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Pareto–Koopmans efficiency and network DEA

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  • Mirdehghan, S. Morteza
  • Fukuyama, Hirofumi

Abstract

Standard or black-box data envelopment analysis (DEA) evaluates the efficiency of the transformation of a DMU׳s exogenous inputs into its final outputs by ignoring what is going on in its divisions (sub-DMUs). To cope with this problem, network DEA (NDEA), which can provide adequate detail to management, has been developed and applied empirically. However, we show that some of the commonly used NDEA methods are inconsistent with the notion of Pareto–Koopmans efficiency. Since the original development of DEA, Pareto–Koopmans efficiency is a fundamental property used in DEA. From a Pareto–Koopmans efficiency perspective, therefore, we propose a two-phase NDEA approach that can provide information on both each DMU׳s overall (system) efficiency status and its divisions׳ efficiency scores. The proposed novel approach is developed based on the enhanced Russell graph model or equivalently the slacks-based model. We also propose several theorems and illustrate the proposed approach using two artificial numerical examples and a real-world data set.

Suggested Citation

  • Mirdehghan, S. Morteza & Fukuyama, Hirofumi, 2016. "Pareto–Koopmans efficiency and network DEA," Omega, Elsevier, vol. 61(C), pages 78-88.
    • Handle: RePEc:eee:jomega:v:61:y:2016:i:c:p:78-88
    DOI: 10.1016/j.omega.2015.07.008
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    3. Hirofumi Fukuyama & William L. Weber, 2017. "Japanese Bank Productivity, 2007–2012: A Dynamic Network Approach," Pacific Economic Review, Wiley Blackwell, vol. 22(4), pages 649-676, October.
    4. Fatemeh Boloori & Rashed Khanjani-Shiraz & Hirofumi Fukuyama, 2021. "Relative partial efficiency: network and black box SBM DEA interpretations in multiplier form," Operational Research, Springer, vol. 21(4), pages 2689-2718, December.
    5. Lozano, Sebastián & Villa, Gabriel, 2016. "Data Envelopment Analysis of systems with multiple modes of functioning," MPRA Paper 76076, University Library of Munich, Germany.
    6. Tai-Hsin Huang & Yi-Chun Lin & Kuo-Jui Huang & Yu-Wei Liao, 2022. "Comparing Cost Efficiency Between Financial and Non-financial Holding Banks and Insurers in Taiwan Under the Framework of Copula Methods and Metafrontier," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(4), pages 735-766, December.
    7. S. Lozano & G. Villa, 2019. "Data envelopment analysis of systems with multiple modes of functioning," Annals of Operations Research, Springer, vol. 278(1), pages 17-41, July.

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