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An Extension of Cross Redundancy of Interval Scale Outputs and Inputs in DEA

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  • Farhad Hosseinzadeh-Lotfi
  • Gholam-Reza Jahanshahloo
  • Mansour Mohammadpour

Abstract

It is well known that data envelopment analysis (DEA) models are sensitive to selection of input and output variables. As the number of variables increases, the ability to discriminate between the decision making units (DMUs) decreases. Thus, to preserve the discriminatory power of a DEA model, the number of inputs and outputs should be kept at a reasonable level. There are many cases in which an interval scale output in the sample is derived from the subtraction of nonnegative linear combination of ratio scale outputs and nonnegative linear combination of ratio scale inputs. There are also cases in which an interval scale input is derived from the subtraction of nonnegative linear combination of ratio scale inputs and nonnegative linear combination of ratio scale outputs. Lee and Choi (2010) called such interval scale output and input a cross redundancy. They proved that the addition or deletion of a cross‐redundant output variable does not affect the efficiency estimates yielded by the CCR or BCC models. In this paper, we present an extension of cross redundancy of interval scale outputs and inputs in DEA models. We prove that the addition or deletion of a cross‐redundant output and input variable does not affect the efficiency estimates yielded by the CCR or BCC models.

Suggested Citation

  • Farhad Hosseinzadeh-Lotfi & Gholam-Reza Jahanshahloo & Mansour Mohammadpour, 2013. "An Extension of Cross Redundancy of Interval Scale Outputs and Inputs in DEA," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:658635
    DOI: 10.1155/2013/658635
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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.
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    Cited by:

    1. Anrong Yang & Zigang Zhang & Yishi Zhang & Dunliang Chen, 2014. "Gap Minimization for Peer‐Evaluation in DEA Cross‐Efficiency," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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