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Farrell revisited–Visualizing properties of DEA production frontiers

Author

Listed:
  • F R Førsund

    (University of Oslo)

  • S A C Kittelsen

    (The Frisch Centre)

  • V E Krivonozhko

    (Institute for Systems Analysis)

Abstract

The contributions of the paper are threefold: (i) compare with mathematical rigour the data envelopment analysis (DEA) model of Charnes, Cooper, and Rhodes 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, and (iii) provide graphical visualization of properties of the frontier function. Both papers by Farrell emphasized the importance of graphical visualization 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 visualization. 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 plots are novel illustrations.

Suggested Citation

  • F R Førsund & S A C Kittelsen & V E Krivonozhko, 2009. "Farrell revisited–Visualizing properties of DEA production frontiers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1535-1545, November.
    • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:11:d:10.1057_jors.2008.185
    DOI: 10.1057/jors.2008.185
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    References listed on IDEAS

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    1. Finn Førsund & Nikias Sarafoglou, 2002. "On the Origins of Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 17(1), pages 23-40, January.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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..
    10. Patricio Meller, 1976. "Efficiency Frontiers for Industrial Establishments of Different Sizes," NBER Chapters, in: Explorations in Economic Research, Volume 3, number 3, pages 379-407, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Victor V. Podinovski & Finn R. Førsund, 2010. "Differential Characteristics of Efficient Frontiers in Data Envelopment Analysis," Operations Research, INFORMS, vol. 58(6), pages 1743-1754, December.
    2. Førsund, Finn R., 2018. "Economic interpretations of DEA," Socio-Economic Planning Sciences, Elsevier, vol. 61(C), pages 9-15.
    3. K. Tone & M. Tsutsui, 2015. "How to Deal with Non-Convex Frontiers in Data Envelopment Analysis," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 1002-1028, September.

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