13. W. Briec and J. B. Lesourd, “Metric distance function and profit: some duality results,” Journal of Optimization Theory and Applications, vol. 101, no. 1, pp. 15–33, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  14. W. Briec and B. Lemaire, “Technical efficiency and distance to a reverse convex set,” European Journal of Operational Research, vol. 114, pp. 178–187, 1999. View at Google Scholar
  15. T. Coelli, “A multi-stage methodology for the solution of orientated DEA models,” Operations Research Letters, vol. 23, no. 3–5, pp. 143–149, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. L. Cherchye and T. Van Puyenbroeck, “A comment on multi-stage DEA methodology,” Operations Research Letters, vol. 28, no. 2, pp. 93–98, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. S. Lozano and G. Villa, “Determining a sequence of targets in DEA,” Journal of Operational Research Society, vol. 56, pp. 1439–1447, 2005. View at Google Scholar
  18. A. Charnes, J. J. Rousseau, and J. H. Semple, “Sensitivity and stability of efficiency classiffications in data envelopment analysis,” Journal of Productivity Analysis, vol. 7, pp. 5–18, 1996. View at Google Scholar
  19. A. Takeda and H. Nishino, “On measuring the inefficiency with the inner-product norm in data envelopment analysis,” European Journal of Operational Research, vol. 133, no. 2, pp. 377–393, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, and M. Zohrehbandian, “Finding the piecewise linear frontier production function in data envelopment analysis,” Applied Mathematics and Computation, vol. 163, no. 1, pp. 483–488, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, H. Zhiani Rezai, and F. Rezai Balf, “Finding strong defining hyperplanes of production possibility set,” European Journal of Operational Research, vol. 177, no. 1, pp. 42–54, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. G. R. Jahanshahloo, J. Vakili, and M. Zarepisheh, “A linear bilevel programming problem for obtaining the closest targets and minimum distance of a unit from the strong efficient frontier,” Asia-Pacific Journal of Operational Research, vol. 29, no. 2, Article ID 1250011, 19 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. W. D. Cook and L. M. Seiford, “Data envelopment analysis (DEA)—thirty years on,” European Journal of Operational Research, vol. 192, no. 1, pp. 1–17, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. M. J. Farrell, “The measurement of productive efficiency,” Journal of the Royal Statistical Society A, vol. 120, pp. 253–281, 1957. View at Google Scholar
  25. 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
  26. 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, pp. 1078–1092, 1984. View at Google Scholar
  27. J. T. Pastor, J. L. Ruiz, and I. Sirvent, “An enhanced DEA russell graph efficiency measure,” European Journal of Operational Research, vol. 115, pp. 596–607, 1999. View at Google Scholar
  28. K. Tone, “A slacks-based measure of efficiency in data envelopment analysis,” European Journal of Operational Research, vol. 130, no. 3, pp. 498–509, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. M. Mitchell, An Introduction to Genetic Algorithm, MIT Press, 1998.
  30. E. Burke, E. Hart, G. Kendall, J. Newall, P. Ross, and S. Schulenburg, “Hyperheuristics: an emerging direction in modern search technology,” KHandbook of Metaheuristics, vol. 16, pp. 457–474, 2003. View at Google Scholar
  31. R. Chandra, R. Menon, and L. Dagum, Parallel Programming in OpenMP, Operations Morgan Kauffman, 2001.
  32. J. J. Dongarra, J. Du Croz, S. Hammarling, and R. J. Hanson, “An extended set of FORTRAN basic linear algebra subroutines,” ACM Transactions on Mathematical Software, vol. 14, pp. 1–17, 1988. View at Google Scholar
  33. E. Anderson, Z. Bai, C. Bischof, J. Demmel, and J. J. Dongarra, LAPACK User's Guide, Society for Industrial and Applied Mathematics, 1995.
  34. R. Clinton Whaley, A. Petitet, and J. Dongarra, “Automated empirical optimizations of software and the ATLAS project,” Parallel Computing, vol. 27, pp. 3–35, 2001. View at Google Scholar