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Spherical frontier DEA model based on a constant sum of inputs

Author

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  • J V Guedes de Avellar

    (Instituto de Estudos Avançados, São José dos campus
    Instituto Tecnológico de Aeronáutica (ITA), São José dos Campos)

  • A Z Milioni

    (Instituto de Estudos Avançados, São José dos campus
    Instituto Tecnológico de Aeronáutica (ITA), São José dos Campos)

  • T N Rabello

    (Instituto de Estudos Avançados, São José dos campus
    Instituto Tecnológico de Aeronáutica (ITA), São José dos Campos)

Abstract

In this paper, a Data Envelopment Analysis (DEA) model in which a fixed input needs to be assigned to a group of Decision-Making Units (DMUs) is presented. This is performed by assuming the existence of a geometric place represented by a sphere that characterizes the DEA frontier. It is shown that, under this assumption, it becomes relatively easy to find a way to distribute the fixed input to all DMUs, by considering that the individual assignments will be fair through the requirement that all DMUs be efficient or, in other words, be located on the spherically shaped efficiency frontier. A model is presented and results are compared to those obtained by using two different methods proposed in the literature within the same context.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:58:y:2007:i:9:d:10.1057_palgrave.jors.2602260
    DOI: 10.1057/palgrave.jors.2602260
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. M P Estellita Lins & L Angulo-Meza & A C Moreira Da Silva, 2004. "A multi-objective approach to determine alternative targets in data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1090-1101, October.
    4. Wei, Quanling & Zhang, Jianzhong & Zhang, Xiangsun, 2000. "An inverse DEA model for inputs/outputs estimate," European Journal of Operational Research, Elsevier, vol. 121(1), pages 151-163, February.
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    6. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. A Z Milioni & J V G de Avellar & T N Rabello & G M de Freitas, 2011. "Hyperbolic frontier model: a parametric DEA approach for the distribution of a total fixed output," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(6), pages 1029-1037, June.
    4. C F Leon & F Palacios, 2009. "Evaluation of rejected cases in an acceptance system with data envelopment analysis and goal programming," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(10), pages 1411-1420, October.
    5. 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.
    6. 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.
    7. 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.
    8. 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.

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