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Efficiency measurement for hierarchical network systems

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  • Kao, Chiang

Abstract

The conventional data envelopment analysis (DEA) models for measuring the relative efficiency of a set of decision making units (DMUs), without considering the operations of the component processes, often produce misleading results, and network models have thus been recommended. This paper discusses the development of a network DEA model for systems with a hierarchical structure. It is shown that the hierarchical structure is equivalent to a parallel structure, with the components being the units at the bottom of the hierarchy. Due to the characteristics of a parallel system, the efficiency of a hierarchical system is thus a weighted average of those of the units at the bottom of the hierarchy. A hypothetic example shows that the proposed model is able to distinguish the order of the efficient DMUs evaluated by the conventional DEA model. Moreover, it provides the efficiencies of the functions of the DMU, which enables managers to identify areas of weakness, and thus better focus efforts to improve overall performance.

Suggested Citation

  • Kao, Chiang, 2015. "Efficiency measurement for hierarchical network systems," Omega, Elsevier, vol. 51(C), pages 121-127.
    • Handle: RePEc:eee:jomega:v:51:y:2015:i:c:p:121-127
    DOI: 10.1016/j.omega.2014.09.008
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    11. Kao, Chiang, 2014. "Network data envelopment analysis: A review," European Journal of Operational Research, Elsevier, vol. 239(1), pages 1-16.
    12. Kao, Chiang & Liu, Shiang-Tai, 2014. "Multi-period efficiency measurement in data envelopment analysis: The case of Taiwanese commercial banks," Omega, Elsevier, vol. 47(C), pages 90-98.
    13. Kao, Chiang, 2009. "Efficiency measurement for parallel production systems," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1107-1112, August.
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    15. Kong, Wei-Hsin & Fu, Tsu-Tan, 2012. "Assessing the performance of business colleges in Taiwan using data envelopment analysis and student based value-added performance indicators," Omega, Elsevier, vol. 40(5), pages 541-549.
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    17. Kao, Chiang, 2014. "Efficiency decomposition in network data envelopment analysis with slacks-based measures," Omega, Elsevier, vol. 45(C), pages 1-6.
    18. Kao, Chiang, 2014. "Efficiency decomposition for general multi-stage systems in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 232(1), pages 117-124.
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    1. Svetlana V. Ratner & Artem M. Shaposhnikov & Andrey V. Lychev, 2023. "Network DEA and Its Applications (2017–2022): A Systematic Literature Review," Mathematics, MDPI, vol. 11(9), pages 1-24, May.
    2. Kao, Chiang, 2016. "Efficiency decomposition and aggregation in network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 255(3), pages 778-786.
    3. Zhang, Linyan & Chen, Kun, 2019. "Hierarchical network systems: An application to high-technology industry in China," Omega, Elsevier, vol. 82(C), pages 118-131.
    4. Xiao, Huijuan & Wang, Daoping & Qi, Yu & Shao, Shuai & Zhou, Ya & Shan, Yuli, 2021. "The governance-production nexus of eco-efficiency in Chinese resource-based cities: A two-stage network DEA approach," Energy Economics, Elsevier, vol. 101(C).
    5. Chen, Chih Cheng, 2017. "Measuring departmental and overall regional performance: applying the multi-activity DEA model to Taiwan׳s cities/counties," Omega, Elsevier, vol. 67(C), pages 60-80.
    6. Meng, Fanyong & Xiong, Beibei, 2021. "Logical efficiency decomposition for general two-stage systems in view of cross efficiency," European Journal of Operational Research, Elsevier, vol. 294(2), pages 622-632.
    7. Shahari, Mohd Ridzwan & See, Kok Fong & Mohammed, Noor Syahireen & Yu, Ming-Miin, 2023. "Constructing the performance index of Malaysia’s district health centers using effectiveness-based hierarchical data envelopment analysis," Socio-Economic Planning Sciences, Elsevier, vol. 89(C).
    8. Kremantzis, Marios Dominikos & Beullens, Patrick & Kyrgiakos, Leonidas Sotirios & Klein, Jonathan, 2022. "Measurement and evaluation of multi-function parallel network hierarchical DEA systems," Socio-Economic Planning Sciences, Elsevier, vol. 84(C).
    9. Kao, Chiang, 2020. "Decomposition of slacks-based efficiency measures in network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 283(2), pages 588-600.
    10. Joe Zhu, 2022. "DEA under big data: data enabled analytics and network data envelopment analysis," Annals of Operations Research, Springer, vol. 309(2), pages 761-783, February.
    11. See, Kok Fong & Ng, Ying Chu & Yu, Ming-Miin, 2022. "An alternative assessment approach to national higher education system evaluation," Evaluation and Program Planning, Elsevier, vol. 94(C).

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