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Farrell Revisited: Visualising the DEA Production Frontier

Author

Listed:
  • 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.

Suggested Citation

  • Førsund, Finn R. & Kittelsen, Sverre A. & Krivonozhko, Vladimir E., 2007. "Farrell Revisited: Visualising the DEA Production Frontier," Memorandum 15/2007, Oslo University, Department of Economics.
    • Handle: RePEc:hhs:osloec:2007_015
    as

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    File URL: http://www.sv.uio.no/econ/english/research/unpublished-works/working-papers/pdf-files/2007/Memo-15-2007.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. V E Krivonozhko & O B Utkin & A V Volodin & I A Sablin & M Patrin, 2004. "Constructions of economic functions and calculations of marginal rates in DEA using parametric optimization methods," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1049-1058, October.
    3. Finn Førsund & Nikias Sarafoglou, 2002. "On the Origins of Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 17(1), pages 23-40, January.
    4. 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.
    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. 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.
    7. 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.
    8. Wesley D. Seitz, 1970. "The Measurement of Efficiency Relative to a Frontier Production Function," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 52(4), pages 505-511.
    9. V E Krivonozhko & O B Utkin & A V Volodin & I A Sablin, 2005. "About the structure of boundary points in DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(12), pages 1373-1378, December.
    10. Seitz, Wesley D, 1971. "Productive Efficiency in the Steam-Electric Generating Industry," Journal of Political Economy, University of Chicago Press, vol. 79(4), pages 878-886, July-Aug..
    11. 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.
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    Cited by:

    1. Krivonozhko, Vladimir E. & Førsund, Finn R. & Lychev, Andrey V., 2014. "Measurement of returns to scale using non-radial DEA models," European Journal of Operational Research, Elsevier, vol. 232(3), pages 664-670.
    2. Halkos, George & Tzeremes, Nickolaos, 2012. "Ranking the ‘Diamond Core’ economic journals: A note," MPRA Paper 36589, University Library of Munich, Germany.
    3. George Emm Halkos & Nickolaos G. Tzeremes, 2011. "Measuring economic journals’ citation efficiency: a data envelopment analysis approach," Scientometrics, Springer;Akadémiai Kiadó, vol. 88(3), pages 979-1001, September.
    4. Vladimir Krivonozhko & Finn Førsund & Andrey Lychev, 2015. "Terminal units in DEA: definition and determination," Journal of Productivity Analysis, Springer, vol. 43(2), pages 151-164, April.
    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. Podinovski, Victor V. & Førsund, Finn R. & Krivonozhko, Vladimir E., 2009. "A simple derivation of scale elasticity in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 197(1), pages 149-153, August.
    7. Halkos, George E. & Tzeremes, Nickolaos G., 2012. "Analyzing the Greek renewable energy sector: A Data Envelopment Analysis approach," Renewable and Sustainable Energy Reviews, Elsevier, vol. 16(5), pages 2884-2893.
    8. 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.
    9. Krivonozhko, Vladimir E. & Førsund, Finn R. & Lychev, Andrey V., 2012. "A note on imposing strong complementary slackness conditions in DEA," European Journal of Operational Research, Elsevier, vol. 220(3), pages 716-721.
    10. Halkos, George & Tzeremes, Nickolaos, 2011. "A nonparametric analysis of the Greek renewable energy sector," MPRA Paper 30467, University Library of Munich, Germany.
    11. 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.
    12. Halkos, George & Tzeremes, Nickolaos, 2012. "Evaluating professional tennis players’ career performance: A Data Envelopment Analysis approach," MPRA Paper 41516, University Library of Munich, Germany.

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    More about this item

    Keywords

    Farrell efficiency measure; DEA; variable returns to scale; visualisation; grouping method;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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