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An ellipsoidal frontier model: Allocating input via parametric DEA

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  • Milioni, Armando Zeferino
  • de Avellar, José Virgílio Guedes
  • Gomes, Eliane Gonçalves
  • Soares de Mello, João Carlos Correia Baptista

Abstract

This paper presents the ellipsoidal frontier model (EFM), a parametric data envelopment analysis (DEA) model for input allocation. EFM addresses the problem of distributing a single total fixed input by assuming the existence of a predefined locus of points that characterizes the DEA frontier. Numeric examples included in the paper show EFM's capacity to allocate shares of the total fixed input to each DMU so that they will all become efficient. By varying the eccentricities, input distribution can be performed in infinite ways, gaining control over DEA weights assigned to the variables in the model. We also show that EFM assures strong efficiency and behaves coherently within the context of sensitivity analysis, two properties that are not observed in other models found in the technical literature.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:209:y:2011:i:2:p:113-121
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    References listed on IDEAS

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    Cited by:

    1. Ruiyue Lin & Zhiping Chen & Zongxin Li, 2016. "An equitable DEA-based approach for assigning fixed resources along with targets," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(11), pages 1373-1381, November.
    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. Jie Wu & Panpan Xia & Qingyuan Zhu & Junfei Chu, 2019. "Measuring environmental efficiency of thermoelectric power plants: a common equilibrium efficient frontier DEA approach with fixed-sum undesirable output," Annals of Operations Research, Springer, vol. 275(2), pages 731-749, April.
    4. Dai, Qianzhi & Li, Yongjun & Lei, Xiyang & Wu, Dengsheng, 2021. "A DEA-based incentive approach for allocating common revenues or fixed costs," European Journal of Operational Research, Elsevier, vol. 292(2), pages 675-686.
    5. Yang, Jiawei & Li, Dan & Li, Yongjun, 2024. "A generalized data envelopment analysis approach for fixed cost allocation with preference information," Omega, Elsevier, vol. 122(C).
    6. Qing Feng & Dengfeng Li & Guichuan Zhou & Zhibin Wu, 2024. "Fairness based unique common equilibrium efficient frontier for evaluating decision-making units with fixed-sum outputs," Annals of Operations Research, Springer, vol. 341(1), pages 427-449, October.
    7. Feng Li & Qingyuan Zhu & Liang Liang, 2019. "A new data envelopment analysis based approach for fixed cost allocation," Annals of Operations Research, Springer, vol. 274(1), pages 347-372, March.
    8. 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.

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