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A note on two-stage network DEA model: Frontier projection and duality

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  • Lim, Sungmook
  • Zhu, Joe

Abstract

In Chen, Cook, Kao, and Zhu (2013), it is demonstrated, as a network DEA pitfall, that while the multiplier and envelopment DEA models are dual models and equivalent under the standard DEA, such is not necessarily true for the two types of network DEA models in deriving divisional efficiency scores and frontier projections. As a reaction to this work, we demonstrate that the duality in the standard DEA naturally migrates to the two-stage network DEA. Formulas are developed to obtain frontier projections and divisional efficiency scores using a DEA model's and its dual solutions. The case of Taiwanese non-life insurance companies is revisited using the newly developed approach.

Suggested Citation

  • Lim, Sungmook & Zhu, Joe, 2016. "A note on two-stage network DEA model: Frontier projection and duality," European Journal of Operational Research, Elsevier, vol. 248(1), pages 342-346.
    • Handle: RePEc:eee:ejores:v:248:y:2016:i:1:p:342-346
    DOI: 10.1016/j.ejor.2015.06.050
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    References listed on IDEAS

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    1. Chen, Yao & Cook, Wade D. & Zhu, Joe, 2010. "Deriving the DEA frontier for two-stage processes," European Journal of Operational Research, Elsevier, vol. 202(1), pages 138-142, April.
    2. Thomas Sexton & Herbert Lewis, 2003. "Two-Stage DEA: An Application to Major League Baseball," Journal of Productivity Analysis, Springer, vol. 19(2), pages 227-249, April.
    3. 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.
    4. Kao, Chiang & Hwang, Shiuh-Nan, 2008. "Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan," European Journal of Operational Research, Elsevier, vol. 185(1), pages 418-429, February.
    5. Lorenzo Castelli & Raffaele Pesenti & Walter Ukovich, 2010. "A classification of DEA models when the internal structure of the Decision Making Units is considered," Annals of Operations Research, Springer, vol. 173(1), pages 207-235, January.
    6. Chen, Yao & Cook, Wade D. & Kao, Chiang & Zhu, Joe, 2013. "Network DEA pitfalls: Divisional efficiency and frontier projection under general network structures," European Journal of Operational Research, Elsevier, vol. 226(3), pages 507-515.
    7. Kao, Chiang, 2014. "Network data envelopment analysis: A review," European Journal of Operational Research, Elsevier, vol. 239(1), pages 1-16.
    8. 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.
    9. Lawrence M. Seiford & Joe Zhu, 1999. "Profitability and Marketability of the Top 55 U.S. Commercial Banks," Management Science, INFORMS, vol. 45(9), pages 1270-1288, September.
    10. Cook, Wade D. & Liang, Liang & Zhu, Joe, 2010. "Measuring performance of two-stage network structures by DEA: A review and future perspective," Omega, Elsevier, vol. 38(6), pages 423-430, December.
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