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About negative efficiencies in Cross Evaluation BCC input oriented models

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  • Soares de Mello, João Carlos C.B.
  • Angulo Meza, Lidia
  • da Silveira, Juliana Quintanilha
  • Gomes, Eliane Gonçalves

Abstract

It will be shown in this paper that the input oriented DEA BCC model can generate negative efficiencies that are usually hidden in the model. The impact of these negative efficiencies becomes obvious when using input oriented Cross Evaluation models. With the help of an example with one input and one output, the conditions for the possible occurrence of negative efficiencies will be shown. Furthermore, we will show that a small intuitive change in the BCC multipliers model, previously presented in other papers, corrects this situation. We show why this change is used and compared it with an alternative formulation, which avoid negative efficiencies, namely the Non-Decreasing Returns to Scale (NDRS) model. We also show that the formulation studied in this paper is less restrictive than the NDRS model. The study of this variation in the DEA BCC model will be complemented with the formulation of the dual envelope model. This model changes the original frontier. Using the concept of non-observed DMUs, those variations can be graphically analyzed. We have also carried out some algebraic studies concerning benchmarks, multipliers and returns to scale.

Suggested Citation

  • Soares de Mello, João Carlos C.B. & Angulo Meza, Lidia & da Silveira, Juliana Quintanilha & Gomes, Eliane Gonçalves, 2013. "About negative efficiencies in Cross Evaluation BCC input oriented models," European Journal of Operational Research, Elsevier, vol. 229(3), pages 732-737.
    • Handle: RePEc:eee:ejores:v:229:y:2013:i:3:p:732-737
    DOI: 10.1016/j.ejor.2013.02.020
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    1. Rödder, W. & Reucher, E., 2012. "Advanced X-efficiencies for CCR- and BCC-models – towards Peer-based DEA controlling," European Journal of Operational Research, Elsevier, vol. 219(2), pages 467-476.
    2. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    3. F R Førsund & L Hjalmarsson, 2004. "Calculating scale elasticity in DEA models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1023-1038, October.
    4. Lins, Marcos P. Estellita & Gomes, Eliane G. & Soares de Mello, Joao Carlos C. B. & Soares de Mello, Adelino Jose R., 2003. "Olympic ranking based on a zero sum gains DEA model," European Journal of Operational Research, Elsevier, vol. 148(2), pages 312-322, July.
    5. Charnes, A. & Cooper, W. W. & Golany, B. & Seiford, L. & Stutz, J., 1985. "Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 91-107.
    6. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    7. Thanassoulis, Emmanuel & Kortelainen, Mika & Allen, Rachel, 2012. "Improving envelopment in Data Envelopment Analysis under variable returns to scale," European Journal of Operational Research, Elsevier, vol. 218(1), pages 175-185.
    8. William W. Cooper & Lawrence M. Seiford & Kaoru Tone, 2006. "Introduction to Data Envelopment Analysis and Its Uses," Springer Books, Springer, number 978-0-387-29122-2, November.
    9. Sowlati, Taraneh & Paradi, Joseph C., 2004. "Establishing the "practical frontier" in data envelopment analysis," Omega, Elsevier, vol. 32(4), pages 261-272, August.
    10. Wu, Jie & Liang, Liang & Chen, Yao, 2009. "DEA game cross-efficiency approach to Olympic rankings," Omega, Elsevier, vol. 37(4), pages 909-918, August.
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    1. Afsharian, Mohsen & Ahn, Heinz & Thanassoulis, Emmanuel, 2017. "A DEA-based incentives system for centrally managed multi-unit organisations," European Journal of Operational Research, Elsevier, vol. 259(2), pages 587-598.
    2. Giannis Karagiannis & Georgia Paschalidou, 2017. "Assessing research effectiveness: a comparison of alternative nonparametric models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(4), pages 456-468, April.
    3. Corrado Lo Storto, 2016. "Ecological Efficiency Based Ranking of Cities: A Combined DEA Cross-Efficiency and Shannon’s Entropy Method," Sustainability, MDPI, vol. 8(2), pages 1-29, January.
    4. Ebrahimi, Bohlool & Dhamotharan, Lalitha & Ghasemi, Mohammad Reza & Charles, Vincent, 2022. "A cross-inefficiency approach based on the deviation variables framework," Omega, Elsevier, vol. 111(C).
    5. Kao, Chiang & Liu, Shiang-Tai, 2020. "A slacks-based measure model for calculating cross efficiency in data envelopment analysis," Omega, Elsevier, vol. 95(C).
    6. Khodadadipour, M. & Hadi-Vencheh, A. & Behzadi, M.H. & Rostamy-malkhalifeh, M., 2021. "Undesirable factors in stochastic DEA cross-efficiency evaluation: An application to thermal power plant energy efficiency," Economic Analysis and Policy, Elsevier, vol. 69(C), pages 613-628.
    7. 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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