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Relative efficiency measurement: The problem of a missing output in a subset of decision making units

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  • Cook, Wade D.
  • Harrison, Julie
  • Rouse, Paul
  • Zhu, Joe

Abstract

Data envelopment analysis (DEA), as originally proposed by Charnes et al. (1978) viewed the efficiency measurement problem as one wherein each of a set of DMUs uses the same input and output measures, albeit in amounts that vary from one DMU to another. In some situations, however, the assumption that all DMUs use the same measures may fail. While there is a well known literature related to the problems of missing data and ‘zeros’ in the data, we argue that there is a difference between the situation where a DMU commits the resources to produce an output (but fails to do so, or else a non-zero amount exists but is unknown), and the situation where the DMU intentionally does not produce that output. In the current paper we examine the problem of measuring the efficiency of a set of steel fabrication plants wherein a subset of those plants produce one less than the full set of outputs produced by the others. We develop a DEA-type model for handling this missing output problem.

Suggested Citation

  • Cook, Wade D. & Harrison, Julie & Rouse, Paul & Zhu, Joe, 2012. "Relative efficiency measurement: The problem of a missing output in a subset of decision making units," European Journal of Operational Research, Elsevier, vol. 220(1), pages 79-84.
    • Handle: RePEc:eee:ejores:v:220:y:2012:i:1:p:79-84
    DOI: 10.1016/j.ejor.2012.01.022
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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. Rolf Färe & Shawna Grosskopf, 2002. "Two Perspectives on DEA: Unveiling the Link between CCR and Shephard," Journal of Productivity Analysis, Springer, vol. 17(1), pages 41-47, January.
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    Cited by:

    1. Wade D. Cook & Julie Harrison & Raha Imanirad & Paul Rouse & Joe Zhu, 2013. "Data Envelopment Analysis with Nonhomogeneous DMUs," Operations Research, INFORMS, vol. 61(3), pages 666-676, June.
    2. Wu, Jie & Li, Mingjun & Zhu, Qingyuan & Zhou, Zhixiang & Liang, Liang, 2019. "Energy and environmental efficiency measurement of China's industrial sectors: A DEA model with non-homogeneous inputs and outputs," Energy Economics, Elsevier, vol. 78(C), pages 468-480.
    3. Ang, Sheng & Chen, Chien-Ming, 2016. "Pitfalls of decomposition weights in the additive multi-stage DEA model," Omega, Elsevier, vol. 58(C), pages 139-153.
    4. Xiaofei Ma & Qiuyan Zhong, 2016. "Missing value imputation method for disaster decision-making using K nearest neighbor," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(4), pages 767-781, March.
    5. Cao, Ting & Cook, Wade D. & Kristal, M. Murat, 2022. "Has the technological investment been worth it? Assessing the aggregate efficiency of non-homogeneous bank holding companies in the digital age," Technological Forecasting and Social Change, Elsevier, vol. 178(C).
    6. Josef Jablonský, 2019. "Data Envelopment Analysis Models in Non-Homogeneous Environment," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 67(6), pages 1535-1540.
    7. Zhu, Weiwei & Yu, Yu & Sun, Panpan, 2018. "Data envelopment analysis cross-like efficiency model for non-homogeneous decision-making units: The case of United States companies’ low-carbon investment to attain corporate sustainability," European Journal of Operational Research, Elsevier, vol. 269(1), pages 99-110.
    8. Liang, Liang & Cook, Wade D. & Zhu, Joe, 2016. "DEA models for non-homogeneous DMUs with different input configurationsAuthor-Name: Li, WangHong," European Journal of Operational Research, Elsevier, vol. 254(3), pages 946-956.
    9. Yu Zhu & Feng Yang & Bengang Gong & Wei Zeng, 2023. "RETRACTED ARTICLE: Assessing the efficiency of innovation entities in China: evidence from a nonhomogeneous data envelopment analysis and Tobit," Electronic Commerce Research, Springer, vol. 23(1), pages 175-205, March.
    10. Fukuyama, Hirofumi & Song, Yao-yao & Ren, Xian-tong & Yang, Guo-liang, 2022. "Using a novel DEA-based model to investigate capacity utilization of Chinese firms," Omega, Elsevier, vol. 106(C).
    11. Fukuyama, Hirofumi & Liu, Hui-hui & Song, Yao-yao & Yang, Guo-liang, 2021. "Measuring the capacity utilization of the 48 largest iron and steel enterprises in China," European Journal of Operational Research, Elsevier, vol. 288(2), pages 648-665.

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