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Farrell Revisited: Visualising the DEA Production Frontier

  • 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)

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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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
Web page:

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  1. Forsund,F.R. & Sarafoglou,N., 2000. "On the origins of data envelopment analysis," Memorandum 24/2000, Oslo University, Department of Economics.
  2. Førsund, Finn R. & Hjalmarsson, Lennart, 1978. "Generalized Farrell Measures of Efficiency: An Application to Milk Processing in Swedish Dairy Plants," Working Paper Series 17, Research Institute of Industrial Economics.
  3. Seitz, Wesley D, 1971. "Productive Efficiency in the Steam-Electric Generating Industry," Journal of Political Economy, University of Chicago Press, vol. 79(4), pages 878-86, July-Aug..
  4. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
  5. Finn Førsund & Lennart Hjalmarsson, 2004. "Are all Scales Optimal in DEA? Theory and Empirical Evidence," Journal of Productivity Analysis, Springer, vol. 21(1), pages 25-48, January.
  6. Forsund, Finn R. & Sarafoglou, Nikias, 2005. "The tale of two research communities: The diffusion of research on productive efficiency," International Journal of Production Economics, Elsevier, vol. 98(1), pages 17-40, October.
  7. 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.
  8. 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.
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