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An ellipsoidal frontier model: Allocating input via parametric DEA

Author

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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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    1. Cook, Wade D. & Kress, Moshe, 1999. "Characterizing an equitable allocation of shared costs: A DEA approach," European Journal of Operational Research, Elsevier, vol. 119(3), pages 652-661, December.
    2. 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.
    3. Sebastián Lozano & Gabriel Villa, 2004. "Centralized Resource Allocation Using Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 22(1), pages 143-161, July.
    4. Du, Juan & Liang, Liang & Chen, Yao & Bi, Gong-bing, 2010. "DEA-based production planning," Omega, Elsevier, vol. 38(1-2), pages 105-112, February.
    5. W. Cooper & L. Seiford & K. Tone & J. Zhu, 2007. "Some models and measures for evaluating performances with DEA: past accomplishments and future prospects," Journal of Productivity Analysis, Springer, vol. 28(3), pages 151-163, December.
    6. 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.
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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. 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.
    3. 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.

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