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Nonlinear inputs and diminishing marginal value in DEA

Author

Listed:
  • W D Cook

    (York University)

  • F Yang

    (York University
    University of Science and Technology of China)

  • J Zhu

    (Worcester Polytechnic Institute)

Abstract

The conventional model structures presented in the data envelopment analysis (DEA) literature view all variables as behaving in a linear fashion, meaning that regardless of the amounts, large or small, of a variable held by the set of decision-making units, we apply the same multiplier to those various amounts. In certain situations this linearity assumption is not appropriate, and the conventional models need to be altered to accommodate nonlinear representations. In the current paper, we propose a modified DEA structure that captures certain forms of nonlinear behaviour within the additive DEA model, namely those that exhibit diminishing marginal value.

Suggested Citation

  • W D Cook & F Yang & J Zhu, 2009. "Nonlinear inputs and diminishing marginal value in DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1567-1574, November.
    • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:11:d:10.1057_jors.2008.121
    DOI: 10.1057/jors.2008.121
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Thompson, Russell G. & Langemeier, Larry N. & Lee, Chih-Tah & Lee, Euntaik & Thrall, Robert M., 1990. "The role of multiplier bounds in efficiency analysis with application to Kansas farming," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 93-108.
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    Cited by:

    1. Despotis, Dimitris K. & Stamati, Lamprini V. & Smirlis, Yiannis G., 2010. "Data envelopment analysis with nonlinear virtual inputs and outputs," European Journal of Operational Research, Elsevier, vol. 202(2), pages 604-613, April.
    2. Tajbakhsh, Alireza & Hassini, Elkafi, 2018. "Evaluating sustainability performance in fossil-fuel power plants using a two-stage data envelopment analysis," Energy Economics, Elsevier, vol. 74(C), pages 154-178.

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