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Extending the Zero-Sum Gains Data Envelopment Analysis Model

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  • Thanasis Bouzidis

    (Department of Economics, University of Macedonia)

  • Giannis Karagiannis

    (Department of Economics, University of Macedonia)

Abstract

In this paper, we adapt the ZSG-DEA model to the case of a reverse output, whose larger (smaller) values reflect lower (higher) achievements. Then, we introduce the zero-sum reverse output redistribution strategies, state the resulting Target’s Assessment Theorem for both the proportional and the equal expansion strategy, and confirm that the Benchmarks’ Contribution Equality Theorem is also applicable to these cases. We also apply the ZSG-DEA model with a forward and a reverse output to estimate respectively teams’ offensive and defensive efficiency in Greek premier soccer league.

Suggested Citation

  • Thanasis Bouzidis & Giannis Karagiannis, 2022. "Extending the Zero-Sum Gains Data Envelopment Analysis Model," Discussion Paper Series 2022_06, Department of Economics, University of Macedonia, revised Aug 2022.
    • Handle: RePEc:mcd:mcddps:2022_06
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    References listed on IDEAS

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    1. Manuel Espitia-Escuer & Lucà a Isabel Garcà a-Cebrià n, 2004. "Measuring the Efficiency of Spanish First-Division Soccer Teams," Journal of Sports Economics, , vol. 5(4), pages 329-346, November.
    2. Thanasis Bouzidis & Giannis Karagiannis, 2022. "A note on the zero-sum gains data envelopment analysis model," Operational Research, Springer, vol. 22(3), pages 1737-1758, July.
    3. Thanasis Bouzidis & Giannis Karagiannis, 2022. "Extending the zero-sum gains data envelopment analysis model," Journal of Productivity Analysis, Springer, vol. 58(2), pages 171-184, December.
    4. Boscá, José E. & Liern, Vicente & Martínez, Aurelio & Sala, Ramøn, 2009. "Increasing offensive or defensive efficiency? An analysis of Italian and Spanish football," Omega, Elsevier, vol. 37(1), pages 63-78, February.
    5. 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.
    6. Gongbing Bi & Chenpeng Feng & Jingjing Ding & Liang Liang & Feng Chu, 2014. "The linear formulation of the ZSG-DEA models with different production technologies," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(8), pages 1202-1211, August.
    7. 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.
    8. Thomas Sexton & Herbert Lewis, 2012. "Measuring efficiency in the presence of head-to-head competition," Journal of Productivity Analysis, Springer, vol. 38(2), pages 183-197, October.
    9. Alireza Amirteimoori & Simin Masrouri & Feng Yang & Sohrab Kordrostami, 2017. "Context-based competition strategy and performance analysis with fixed-sum outputs: an application to banking sector," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1461-1469, November.
    10. Olesen, Ole Bent & Petersen, Niels Christian & Podinovski, Victor V., 2015. "Efficiency analysis with ratio measures," European Journal of Operational Research, Elsevier, vol. 245(2), pages 446-462.
    11. 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.
    12. W. Liu & W. Meng & X. Li & D. Zhang, 2010. "DEA models with undesirable inputs and outputs," Annals of Operations Research, Springer, vol. 173(1), pages 177-194, January.
    13. Herbert Lewis & Thomas Sexton, 2004. "Data Envelopment Analysis with Reverse Inputs and Outputs," Journal of Productivity Analysis, Springer, vol. 21(2), pages 113-132, March.
    14. Trevor Collier & Andrew L. Johnson & John Ruggiero, 2011. "Measuring Technical Efficiency in Sports," Journal of Sports Economics, , vol. 12(6), pages 579-598, December.
    15. J-L Hu & C-Y Fang, 2010. "Do market share and efficiency matter for each other? An application of the zero-sum gains data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(4), pages 647-657, April.
    16. Chenpeng Feng & Feng Chu & Nan Zhou & Gongbing Bi & Jingjing Ding, 2019. "Performance evaluation and quota allocation for multiple undesirable outputs based on the uniform frontier," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(3), pages 472-486, March.
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    1. Thanasis Bouzidis & Giannis Karagiannis, 2022. "Extending the zero-sum gains data envelopment analysis model," Journal of Productivity Analysis, Springer, vol. 58(2), pages 171-184, December.

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    More about this item

    Keywords

    Data Envelopment Analysis (DEA); Zero-Sum Gains (ZSG); Output Interdependency; Forward/Reverse Fixed-Sum Output; Offensive/Defensive Efficiency; Soccer Teams;
    All these keywords.

    JEL classification:

    • Z2 - Other Special Topics - - Sports Economics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Restaurants; Recreation; Tourism

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