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Returns-to-scale properties in DEA models: the fundamental role of interior points

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  • Vladimir Krivonozhko
  • Finn Førsund
  • Andrey Lychev

Abstract

Attempts can be found in the data envelopment analysis (DEA) literature to identify returns to scale at efficient interior points of a face on the basis of returns to scale at points of the corresponding reference sets of the production possibility set. The purpose of this paper is to show that only an interior point of a face can identify returns-to-scale properties of points lying on this face. We consider all possible cases of dispositions of faces from this point of view. Returns-to-scale properties of the corresponding reference units are then established. We also show that to find returns-to-scale at an interior point of a face is a much easier problem than to find all vertices of this face. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Vladimir Krivonozhko & Finn Førsund & Andrey Lychev, 2012. "Returns-to-scale properties in DEA models: the fundamental role of interior points," Journal of Productivity Analysis, Springer, vol. 38(2), pages 121-130, October.
    • Handle: RePEc:kap:jproda:v:38:y:2012:i:2:p:121-130
    DOI: 10.1007/s11123-011-0253-z
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    1. Starrett, David A, 1977. "Measuring Returns to Scale in the Aggregate, and the Scale Effect of Public Goods," Econometrica, Econometric Society, vol. 45(6), pages 1439-1455, September.
    2. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2009. "An occurrence of multiple projections in DEA-based measurement of technical efficiency: Theoretical comparison among DEA models from desirable properties," European Journal of Operational Research, Elsevier, vol. 196(2), pages 764-794, July.
    3. Banker, Rajiv D. & Thrall, R. M., 1992. "Estimation of returns to scale using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 62(1), pages 74-84, October.
    4. 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.
    5. 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.
    6. Banker, Rajiv D. & Cooper, William W. & Seiford, Lawrence M. & Thrall, Robert M. & Zhu, Joe, 2004. "Returns to scale in different DEA models," European Journal of Operational Research, Elsevier, vol. 154(2), pages 345-362, April.
    7. 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.
    8. Seiford, Lawrence M. & Thrall, Robert M., 1990. "Recent developments in DEA : The mathematical programming approach to frontier analysis," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 7-38.
    9. 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.
    10. 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.
    11. Hanoch, Giora, 1970. "Homotheticity in joint production," Journal of Economic Theory, Elsevier, vol. 2(4), pages 423-426, December.
    12. 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.
    13. John C. Panzar & Robert D. Willig, 1977. "Economies of Scale in Multi-Output Production," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(3), pages 481-493.
    14. William W. Cooper & Lawrence M. Seiford & Kaoru Tone, 2006. "Introduction to Data Envelopment Analysis and Its Uses," Springer Books, Springer, number 978-0-387-29122-2, December.
    15. 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.
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    1. 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.
    2. 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.
    3. Mehdiloozad, Mahmood & Mirdehghan, S. Morteza & Sahoo, Biresh K. & Roshdi, Israfil, 2015. "On the identification of the global reference set in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 245(3), pages 779-788.

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    More about this item

    Keywords

    Returns to scale; DEA; Interior points; Vertices; C61; D20;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D20 - Microeconomics - - Production and Organizations - - - General

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