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Studies of some duality properties in the Li and Reeves model

Author

Listed:
  • Maria Cecilia de Carvalho Chaves

    (Rio de Janeiro Federal University, Rio de Janeiro, Brazil)

  • João Carlos C B Soares de Mello

    (Fluminense Federal University, Niterói, Brazil)

  • Lidia Angulo-Meza

    (Fluminense Federal University, Niterói, Brazil)

Abstract

In 1999, Li and Reeves presented the so-called MCDEA (Multiple Criteria Data Envelopment Analysis) model. This model is in fact a three objective linear model. It may be used to improve the discriminatory power of the DEA models, as well as generate a more reasonable distribution of the inputs and outputs weights. Besides the classical optimization of the efficiency index, Li and Reeves introduced two other objective functions, called minisum and minimax. Despite of being an important approach, it does not provide benchmarks or targets for inefficient DMUs. Benchmarks and targets are one of the most important DEA features and in standard DEA are determined using the dual (envelope) model. In this paper, we introduce an approach of the MCDEA dual formulation taking into account only two objective functions at each time. Combining both partial models we suggest benchmarks for each inefficient DMU.

Suggested Citation

  • Maria Cecilia de Carvalho Chaves & João Carlos C B Soares de Mello & Lidia Angulo-Meza, 2016. "Studies of some duality properties in the Li and Reeves model," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(3), pages 474-482, March.
    • Handle: RePEc:pal:jorsoc:v:67:y:2016:i:3:p:474-482
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    Cited by:

    1. Rubem, Ana Paula dos Santos & Soares de Mello, João Carlos C.B. & Angulo Meza, Lidia, 2017. "A goal programming approach to solve the multiple criteria DEA model," European Journal of Operational Research, Elsevier, vol. 260(1), pages 134-139.
    2. Mahdiloo, Mahdi & Lim, Sungmook & Duong, Thach-Thao & Harvie, Charles, 2021. "Some comments on improving discriminating power in data envelopment models based on deviation variables framework," European Journal of Operational Research, Elsevier, vol. 295(1), pages 394-397.
    3. Pereira, Deivison da Silveira & Soares de Mello, João Carlos C.B., 2021. "Efficiency evaluation of Brazilian airlines operations considering the Covid-19 outbreak," Journal of Air Transport Management, Elsevier, vol. 91(C).
    4. Tommaso Agasisti & Giuseppe Munda, 2017. "Efficiency of investment in compulsory education: An Overview of Methodological Approaches," JRC Research Reports JRC106681, Joint Research Centre.
    5. Rezaeiani, M.J. & Foroughi, A.A., 2018. "Ranking efficient decision making units in data envelopment analysis based on reference frontier share," European Journal of Operational Research, Elsevier, vol. 264(2), pages 665-674.

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