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Network DEA Pitfalls: Divisional Efficiency and Frontier Projection

In: Data Envelopment Analysis

Author

Listed:
  • Yao Chen

    (University of Massachusetts at Lowell)

  • Wade D. Cook

    (York University)

  • Chiang Kao

    (National Cheng Kung University)

  • Joe Zhu

    (Worcester Polytechnic Institute)

Abstract

Recently network DEA models have been developed to examine the efficiency of DMUs with internal structures. The internal network structures range from a simple two-stage process to a complex system where multiple divisions are linked together with intermediate measures. In general, there are two types of network DEA models. One is developed under the standard multiplier DEA models based upon the DEA ratio efficiency, and the other under the envelopment DEA models based upon production possibility sets. While the multiplier and envelopment DEA models are dual models and equivalent under the standard DEA, such is not necessarily true for the two types of network DEA models. Pitfalls in network DEA are discussed with respect to the determination of divisional efficiency, frontier type, and projections. We point out that the envelopment-based network DEA model should be used for determining the frontier projection for inefficient DMUs while the multiplier-based network DEA model should be used for determining the divisional efficiency. Finally, we demonstrate that under general network structures, the multiplier and envelopment network DEA models are two different approaches. The divisional efficiency obtained from the multiplier network DEA model can be infeasible in the envelopment network DEA model. This indicates that these two types of network DEA models use different concepts of efficiency. We further demonstrate that the envelopment model’s divisional efficiency may actually be the overall efficiency.

Suggested Citation

  • Yao Chen & Wade D. Cook & Chiang Kao & Joe Zhu, 2014. "Network DEA Pitfalls: Divisional Efficiency and Frontier Projection," International Series in Operations Research & Management Science, in: Wade D. Cook & Joe Zhu (ed.), Data Envelopment Analysis, edition 127, chapter 0, pages 31-54, Springer.
    • Handle: RePEc:spr:isochp:978-1-4899-8068-7_2
    DOI: 10.1007/978-1-4899-8068-7_2
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    Cited by:

    1. Khezrimotlagh, Dariush & Kaffash, Sepideh & Zhu, Joe, 2022. "U.S. airline mergers’ performance and productivity change," Journal of Air Transport Management, Elsevier, vol. 102(C).
    2. Mergoni, Anna & Soncin, Mara & Agasisti, Tommaso, 2023. "The effect of ICT on schools’ efficiency: Empirical evidence on 23 European countries," Omega, Elsevier, vol. 119(C).
    3. Tang, Yesi & Yang, Shudong, 2024. "Mineral resource sustainability in the face of the resource exploitation and green recovery: Challenges and solutions," Resources Policy, Elsevier, vol. 88(C).
    4. Ang, Sheng & Liu, Pei & Yang, Feng, 2020. "Intra-Organizational and inter-organizational resource allocation in two-stage network systems," Omega, Elsevier, vol. 91(C).
    5. Zhou, Haibo & Yang, Yi & Chen, Yao & Zhu, Joe, 2018. "Data envelopment analysis application in sustainability: The origins, development and future directions," European Journal of Operational Research, Elsevier, vol. 264(1), pages 1-16.
    6. Fenfen Li & Bo Dai & Qifan Wu, 2021. "Dynamic Green Growth Assessment of China’s Industrial System with an Improved SBM Model and Global Malmquist Index," Mathematics, MDPI, vol. 9(20), pages 1-26, October.

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