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A variant of radial measure capable of dealing with negative inputs and outputs in data envelopment analysis

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  • Cheng, Gang
  • Zervopoulos, Panagiotis
  • Qian, Zhenhua

Abstract

Data envelopment analysis (DEA) is a linear programming methodology to evaluate the relative technical efficiency for each member of a set of peer decision making units (DMUs) with multiple inputs and multiple outputs. It has been widely used to measure performance in many areas. A weakness of the traditional DEA model is that it cannot deal with negative input or output values. There have been many studies exploring this issue, and various approaches have been proposed. In this paper, we develop a variant of the traditional radial model whereby original values are replaced with absolute values as the basement to quantify the proportion of improvements to reach the frontier. The new radial measure is units invariant and can deal with all cases of the presence of negative data. In addition, the VRM model preserves the property of proportionate improvement of a traditional radial model, and provides the exact same results in the cases that the traditional radial model can deal with. Examples show the advantages of the new approach.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 30951.

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Date of creation: 17 May 2011
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Handle: RePEc:pra:mprapa:30951

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Keywords: Data Envelopment Analysis; Negative data in DEA; Variant of radial measure; Unit invariance;

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  1. Seiford, Lawrence M. & Zhu, Joe, 2002. "Modeling undesirable factors in efficiency evaluation," European Journal of Operational Research, Elsevier, Elsevier, vol. 142(1), pages 16-20, October.
  2. Emrouznejad, Ali & Anouze, Abdel Latef & Thanassoulis, Emmanuel, 2010. "A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA," European Journal of Operational Research, Elsevier, Elsevier, vol. 200(1), pages 297-304, January.
  3. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, Elsevier, vol. 2(6), pages 429-444, November.
  4. Lamb, John D. & Tee, Kai-Hong, 2012. "Data envelopment analysis models of investment funds," European Journal of Operational Research, Elsevier, Elsevier, vol. 216(3), pages 687-696.
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  6. Scheel, Holger, 2001. "Undesirable outputs in efficiency valuations," European Journal of Operational Research, Elsevier, Elsevier, vol. 132(2), pages 400-410, July.
  7. Emrouznejad, Ali & Amin, Gholam R. & Thanassoulis, Emmanuel & Anouze, Abdel Latef, 2010. "On the boundedness of the SORM DEA models with negative data," European Journal of Operational Research, Elsevier, Elsevier, vol. 206(1), pages 265-268, October.
  8. Shawna Grosskopf & Kathy J. Hayes & Lori L. Taylor & William L. Weber, 1999. "Anticipating the Consequences of School Reform: A New Use of DEA," Management Science, INFORMS, INFORMS, vol. 45(4), pages 608-620, April.
  9. Portela, Maria Conceicao A. Silva & Thanassoulis, Emmanuel, 2007. "Comparative efficiency analysis of Portuguese bank branches," European Journal of Operational Research, Elsevier, Elsevier, vol. 177(2), pages 1275-1288, March.
  10. Charnes, A. & Cooper, W. W. & Golany, B. & Seiford, L. & Stutz, J., 1985. "Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions," Journal of Econometrics, Elsevier, Elsevier, vol. 30(1-2), pages 91-107.
  11. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, Elsevier, vol. 70(2), pages 407-419, August.
  12. Edirisinghe, N.C.P. & Zhang, X., 2007. "Generalized DEA model of fundamental analysis and its application to portfolio optimization," Journal of Banking & Finance, Elsevier, Elsevier, vol. 31(11), pages 3311-3335, November.
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Cited by:
  1. Kerstens, Kristiaan & Van de Woestyne, Ignace, 2014. "A note on a variant of radial measure capable of dealing with negative inputs and outputs in DEA," European Journal of Operational Research, Elsevier, Elsevier, vol. 234(1), pages 341-342.
  2. Cordero Ferrera, Jose Manuel & Alonso Morán, Edurne & Nuño Solís, Roberto & Orueta, Juan F. & Souto Arce, Regina, 2013. "Efficiency assessment of primary care providers: A conditional nonparametric approach," MPRA Paper 51926, University Library of Munich, Germany.

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