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A generalized multiplicative directional distance function for efficiency measurement in DEA

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  • Mehdiloozad, Mahmood
  • Sahoo, Biresh K.
  • Roshdi, Israfil

Abstract

For measuring technical efficiency relative to a log-linear technology, a generalized multiplicative directional distance function (GMDDF) is developed using the framework of multiplicative directional distance function (MDDF). Furthermore, a computational procedure is suggested for its estimation. The GMDDF serves as a comprehensive measure of efficiency in revealing Pareto-efficient targets as it accounts for all possible input and output slacks. This measure satisfies several desirable properties of an ideal efficiency measure such as strong monotonicity, unit invariance, translation invariance, and positive affine transformation invariance. This measure can be easily implemented in any standard DEA software and provides the decision makers with the option of specifying preferable direction vectors for incorporating their decision-making preferences. Finally, to demonstrate the ready applicability of our proposed measure, an illustrative empirical analysis is conducted based on real-life data set of 20 hardware computer companies in India.

Suggested Citation

  • Mehdiloozad, Mahmood & Sahoo, Biresh K. & Roshdi, Israfil, 2014. "A generalized multiplicative directional distance function for efficiency measurement in DEA," European Journal of Operational Research, Elsevier, vol. 232(3), pages 679-688.
    • Handle: RePEc:eee:ejores:v:232:y:2014:i:3:p:679-688
    DOI: 10.1016/j.ejor.2013.07.042
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    Cited by:

    1. Valadkhani, Abbas & Roshdi, Israfil & Smyth, Russell, 2016. "A multiplicative environmental DEA approach to measure efficiency changes in the world's major polluters," Energy Economics, Elsevier, vol. 54(C), pages 363-375.
    2. Biresh K Sahoo & Ramadhar Singh & Bineet Mishra & Krithiga Sankaran, 2015. "Research Productivity in Management Schools of India: A Directional Benefit-of-Doubt Model Analysis," Working Papers id:7139, eSocialSciences.
    3. Briec, Walter & Fukuyama, Hirofumi & Ravelojaona, Paola, 2021. "Exponential distance function and duality theory," European Journal of Operational Research, Elsevier, vol. 293(3), pages 1002-1014.
    4. Mehdiloozad, Mahmood & Podinovski, Victor V., 2018. "Nonparametric production technologies with weakly disposable inputs," European Journal of Operational Research, Elsevier, vol. 266(1), pages 247-258.
    5. Ouyang, Wendi & Yang, Jian-bo, 2020. "The network energy and environment efficiency analysis of 27 OECD countries: A multiplicative network DEA model," Energy, Elsevier, vol. 197(C).
    6. Mehdiloozad, Mahmood & Zhu, Joe & Sahoo, Biresh K., 2018. "Identification of congestion in data envelopment analysis under the occurrence of multiple projections: A reliable method capable of dealing with negative data," European Journal of Operational Research, Elsevier, vol. 265(2), pages 644-654.
    7. Mahmood Mehdiloozad & Mohammad Bagher Ahmadi & Biresh K. Sahoo, 2017. "On classifying decision making units in DEA: a unified dominance-based model," Annals of Operations Research, Springer, vol. 250(1), pages 167-184, March.
    8. Sahoo, Biresh K. & Mehdiloozad, Mahmood & Tone, Kaoru, 2014. "Cost, revenue and profit efficiency measurement in DEA: A directional distance function approach," European Journal of Operational Research, Elsevier, vol. 237(3), pages 921-931.
    9. Roshdi, Israfil & Hasannasab, Maryam & Margaritis, Dimitris & Rouse, Paul, 2018. "Generalised weak disposability and efficiency measurement in environmental technologies," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1000-1012.
    10. A. Abad & P. Ravelojaona, 2017. "Exponential environmental productivity index and indicators," Journal of Productivity Analysis, Springer, vol. 48(2), pages 147-166, December.
    11. Diogo Cunha Ferreira & Rui Cunha Marques & Alexandre Morais Nunes, 2021. "Pay for performance in health care: a new best practice tariff-based tool using a log-linear piecewise frontier function and a dual–primal approach for unique solutions," Operational Research, Springer, vol. 21(3), pages 2101-2146, September.
    12. Tao, Xiangyang & An, Qingxian & Goh, Mark, 2024. "Plant capacity utilization with piecewise Cobb-Douglas technology: Definition and interpretation," European Journal of Operational Research, Elsevier, vol. 316(3), pages 1034-1043.
    13. Sahoo, Biresh K & Khoveyni, Mohammad & Eslami, Robabeh & Chaudhury, Pradipta, 2016. "Returns to scale and most productive scale size in DEA with negative data," European Journal of Operational Research, Elsevier, vol. 255(2), pages 545-558.
    14. Briec, Walter & Dumas, Audrey & Kerstens, Kristiaan & Stenger, Agathe, 2022. "Generalised commensurability properties of efficiency measures: Implications for productivity indicators," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1481-1492.
    15. A. Davoodi & M. Zarepisheh & H. Rezai, 2015. "The nearest MPSS pattern in data envelopment analysis," Annals of Operations Research, Springer, vol. 226(1), pages 163-176, March.
    16. Mehdiloozad, Mahmood & Mirdehghan, S. Morteza & Sahoo, Biresh K. & Roshdi, Israfil, 2015. "On the identification of the global reference set in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 245(3), pages 779-788.
    17. Arnaud Abad & Paola Ravelojaona & Ziyi Shen, 2022. "An exponential analysis of total factor productivity," Working Papers hal-03419905, HAL.
    18. Sahoo, Biresh K. & Singh, Ramadhar & Mishra, Bineet & Sankaran, Krithiga, 2017. "Research productivity in management schools of India during 1968-2015: A directional benefit-of-doubt model analysis," Omega, Elsevier, vol. 66(PA), pages 118-139.

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