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A Comment on Decomposition of Efficiency in Network Production Models

Author

Listed:
  • Antonio Peyrache

    (School of Economics and Centre for Efficiency and Productivity Analysis (CEPA) at The University of Queensland, Australia)

  • Maria C. A. Silva

    (CEGE - Cat´olica Porto Business School, Rua Diogo Botelho, 1327, 4169-005 Porto, Portugal.)

Abstract

Kao (2012) proposed a method to decompose DMU efficiency into sub-unit efficiencies for parallel production systems. We provide a numerical example showing that the proposed method can yield negative sub-unit efficiency scores under variable returns to scale, against common sense and standard postulates requiring this score to be non-negative. As a solution, we propose a decomposition based on the directional distance function that does not suffer from this problem and can be also applied to non-convex technologies, therefore providing a more general method to implement such a decomposition. Given the connection between the directional distance function and slack-based efficiency measurement, the method can easily be extended to this case as well.

Suggested Citation

  • Antonio Peyrache & Maria C. A. Silva, 2022. "A Comment on Decomposition of Efficiency in Network Production Models," CEPA Working Papers Series WP072022, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uqcepa:179
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    File URL: https://economics.uq.edu.au/files/35882/WP072022.pdf
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    References listed on IDEAS

    as
    1. Kao, Chiang, 2009. "Efficiency decomposition in network data envelopment analysis: A relational model," European Journal of Operational Research, Elsevier, vol. 192(3), pages 949-962, February.
    2. Kao, Chiang, 2013. "Dynamic data envelopment analysis: A relational analysis," European Journal of Operational Research, Elsevier, vol. 227(2), pages 325-330.
    3. Pachkova, Elena V., 2009. "Restricted reallocation of resources," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1049-1057, August.
    4. Antonio Peyrache & Maria C. A. Silva, 2021. "Multi-Level Parallel Production Networks," CEPA Working Papers Series WP052021, School of Economics, University of Queensland, Australia.
    5. Walter Briec & Kristiaan Kerstens, 2006. "Input, output and graph technical efficiency measures on non-convex FDH models with various scaling laws: An integrated approach based upon implicit enumeration algorithms," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 135-166, June.
    6. Podinovski, V. V., 2004. "On the linearisation of reference technologies for testing returns to scale in FDH models," European Journal of Operational Research, Elsevier, vol. 152(3), pages 800-802, February.
    7. Kao, Chiang, 2019. "Inefficiency identification for closed series production systems," European Journal of Operational Research, Elsevier, vol. 275(2), pages 599-607.
    8. 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.
    9. C Kao, 2012. "Efficiency decomposition for parallel production systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(1), pages 64-71, January.
    10. Kao, Chiang, 2018. "Multiplicative aggregation of division efficiencies in network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 270(1), pages 328-336.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Antonio Peyrache & Maria C. A. Silva, 2023. "Efficiency decomposition for multi-level multi-components production technologies," Journal of Productivity Analysis, Springer, vol. 60(3), pages 273-294, December.

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    More about this item

    Keywords

    DEA; FDH; Networks; Directional Distance Function; Inefficiency;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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