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Data Envelopment Analysis With Missing Data

In: Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis

Author

Listed:
  • Chiang Kao

    (National Cheng Kung University)

  • Shiang-Tai Liu

    (Vanung University)

Abstract

In data envelopment analysis (DEA), the input and output data from all of the decision making units (DMUs) to be compared are required. If, for any reason, some data are missing, then the associated DMU must be eliminated to make the approach applicable. This study proposes a fuzzy set approach to deal with missing values. The value of a DMU in an input (or output) which is missing is represented by a triangular fuzzy number constructed from the values of other DMUs in that input (or output). A fuzzy DEA model is then used to calculate the efficiencies, which are usually also fuzzy numbers. We use a problem with complete data to investigate the effect of this approach when 1%, 2%, and 5% of the values are missing. While the conventional DMU-deletion method will overestimate the efficiencies of the remaining DMUs, the fuzzy set approach produces results which are very close to those calculated from complete data. The average error in estimating the true efficiency is less than 0.3%. Most importantly, the fuzzy set approach is able to calculate the efficiencies of all DMUs, including those with some values missing.

Suggested Citation

  • Chiang Kao & Shiang-Tai Liu, 2007. "Data Envelopment Analysis With Missing Data," Springer Books, in: Joe Zhu & Wade D. Cook (ed.), Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis, chapter 0, pages 291-304, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-71607-7_16
    DOI: 10.1007/978-0-387-71607-7_16
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    Cited by:

    1. Hatami-Marbini, Adel & Emrouznejad, Ali & Tavana, Madjid, 2011. "A taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making," European Journal of Operational Research, Elsevier, vol. 214(3), pages 457-472, November.

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