Kybernetika 49 no. 4, 619-635, 2013

Finding target units in FDH model by least-distance measure model

Ali Ebrahimnejad, Reza Shahverdi, Farzad Rezaee Balf and Maryam Hatefi


Recently, some authors used the Least-Distance Measure model in order to obtain the shortest distance between the evaluated Decision Making Unit (DMU) and the strongly efficient production frontier. But, their model is not applicable for situation in which the production possibility set satisfies free disposability property. In this paper, we propose a new approach to this end in FDH model which improves the application potential of the Least-Distance Measure and overcomes the mentioned shortcoming. The applicability of the proposed method is illustrated with two numerical examples and proves to be persuasive and acceptable to real-world problem.


data envelopment analysis, least distance, FDH, target unit


90C05, 90BXX


  1. C. Baek and J. Lee: The relevance of DEA benchmarking information and the least-distance measure. Math. Comput. Modelling 49 (2009), 265-275.   CrossRef
  2. P. Bogetoft and J. L. Hougaard: Efficiency evaluations based on potential (non-proportional) improvements. J. Productivity Anal. 12 (1998), 233-249.   CrossRef
  3. P. Bogetoft and K. Nielsen: Internet based benchmarking. Group Decision and Negotiation 14 (2005), 195-215.   CrossRef
  4. A. Charnes, W. Cooper and E. Rhodes: Measuring the efficiency of decision making units. European J. Oper. Res. 2 (1978), 429-444.   CrossRef
  5. L. Cherchye and T. V. Puyenbroeck: A comment on multi-stage DEA methodology. Oper. Res. Lett. 28 (2001), 93-98.   CrossRef
  6. T. Coelli: A multi-stage methodology and for the solution of oriented DEA models. Oper. Res. Lett. 23 (1998), 143-149.   CrossRef
  7. W. W. Cooper, K. S. Park, J. T. Pastor and RAM: A range adjusted measure of inefficiency for use with additive models and relations to other models and measures in DEA. J. Productivity Anal. 11 (1999), 5-42.   CrossRef
  8. D. Deprins, L. Simar and H. Tulkens: Measuring labor inefficiency in post offices. In: The Performance of Public Enterprises: Concepts and Measurements (M. Marchand, P. Pestieau, and H. Tulkens, eds.), North-Holland, Amsterdam 1984.   CrossRef
  9. M. P. Estellita Lins, L. Angulo-Meza and A. C. Moreira da Silva: A multi-objective approach to determine alternative targets in data envelopment analysis. J. Oper. Res. Soc. 55 (2004), 1090-1101.   CrossRef
  10. A. Ebrahimnejad and F. Hosseinzadeh Lotfi: Equivalence relationship between the general combined-oriented CCR model and the weighted minimax MOLP formulation. J. King Saud Univ. Sci. 24 (2012), 47-54.   CrossRef
  11. F. X. Frei and P. T. Harker: Projections onto efficient frontier: Theoretical and computational extension to DEA. J. Productivity Anal. 11 (1999), 275-300.   CrossRef
  12. B. Golany: An interactive MOLP procedure for the extension of DEA to effectiveness analysis. J. Oper. Res. Soc. 39 (1988), 725-734.   CrossRef
  13. E. González and A. Álvarez: From efficiency measurement to efficiency improvement: The choice of a relevant benchmark. European J. Oper. Res. 133 (2001), 512-520.   CrossRef
  14. X. B. Li and G. R. Reeves: A multiple criteria approach to data envelopment analysis. European J. Oper. Res. 115 (1999), 507-517.   CrossRef
  15. J. T. Pastor and J. Aparicio: The relevance of DEA benchmarking information and the least-distance measure: Comment. Math. Comput. Modelling 52 (2010), 397-399.   CrossRef
  16. M. C. A. S. Portela, P. C. Borges and E. Thanassoulis: Finding closest targets in non-oriented DEA models: The case of convex and non-convex technology. J. Productivity Anal. 19 (2003), 251-269.   CrossRef
  17. T. Post and J. Spronk: Performance benchmarking using interactive data envelopment analysis. European J. Oper. Res. 115 (1999), 472-487.   CrossRef
  18. E. Thanassoulis and R. G. Dyson: Estimating preferred target input output levels using data envelopment analysis. European J. Oper. Res. 56 (1992), 80-97.   CrossRef
  19. K. Tone: A slack-based measure of efficient in data envelopment analysis. European J. Oper. Res. 130 (2001), 498-509.   CrossRef
  20. J. B. Yang, B. Y. Wang, D. L. Xu and T. Stewart: Integrating DEA-oriented performance assessment and target setting using interactive MOLP methods. European J. Oper. Res. 195 (2009), 205-222.   CrossRef