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On some generalization of the DEA models

Author

Listed:
  • V E Krivonozhko

    (Institute for Systems Analysis)

  • O B Utkin

    (Global S. Consulting)

  • M M Safin

    (Global S. Consulting)

  • A V Lychev

    (Global S. Consulting)

Abstract

Inadequate results may arise in some instances of DEA model applications. For example, a data envelopment analysis (DEA) model may show ‘a notoriously inefficient unit’ as an efficient one. In addition, too many efficient units may appear in some DEA models. An elegant and subtle approach was proposed to deal with these problems, which is based on incorporating domination cones in DEA models. Yu, Wei and Brockett suggested the generalized DEA (GDEA) model that unifies and extends most of the well-known DEA models based on using domination cones. In this paper, we propose a model that is more general than the GDEA model, on the one hand, as it covers situations that the GDEA model cannot describe. On the other hand, our model enables one to construct step-by-step any model from the family of the GDEA models by incorporating artificial units and rays in the space of inputs and outputs in the Banker, Charnes, Cooper (BCC) model, which makes the process of model construction visible and more understandable. Moreover, we show that any GDEA model can be approximated by some BCC model.

Suggested Citation

  • V E Krivonozhko & O B Utkin & M M Safin & A V Lychev, 2009. "On some generalization of the DEA models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1518-1527, November.
    • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:11:d:10.1057_jors.2009.64
    DOI: 10.1057/jors.2009.64
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    References listed on IDEAS

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    1. Charnes, A. & Cooper, W. W. & Huang, Z. M. & Sun, D. B., 1990. "Polyhedral Cone-Ratio DEA Models with an illustrative application to large commercial banks," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 73-91.
    2. 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.
    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. Fare, Rolf & Grosskopf, Shawna, 1985. " Nonparametric Cost Approach to Scale Efficiency," Scandinavian Journal of Economics, Wiley Blackwell, vol. 87(4), pages 594-604.
    5. 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.
    6. 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.
    7. Thompson, Russell G. & Brinkmann, Emile J. & Dharmapala, P. S. & Gonzalez-Lima, M. D. & Thrall, Robert M., 1997. "DEA/AR profit ratios and sensitivity of 100 large U.S. banks," European Journal of Operational Research, Elsevier, vol. 98(2), pages 213-229, April.
    8. Wei, Quanling & Yan, Hong & Xiong, Lin, 2008. "A bi-objective generalized data envelopment analysis model and point-to-set mapping projection," European Journal of Operational Research, Elsevier, vol. 190(3), pages 855-876, November.
    9. Brockett, P. L. & Charnes, A. & Cooper, W. W. & Huang, Z. M. & Sun, D. B., 1997. "Data transformations in DEA cone ratio envelopment approaches for monitoring bank performances," European Journal of Operational Research, Elsevier, vol. 98(2), pages 250-268, April.
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    Cited by:

    1. Vladimir Krivonozhko & Finn Førsund & Andrey Lychev, 2015. "Terminal units in DEA: definition and determination," Journal of Productivity Analysis, Springer, vol. 43(2), pages 151-164, April.
    2. Vladimir E. Krivonozhko & Finn R. Førsund & Andrey V. Lychev, 2017. "On comparison of different sets of units used for improving the frontier in DEA models," Annals of Operations Research, Springer, vol. 250(1), pages 5-20, March.
    3. Alexander P. Afanasiev & Vladimir E. Krivonozhko & Andrey V. Lychev & Oleg V. Sukhoroslov, 2020. "Multidimensional frontier visualization based on optimization methods using parallel computations," Journal of Global Optimization, Springer, vol. 76(3), pages 563-574, March.
    4. Finn Førsund, 2013. "Weight restrictions in DEA: misplaced emphasis?," Journal of Productivity Analysis, Springer, vol. 40(3), pages 271-283, December.
    5. Førsund, Finn & Krivonozhko, Vladimir W & Lychev, Andrey V., 2016. "Smoothing the frontier in the DEA models," Memorandum 11/2016, Oslo University, Department of Economics.
    6. Krivonozhko, Vladimir E. & Førsund, Finn R. & Lychev, Andrey V., 2012. "Identifying Suspicious Efficient Units in DEA Models," Memorandum 30/2012, Oslo University, Department of Economics.
    7. Svetlana Ratner & Andrey Lychev & Aleksei Rozhnov & Igor Lobanov, 2021. "Efficiency Evaluation of Regional Environmental Management Systems in Russia Using Data Envelopment Analysis," Mathematics, MDPI, vol. 9(18), pages 1-21, September.

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