IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v196y2009i2p764-794.html
   My bibliography  Save this article

An occurrence of multiple projections in DEA-based measurement of technical efficiency: Theoretical comparison among DEA models from desirable properties

Author

Listed:
  • Sueyoshi, Toshiyuki
  • Sekitani, Kazuyuki

Abstract

This study discusses nine desirable properties that a measure of technical efficiency (TE) needs to satisfy from the perspective of production economics and optimization. Seven data envelopment analysis (DEA) models are theoretically compared from a viewpoint of nine TE criteria. All the seven DEA models suffer from a problem of multiple projections even though a unique projection for efficiency comparison is one of the nine desirable properties. Furthermore, all the DEA models violate the property on aggregation of inputs and outputs. Thus, the seven DEA models do not satisfy all desirable TE properties. In addition, the comparison provides us with the following guidelines: (a) The additive model violates all desirable TE properties. (b) Russell measure and SBM (=ERGM) perform as well as RAM as a non-radial measure. If we are interested in strict monotonicity, the two models outperform the other DEA models including RAM. In contrast, if we are interested in translation invariance, RAM is better than Russell measure and SBM (=ERGM). (c) The radial measures (CCR and BCC) have the property of linear homogeneity. (d) The CCR model is useful for measuring a frontier shift among different periods. (e) If a data set contains a negative value, RAM becomes a DEA model to handle the negative value because it has the property of translation invariance. After examining the desirable TE properties, this study proposes a new approach to deal with an occurrence of multiple projections. The proposed approach includes a test to examine an occurrence of multiple projections, a mathematical expression of a projection set, and a selection process of a unique reference set as the largest one covering all the possible reference sets.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:196:y:2009:i:2:p:764-794
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00172-0
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cooper, William W. & Ruiz, Jose L. & Sirvent, Inmaculada, 2007. "Choosing weights from alternative optimal solutions of dual multiplier models in DEA," European Journal of Operational Research, Elsevier, vol. 180(1), pages 443-458, July.
    2. Sueyoshi, Toshiyuki, 2001. "Extended DEA-Discriminant Analysis," European Journal of Operational Research, Elsevier, vol. 131(2), pages 324-351, June.
    3. Dmitruk, Andrei V. & Koshevoy, Gleb A., 1991. "On the existence of a technical efficiency criterion," Journal of Economic Theory, Elsevier, vol. 55(1), pages 121-144, October.
    4. Fukuyama, Hirofumi, 2000. "Returns to scale and scale elasticity in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 125(1), pages 93-112, August.
    5. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2007. "The measurement of returns to scale under a simultaneous occurrence of multiple solutions in a reference set and a supporting hyperplane," European Journal of Operational Research, Elsevier, vol. 181(2), pages 549-570, September.
    6. Wei, Quanling & Yu, Gang, 1997. "Analyzing properties of K-cones in the generalized data envelopment analysis model," Journal of Econometrics, Elsevier, vol. 80(1), pages 63-84, September.
    7. Cooper, W.W. & Huang, Zhimin & Li, Susan X. & Parker, Barnett R. & Pastor, Jesus T., 2007. "Efficiency aggregation with enhanced Russell measures in data envelopment analysis," Socio-Economic Planning Sciences, Elsevier, vol. 41(1), pages 1-21, March.
    8. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2005. "Returns to scale in dynamic DEA," European Journal of Operational Research, Elsevier, vol. 161(2), pages 536-544, March.
    9. Charles Blackorby & R. Russell, 1999. "Aggregation of Efficiency Indices," Journal of Productivity Analysis, Springer, vol. 12(1), pages 5-20, August.
    10. Robert Russell, R., 1990. "Continuity of measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 51(2), pages 255-267, August.
    11. Maria Portela & Emmanuel Thanassoulis, 2006. "Malmquist Indexes Using a Geometric Distance Function (GDF). Application to a Sample of Portuguese Bank Branches," Journal of Productivity Analysis, Springer, vol. 25(1), pages 25-41, April.
    12. Robert Thrall, 2000. "Measures in DEA with an Application to the Malmquist Index," Journal of Productivity Analysis, Springer, vol. 13(2), pages 125-137, March.
    13. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2007. "Measurement of returns to scale using a non-radial DEA model: A range-adjusted measure approach," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1918-1946, February.
    14. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2007. "Computational strategy for Russell measure in DEA: Second-order cone programming," European Journal of Operational Research, Elsevier, vol. 180(1), pages 459-471, July.
    15. David Lambert, 1999. "Scale and the Malmquist productivity index," Applied Economics Letters, Taylor & Francis Journals, vol. 6(9), pages 593-596.
    16. O. B. Olesen & N. C. Petersen, 1996. "Indicators of Ill-Conditioned Data Sets and Model Misspecification in Data Envelopment Analysis: An Extended Facet Approach," Management Science, INFORMS, vol. 42(2), pages 205-219, February.
    17. 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, vol. 30(1-2), pages 91-107.
    18. Sueyoshi, Toshiyuki, 2004. "Mixed integer programming approach of extended DEA-discriminant analysis," European Journal of Operational Research, Elsevier, vol. 152(1), pages 45-55, January.
    19. 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.
    20. Bjurek, Hans, 1996. " The Malmquist Total Factor Productivity Index," Scandinavian Journal of Economics, Wiley Blackwell, vol. 98(2), pages 303-313, June.
    21. 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.
    22. Robert Russell, R., 1985. "Measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 35(1), pages 109-126, February.
    23. W. Cooper & Dr. Park & Professor Ciurana, 2000. "Marginal Rates and Elasticities of Substitution with Additive Models in DEA," Journal of Productivity Analysis, Springer, vol. 13(2), pages 105-123, March.
    24. Ahn, Taesik & Charnes, Abraham & Cooper, William W., 1988. "Some statistical and DEA evaluations of relative efficiencies of public and private institutions of higher learning," Socio-Economic Planning Sciences, Elsevier, vol. 22(6), pages 259-269.
    25. Sueyoshi, Toshiyuki, 2006. "DEA-Discriminant Analysis: Methodological comparison among eight discriminant analysis approaches," European Journal of Operational Research, Elsevier, vol. 169(1), pages 247-272, February.
    26. Aida, Kazuo & Cooper, William W. & Pastor, Jésus T. & Sueyoshi, Toshiyuki, 1998. "Evaluating Water Supply Services in Japan with RAM: a Range-adjusted Measure of Inefficiency," Omega, Elsevier, vol. 26(2), pages 207-232, April.
    27. Ole Olesen & N. Petersen, 2003. "Identification and Use of Efficient Faces and Facets in DEA," Journal of Productivity Analysis, Springer, vol. 20(3), pages 323-360, November.
    28. E. Grifell-Tatjé & C. Lovell & J. Pastor, 1998. "A Quasi-Malmquist Productivity Index," Journal of Productivity Analysis, Springer, vol. 10(1), pages 7-20, July.
    29. Tone, Kaoru, 2001. "A slacks-based measure of efficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 130(3), pages 498-509, May.
    30. Fare, Rolf & Shawna Grosskopf & Mary Norris & Zhongyang Zhang, 1994. "Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries," American Economic Review, American Economic Association, vol. 84(1), pages 66-83, March.
    31. William Cooper & Kyung Park & Jesus Pastor, 2001. "The Range Adjusted Measure (RAM) in DEA: A Response to the Comment by Steinmann and Zweifel," Journal of Productivity Analysis, Springer, vol. 15(2), pages 145-152, March.
    32. Yu, Gang & Wei, Quanling & Brockett, Patrick & Zhou, Li, 1996. "Construction of all DEA efficient surfaces of the production possibility set under the Generalized Data Envelopment Analysis Model," European Journal of Operational Research, Elsevier, vol. 95(3), pages 491-510, December.
    33. Sueyoshi, Toshiyuki & Aoki, Shingo, 2001. "A use of a nonparametric statistic for DEA frontier shift: the Kruskal and Wallis rank test," Omega, Elsevier, vol. 29(1), pages 1-18, February.
    34. Charnes, A. & Neralic, L., 1990. "Sensitivity analysis of the additive model in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 48(3), pages 332-341, October.
    35. Pastor, J. T. & Ruiz, J. L. & Sirvent, I., 1999. "An enhanced DEA Russell graph efficiency measure," European Journal of Operational Research, Elsevier, vol. 115(3), pages 596-607, June.
    Full references (including those not matched with items on IDEAS)

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:196:y:2009:i:2:p:764-794. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/eor .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.