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Farrell Revisited: Visualising the DEA Production Frontier

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Author Info

  • Førsund , Finn R.

    ()
    (Dept. of Economics, University of Oslo)

  • Kittelsen , Sverre A.

    (Ragnar Frisch Centre of Economic Research)

  • Krivonozhko , Vladimir E.

    (Institute for Systems Analysis)

Abstract

The contributions of the paper are threefold: i) compare with mathematical rigour the Charnes, Cooper, and Rhodes DEA model and the Farrell model exhibiting constant returns to scale, ii) reinterpret the contribution of Farrell and Fieldhouse that extended the analysis to variables returns to scale and establish the connection with the approach in Banker, Charnes and Cooper, iii) provide graphical visualisation of properties of the frontier function. Both papers by Farrell emphasised the importance of graphical visualisation of non-parametric frontier functions, but, to our knowledge, this is seldom followed up in the literature. We use a graphical package (EffiVision) with a numerical representation of the frontier functions, representing the contemporary development of visualisation. By making suitable cuts through the DEA frontier in multidimensional space, various graphical representations of features of economic interest can be done. Development of ray average cost function and scale elasticity are novel illustrations.

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File URL: http://www.sv.uio.no/econ/english/research/memorandum/pdf-files/2007/Memo-15-2007.pdf
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Bibliographic Info

Paper provided by Oslo University, Department of Economics in its series Memorandum with number 15/2007.

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Length: 31 pages
Date of creation: 01 Feb 2007
Date of revision:
Publication status: Published in Journal of the Operational Research Society, 2009, pages 1535-1545.
Handle: RePEc:hhs:osloec:2007_015

Contact details of provider:
Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway
Phone: 22 85 51 27
Fax: 22 85 50 35
Email:
Web page: http://www.oekonomi.uio.no/indexe.html
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Related research

Keywords: Farrell efficiency measure; DEA; variable returns to scale; visualisation; grouping method;

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References

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  1. Førsund, Finn R. & Hjalmarsson, Lennart, 2002. "Are all Scales Optimal in DEA? Theory and Empirical Evidence," Working Papers in Economics 66, University of Gothenburg, Department of Economics.
  2. Finn Førsund & Nikias Sarafoglou, 2002. "On the Origins of Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 17(1), pages 23-40, January.
  3. Forsund, Finn R & Hjalmarsson, Lennart, 1979. "Generalised Farrell Measures of Efficiency: An Application to Milk Processing in Swedish Dairy Plants," Economic Journal, Royal Economic Society, vol. 89(354), pages 294-315, June.
  4. Finn Førsund & Lennart Hjalmarsson & Vladimir Krivonozhko & Oleg Utkin, 2007. "Calculation of scale elasticities in DEA models: direct and indirect approaches," Journal of Productivity Analysis, Springer, vol. 28(1), pages 45-56, October.
  5. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
  6. Førsund, Finn R. & Sarafoglou, Nikias, 2003. "The Tale of two Research Communities: The Diffusion of Research on Productive Efficiency," Memorandum 08/2003, Oslo University, Department of Economics.
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Citations

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Cited by:
  1. Halkos, George & Tzeremes, Nickolaos, 2011. "Applying conditional DEA to measure football clubs’ performance: Evidence from the top 25 European clubs," MPRA Paper 31278, University Library of Munich, Germany.
  2. Halkos, George & Tzeremes, Nickolaos, 2012. "Evaluating professional tennis players’ career performance: A Data Envelopment Analysis approach," MPRA Paper 41516, University Library of Munich, Germany.
  3. Krivonozhko, Vladimir & R. Førsund, Finn & V. Lychev, Andrey, 2011. "Terminal units in DEA: Definition and Determination," Memorandum 04/2011, Oslo University, Department of Economics.
  4. Halkos, George & Tzeremes, Nickolaos, 2012. "Ranking the ‘Diamond Core’ economic journals: A note," MPRA Paper 36589, University Library of Munich, Germany.
  5. Halkos, George & Tzeremes, Nickolaos, 2011. "A non-parametric analysis of the efficiency of the top European football clubs," MPRA Paper 31173, University Library of Munich, Germany.
  6. Halkos, George & Tzeremes, Nickolaos, 2011. "Measuring economic journals’ citation efficiency: A data envelopment analysis approach," MPRA Paper 29893, University Library of Munich, Germany.
  7. Krivonozhko, Vladimir E. & Førsund, Finn R. & Lychev, Andrey V., 2012. "Identifying Suspicious Efficient Units in DEA Models," Memorandum 30/2012, Oslo University, Department of Economics.
  8. Krivonozhko, Vladimir E. & Førsund, Finn R. & Lychev, Andrey V., 2012. "Measurement of Returns to Scale Using Non-Radial DEA Models," Memorandum 29/2012, Oslo University, Department of Economics.
  9. Halkos, George & Tzeremes, Nickolaos, 2011. "A nonparametric analysis of the Greek renewable energy sector," MPRA Paper 30467, University Library of Munich, Germany.

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