Slacks-Based Efficiency Measures

  • Chiang Kao
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 240)


The output–input ratio and radial distance function measures discussed in the preceding two chapters are essentially the same approach expressed in different forms, bearing the primal-dual relationship. The basic idea is to measure the relative distance between the DMU being evaluated and its projection on the production frontier along the ray from the origin pointing at the DMU. The efficiencies are thus radial measures. In contrast, there are also non-radial measures, and slacks-based measures are the major branch of these.


  1. Ali A, Seiford LM (1990) Translation invariance in data envelopment analysis. Oper Res Lett 9:403–405CrossRefGoogle Scholar
  2. Aparicio J, Pastor JT (2013) A well-defined efficiency measure for dealing with closest targets in DEA. Appl Math Comput 219:9142–9154Google Scholar
  3. Arabi B, Munisamy S, Emrouznejad A (2015) A new slacks-based measure of Malmquist-Luenberger index in the presence of undesirable outputs. Omega 51:29–37CrossRefGoogle Scholar
  4. Avkiran NK, Tone K, Tsutsui M (2008) Bridging radial and non-radial measures of efficiency in DEA. Ann Oper Res 164:127–138CrossRefGoogle Scholar
  5. Azadi M, Saen RF (2011) Developing an output-oriented super slacks-based measure model with an application to third-party reverse logistics providers. J Multi-Criteria Decis Anal 18:267–277CrossRefGoogle Scholar
  6. Azizi H, Kordrostami S, Amirteimoori A (2015) Slacks-based measures of efficiency in imprecise data envelopment analysis: an approach based on data envelopment analysis with double frontiers. Comput Ind Eng 79:42–51CrossRefGoogle Scholar
  7. Banker RD, Cooper WW (1994) Validation and generalization of DEA and its uses. TOP 2:249–314CrossRefGoogle Scholar
  8. Briec W (2000) An extended Färe-Lovell technical efficiency measure. Int J Prod Econ 65:191–199CrossRefGoogle Scholar
  9. Charnes A, Cooper WW (1962) Programming with linear fractionals. Nav Res Logist Q 9:181–186CrossRefGoogle Scholar
  10. Charnes A, Cooper WW, Golany B, Seiford LM, Stutz J (1985) Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production function. J Econ 30:91–107CrossRefGoogle Scholar
  11. Chen CM (2013) Super efficiencies or super inefficiencies? Insights from a joint computation model for slacks-based measures in DEA. Eur J Oper Res 226:258–267CrossRefGoogle Scholar
  12. Cooper WW, Park KS, Pastor JT (1999) RAM: a range adjusted measure of inefficiency for use with additive models, and relations to other models and measures in DEA. J Prod Anal 11:5–42CrossRefGoogle Scholar
  13. Cooper WW, Pastor JT, Aparicio J, Borras F (2011a) Decomposing profit inefficiency in DEA through the weighted additive model. Eur J Oper Res 212:411–416CrossRefGoogle Scholar
  14. Cooper WW, Pastor JT, Borras F, Aparicio J, Pastor D (2011b) BAM: a bounded adjusted measure of efficiency for use with bounded additive models. J Prod Anal 35:85–94CrossRefGoogle Scholar
  15. De Borger B, Kerstens K (1996) Radial and nonradial measures of technical efficiency: an empirical illustration for Belgian local governments using an FDH reference technology. J Prod Anal 7:41–62CrossRefGoogle Scholar
  16. Emrouznejad A, Anouze AL, Thanassoulis E (2010) A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA. Eur J Oper Res 200:297–304CrossRefGoogle Scholar
  17. Fang HH, Lee HS, Hwang SN, Chung CC (2013) A slacks-based measure of super-efficiency in data envelopment analysis: an alternative approach. Omega 41:731–734CrossRefGoogle Scholar
  18. Färe R, Grosskopf S (2010) Directional distance functions and slacks-based measures of efficiency. Eur J Oper Res 200:320–322CrossRefGoogle Scholar
  19. Färe R, Grosskopf S, Lovell CAK (1985) The measurement of efficiency of production. Kluwer-Nijhoff, DordrechtCrossRefGoogle Scholar
  20. Färe R, Grosskopf S, Whittaker G (2013) Directional output distance functions: endogenous directions based on exogenous normalization constraints. J Prod Anal 40:267–269CrossRefGoogle Scholar
  21. Färe R, Lovell CAK (1978) Measuring the technical efficiency of production. J Econ Theory 19:150–162CrossRefGoogle Scholar
  22. Färe R, Lovell CAK, Zieschang K (1983) Measuring the technical efficiency of multiple outputs technologies. In: Eichhorn W, Henn R, Neumann K, Shephard RW (eds) Quantitative studies on production and prices. Physica-Verlag, Würzburg and ViennaGoogle Scholar
  23. Levkoff SB, Russell RR, Schworm W (2012) Boundary problems with the “Russell” graph measure of technical efficiency: a refinement. J Prod Anal 37:239–248CrossRefGoogle Scholar
  24. Mahlberg B, Sahoo BK (2011) Radial and non-radial decompositions of Luenberger productivity indicator with an illustrative application. Int J Prod Econ 131:721–726CrossRefGoogle Scholar
  25. Mirsalehy A, Abu Bakar MR, Jahanshahloo GR, Lotfi FH, Lee LS (2014) Centralized resource allocation for connecting radial and nonradial models. J Appl Math 2014:1–12. doi: 10.1155/2014/974075 CrossRefGoogle Scholar
  26. Morita H, Hirokawa K, Zhu J (2005) A slacks-based measure of efficiency in context-dependent data envelopment analysis. Omega 33:357–362CrossRefGoogle Scholar
  27. Pastor JT, Ruiz JL, Sirvent I (1999) An enhanced DEA Russell graph efficiency measure. Eur J Oper Res 115:596–607CrossRefGoogle Scholar
  28. Ruggiero J, Bretschneider S (1998) The weighted Russell measure of technical efficiency. Eur J Oper Res 108:438–451CrossRefGoogle Scholar
  29. Russell RR (1985) Measures of technical efficiency. J Econ Theory 35:109–126CrossRefGoogle Scholar
  30. Russell RR, Schworm W (2009) Axiomatic foundations of efficiency measurement on data-generated technologies. J Prod Anal 31:77–86CrossRefGoogle Scholar
  31. Sharp JA, Meng W, Liu W (2007) A modified slacks-based measure model for data envelopment analysis with ‘natural’ negative outputs and inputs. J Oper Res Soc 56:1672–1677CrossRefGoogle Scholar
  32. Steinmann L, Zweifel P (2001) The range adjusted measure (RAM) in DEA: comment. J Prod Anal 15:139–144CrossRefGoogle Scholar
  33. Sueyoshi T, Sekitani K (2007) Computational strategy for Russell measure in DEA: second-order cone programming. Eur J Oper Res 180:459–471CrossRefGoogle Scholar
  34. Tone K (2001) A slacks-based measure of efficiency in data envelopment analysis. Eur J Oper Res 130:498–509CrossRefGoogle Scholar
  35. Tone K (2002) A slacks-based measure of super-efficiency in data envelopment analysis. Eur J Oper Res 143:32–41CrossRefGoogle Scholar
  36. Tone K (2010) Variations on the theme of slacks-based measure of efficiency in DEA. Eur J Oper Res 200:901–907CrossRefGoogle Scholar
  37. Zhu J (1996) Data envelopment analysis with preference structure. J Oper Res Soc 47:136–150CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Chiang Kao
    • 1
  1. 1.Department of Industrial and Information ManagementNational Cheng Kung UniversityTainanTaiwan

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