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Convex Input and Output Projections of Nonconvex Production Possibility Sets

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Author Info

  • Peter Bogetoft

    ()
    (Department of Economics and Natural Resources, The Royal Veterinary and Agricultural University, Rolighedsvej 26, 1958 Frederiksberg C, Denmark)

  • Joseph M. Tama

    ()
    (Management Department, College of Business Administration, University of Notre Dame, P. O. Box 399, Notre Dame, Indiana 46556-0399)

  • Jørgen Tind

    ()
    (Department of Operations Research, Institute for Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark)

Abstract

In this paper we characterize the smallest production possibility set that contains a specified set of (input, output) combinations. In accordance with neoclassical production economics, this possibility set has convex projections into the input and output spaces (convex isoquants), and it satisfies the assumption of free disposability. We obtain it by means of a possibly infinite recursion which builds the possibility set as an ever larger union of convex sets. We remark on the nature of the approximations obtained by truncating the recursion, and we obtain a necessary and sufficient condition, checkable in one iteration for the recursion to stop in the next. For the case in which the recursion stops, we provide a succinct characterization of the dominance relations among the constituent sets produced by the procedure. Finally, we present examples of both finite and infinite cases. The example for the finite case illustrates the construction of the possibility set along with its associated production and consumption sets.

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File URL: http://dx.doi.org/10.1287/mnsc.46.6.858.11938
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 46 (2000)
Issue (Month): 6 (June)
Pages: 858-869

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Handle: RePEc:inm:ormnsc:v:46:y:2000:i:6:p:858-869

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Related research

Keywords: data envelopment analysis; convexity;

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Cited by:
  1. Bogetoft, Peter & Fare, Rolf, 1999. "Allocative Efficiency of Technically Inefficient Production Units," Unit of Economics Working papers 24217, Royal Veterinary and Agricultural University, Food and Resource Economic Institute.
  2. Park, K. Sam & Park, Kwangtae, 2009. "Measurement of multiperiod aggregative efficiency," European Journal of Operational Research, Elsevier, vol. 193(2), pages 567-580, March.
  3. Kuosmanen, Timo, 2001. "DEA with efficiency classification preserving conditional convexity," European Journal of Operational Research, Elsevier, vol. 132(2), pages 326-342, July.
  4. Post, Thierry, 2001. "Estimating non-convex production sets - imposing convex input sets and output sets in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 131(1), pages 132-142, May.
  5. Anne-Kathrin Last & Heike Wetzel, 2009. "Effizienzmessverfahren – eine Einführung," Working Paper Series in Economics 145, University of Lüneburg, Institute of Economics.
  6. Podinovski, Victor V. & Kuosmanen, Timo, 2011. "Modelling weak disposability in data envelopment analysis under relaxed convexity assumptions," European Journal of Operational Research, Elsevier, vol. 211(3), pages 577-585, June.
  7. Agrell, Per J. & Bogetoft, Peter & Tind, Jorgen, 2000. "Polarity in DEA Models," Unit of Economics Working papers 24188, Royal Veterinary and Agricultural University, Food and Resource Economic Institute.
  8. Cinzia Daraio & Léopold Simar, 2007. "Conditional nonparametric frontier models for convex and nonconvex technologies: a unifying approach," Journal of Productivity Analysis, Springer, vol. 28(1), pages 13-32, October.
  9. Botti, Laurent & Briec, Walter & Cliquet, Gérard, 2009. "Plural forms versus franchise and company-owned systems: A DEA approach of hotel chain performance," Omega, Elsevier, vol. 37(3), pages 566-578, June.
  10. Brandon Pope & Andrew Johnson, 2013. "Returns to scope: a metric for production synergies demonstrated for hospital production," Journal of Productivity Analysis, Springer, vol. 40(2), pages 239-250, October.
  11. Hougaard, Jens Leth & Tind, Jørgen, 2009. "Cost allocation and convex data envelopment," European Journal of Operational Research, Elsevier, vol. 194(3), pages 939-947, May.
  12. Ehrgott, Matthias & Tind, Jørgen, 2009. "Column generation with free replicability in DEA," Omega, Elsevier, vol. 37(5), pages 943-950, October.
  13. Podinovski, V. V., 2005. "Selective convexity in DEA models," European Journal of Operational Research, Elsevier, vol. 161(2), pages 552-563, March.
  14. Cherchye, L. & Post, G.T., 2001. "Methodological Advances in Dea," ERIM Report Series Research in Management ERS-2001-53-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus Uni.

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