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A generalized equilibrium efficient frontier data envelopment analysis approach for evaluating DMUs with fixed-sum outputs

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  • Yang, Min
  • Li, Yong Jun
  • Liang, Liang

Abstract

The recently published equilibrium efficient frontier data envelopment analysis (EEFDEA) approach (Yang et al., 2014) represents a step forward in evaluating decision-making units (DMUs) with fixed-sum outputs when compared to prior approaches such as FSODEA (fixed-sum outputs DEA) approach (Yang et al., 2011) and ZSG-DEA (zero sum gains DEA) approach (Lins et al., 2003) and so on. Based on the EEFDEA approach, in this paper, we proposed a generalized equilibrium efficient frontier data envelopment analysis approach (GEEFDEA) which improves and strengthens the EEFDEA approach. Compared to EEFDEA approach, this approach makes several improvements in evaluation, namely that (1) it is not necessary to determine the evaluation order in advance, which overcomes the limitation that different evaluation orders will lead to different results; (2) the equilibrium efficient frontier can be achieved in only one step no matter how many DMUs they are, which greatly simplifies the procedure to reach the equilibrium efficient frontier especially when the number of DMUs is large; and (3) the constraint that signs of outputs’ adjustment of each DMU must be same (all non-positive or all non-negative) in prior approaches has been relaxed. In this sense, the result obtained by the proposed approach is more consistent with the demand of practical applications. Finally, the proposed approach combined with assurance regions (AR) is applied to the data set of 2012 London Olympic Games.

Suggested Citation

  • Yang, Min & Li, Yong Jun & Liang, Liang, 2015. "A generalized equilibrium efficient frontier data envelopment analysis approach for evaluating DMUs with fixed-sum outputs," European Journal of Operational Research, Elsevier, vol. 246(1), pages 209-217.
    • Handle: RePEc:eee:ejores:v:246:y:2015:i:1:p:209-217
    DOI: 10.1016/j.ejor.2015.04.023
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    1. Du, Juan & Cook, Wade D. & Liang, Liang & Zhu, Joe, 2014. "Fixed cost and resource allocation based on DEA cross-efficiency," European Journal of Operational Research, Elsevier, vol. 235(1), pages 206-214.
    2. Silva, Rodrigo Cesar & Milioni, Armando Zeferino, 2012. "The Adjusted Spherical Frontier Model with weight restrictions," European Journal of Operational Research, Elsevier, vol. 220(3), pages 729-735.
    3. Beasley, J. E., 2003. "Allocating fixed costs and resources via data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 147(1), pages 198-216, May.
    4. Milioni, Armando Zeferino & de Avellar, José Virgílio Guedes & Gomes, Eliane Gonçalves & Soares de Mello, João Carlos Correia Baptista, 2011. "An ellipsoidal frontier model: Allocating input via parametric DEA," European Journal of Operational Research, Elsevier, vol. 209(2), pages 113-121, March.
    5. S Lozano & G Villa & F Guerrero & P Cortés, 2002. "Measuring the performance of nations at the Summer Olympics using data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(5), pages 501-511, May.
    6. Yang, Feng & Wu, Desheng Dash & Liang, Liang & O'Neill, Liam, 2011. "Competition strategy and efficiency evaluation for decision making units with fixed-sum outputs," European Journal of Operational Research, Elsevier, vol. 212(3), pages 560-569, August.
    7. 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.
    8. Li, Yongjun & Yang, Feng & Liang, Liang & Hua, Zhongsheng, 2009. "Allocating the fixed cost as a complement of other cost inputs: A DEA approach," European Journal of Operational Research, Elsevier, vol. 197(1), pages 389-401, August.
    9. E C C Guedes & A Z Milioni & J V G de Avellar & R C Silva, 2012. "Adjusted spherical frontier model: allocating input via parametric DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(3), pages 406-417, March.
    10. Li, Yongjun & Liang, Liang & Chen, Yao & Morita, Hiroshi, 2008. "Models for measuring and benchmarking olympics achievements," Omega, Elsevier, vol. 36(6), pages 933-940, December.
    11. 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.
    12. E G Gomes & M P E Lins, 2008. "Modelling undesirable outputs with zero sum gains data envelopment analysis models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(5), pages 616-623, May.
    13. Li, Yongjun & Yang, Min & Chen, Ya & Dai, Qianzhi & Liang, Liang, 2013. "Allocating a fixed cost based on data envelopment analysis and satisfaction degree," Omega, Elsevier, vol. 41(1), pages 55-60.
    14. 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.
    15. Yang, Min & Li, Yongjun & Chen, Ya & Liang, Liang, 2014. "An equilibrium efficiency frontier data envelopment analysis approach for evaluating decision-making units with fixed-sum outputs," European Journal of Operational Research, Elsevier, vol. 239(2), pages 479-489.
    16. Joe Zhu, 2014. "DEA Cross Efficiency," International Series in Operations Research & Management Science, in: Quantitative Models for Performance Evaluation and Benchmarking, edition 3, chapter 4, pages 61-92, Springer.
    17. J V Guedes de Avellar & A Z Milioni & T N Rabello, 2007. "Spherical frontier DEA model based on a constant sum of inputs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(9), pages 1246-1251, September.
    Full references (including those not matched with items on IDEAS)

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    14. Sekitani, Kazuyuki & Zhao, Yu, 2021. "Performance benchmarking of achievements in the Olympics: An application of Data Envelopment Analysis with restricted multipliers," European Journal of Operational Research, Elsevier, vol. 294(3), pages 1202-1212.
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    19. Qingyuan Zhu & Jie Wu & Malin Song & Liang Liang, 2017. "A unique equilibrium efficient frontier with fixed-sum outputs in data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(12), pages 1483-1490, December.
    20. Li, Feng & Zhang, Danlu & Zhang, Jinyu & Kou, Gang, 2022. "Measuring the energy production and utilization efficiency of Chinese thermal power industry with the fixed-sum carbon emission constraint," International Journal of Production Economics, Elsevier, vol. 252(C).
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