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

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Author Info

  • 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

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Bibliographic Info

Article provided by Springer in its journal Journal of Productivity Analysis.

Volume (Year): 38 (2012)
Issue (Month): 2 (October)
Pages: 121-130

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Handle: RePEc:kap:jproda:v:38:y:2012:i:2:p:121-130

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Web page: http://www.springerlink.com/link.asp?id=100296

Related research

Keywords: Returns to scale; DEA; Interior points; Vertices; C61; D20;

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References

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  1. Hanoch, Giora, 1970. "Homotheticity in joint production," Journal of Economic Theory, Elsevier, vol. 2(4), pages 423-426, December.
  2. 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.
  3. 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.
  4. Panzar, John C & Willig, Robert D, 1977. "Economies of Scale in Multi-Output Production," The Quarterly Journal of Economics, MIT Press, vol. 91(3), pages 481-93, August.
  5. 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.
  6. 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.
  7. 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.
  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.
  9. 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.
  10. 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.
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Cited by:
  1. 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.
  2. 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.

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