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Measuring Olympics achievements based on a parallel DEA approach

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Abstract

Measuring the performance of participating nations in the Olympic Games is an important application of data envelopment analysis (DEA). Prior literature only considers participating nations’ performance in the Summer Olympic Games. It may be unfair to some nations who are good at the Winter Olympics, but poor at the Summer Olympics. Therefore, we believe it is better to consider the two Olympics together when measuring performance of participants. This paper treats the two Olympics as a parallel system in which each subsystem corresponds to a Summer Olympics or a Winter Olympics, and extends a parallel DEA approach to evaluate the efficiency of each participant. An efficiency decomposition procedure is proposed to obtain the efficiency rang of each Olympic subsystem. Finally, we apply the proposed approach to the latest real data set of the 2012 Summer Olympics and 2010 Winter Olympics.

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Notes

  1. In this paper, we set \(\varepsilon =\hbox {0.01}\). The smaller \(\varepsilon \) value we select, the more impossible the maximum efficiency scores will be missed.

References

  • Ali, A. I. (1994). Computational aspects of DEA. In A. Charnes, W. W. Cooper, A. Lewin, & L. M. Seiford (Eds.), Data envelopment analysis: Theory, methodology and applications (pp. 63–88). Boston: Kluwer.

    Chapter  Google Scholar 

  • Amirteimoori, A., & Nashtaei, R. A. (2006). The role of time in multi-component efficiency analysis: An application. Applied Mathematics and Computation, 177(1), 11–17.

    Article  Google Scholar 

  • Azizi, H., & Wang, Y. M. (2013). Improved DEA models for measuring interval efficiencies of decision-making units. Measurement, 46(3), 1325–1332.

    Article  Google Scholar 

  • Beasley, J. E. (1995). Determining teaching and research efficiencies. Journal of the Operational Research Society, 46, 441–452.

    Article  Google Scholar 

  • Bogetoft, P. (1997). DEA-based yardstick competition: The optimality of best practice regulation. Annals of Operations Research, 73, 277–298.

    Article  Google Scholar 

  • Bougnol, M. L., & Dulá, J. H. (2006). Validating DEA as a ranking tool: An application of DEA to assess performance in higher education. Annals of Operations Research, 145(1), 339–365.

    Article  Google Scholar 

  • Castelli, L., Pesenti, R., & Ukovich, W. (2010). A classification of DEA models when the internal structure of the decision making units is considered. Annals of Operations Research, 173(1), 207–235.

    Article  Google Scholar 

  • Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429–444.

    Article  Google Scholar 

  • Chen, Y., Cook, W. D., Li, N., & Zhu, J. (2009). Additive efficiency decomposition in two-stage DEA. European Journal of Operational Research, 196(3), 1170–1176.

    Article  Google Scholar 

  • Chen, Y., Du, J., David Sherman, H., & Zhu, J. (2010). DEA model with shared resources and efficiency decomposition. European Journal of Operational Research, 207(1), 339–349.

    Article  Google Scholar 

  • Chen, W. C., & Johnson, A. L. (2010). The dynamics of performance space of Major League Baseball pitchers 1871–2006. Annals of Operations Research, 181(1), 287–302.

    Article  Google Scholar 

  • Chen, Y., Liang, L., & Yang, F. (2006). A DEA game model approach to supply chain efficiency. Annals of Operations Research, 145(1), 5–13.

    Article  Google Scholar 

  • Chiang, C. I., Hwang, M. J., & Liu, Y. H. (2011). Determining a common set of weights in a DEA problem using a separation vector. Mathematical and Computer Modelling, 54(9), 2464–2470.

    Article  Google Scholar 

  • Churilov, L., & Flitman, A. (2006). Towards fair ranking of Olympics achievements: The case of Sydney 2000. Computers & Operations Research, 33(7), 2057–2082.

    Article  Google Scholar 

  • Cook, W. D., & Green, R. H. (2004). Multicomponent efficiency measurement and core business identification in multiplant firms: A DEA model. European Journal of Operational Research, 157(3), 540–551.

    Article  Google Scholar 

  • Cook, W. D., Hababou, M., & Tuenter, H. J. (2000). Multicomponent efficiency measurement and shared inputs in data envelopment analysis: An application to sales and service performance in bank branches. Journal of Productivity Analysis, 14(3), 209–224.

    Article  Google Scholar 

  • Cook, W. D., & Zhu, J. (2010). Context-dependent performance standards in DEA. Annals of Operations Research, 173(1), 163–175.

    Article  Google Scholar 

  • De França, J. M. F., de Figueiredo, J. N., & dos Santos Lapa, J. (2010). A DEA methodology to evaluate the impact of information asymmetry on the efficiency of not-for-profit organizations with an application to higher education in Brazil. Annals of Operations Research, 173(1), 39–56.

    Article  Google Scholar 

  • Du, J., Liang, L., Chen, Y., Cook, W. D., & Zhu, J. (2011). A bargaining game model for measuring performance of two-stage network structures. European Journal of Operational Research, 210(2), 390–397.

  • Du, J., Wang, J., Chen, Y., Chou, S. Y., & Zhu, J. (2014). Incorporating health outcomes in Pennsylvania hospital efficiency: An additive super-efficiency DEA approach. Annals of Operations Research, 221, 161–172.

  • Emrouznejad, A. (2014). Advances in data envelopment analysis. Annals of Operations Research, 214, 1–4.

    Article  Google Scholar 

  • Emrouznejad, A., Anouze, A. L., & Thanassoulis, E. (2010). A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA. European Journal of Operational Research, 200(1), 297–304.

    Article  Google Scholar 

  • Emrouznejad, A., Parker, B. R., & Tavares, G. (2008). Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA. Socio-Economic Planning Sciences, 42(3), 151–157.

    Article  Google Scholar 

  • Färe, R., Grabowski, R., Grosskopf, S., & Kraft, S. (1997). Efficiency of a fixed but allocatable input: A non-parametric approach. Economics Letters, 56(2), 187–193.

    Article  Google Scholar 

  • Grigoroudis, E., Tsitsiridi, E., & Zopounidis, C. (2013). Linking customer satisfaction, employee appraisal, and business performance: An evaluation methodology in the banking sector. Annals of Operations Research, 205(1), 5–27.

    Article  Google Scholar 

  • Hai, H. L. (2007). Using vote-ranking and cross-evaluation methods to assess the performance of nations at the Olympics. WSEAS Transactions on Systems, 6(6), 1196–1198.

    Google Scholar 

  • Jahanshahloo, G. R., Amirteimoori, A. R., & Kordrostami, S. (2004). Measuring the multi-component efficiency with shared inputs and outputs in data envelopment analysis. Applied Mathematics and Computation, 155(1), 283–293.

    Article  Google Scholar 

  • Kao, C. (2012). Efficiency decomposition for parallel production systems. Journal of the Operational Research Society, 63(1), 64–71.

    Article  Google Scholar 

  • Kao, C., & Hwang, S. N. (2008). Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan. European Journal of Operational Research, 185(1), 418–429.

    Article  Google Scholar 

  • Kao, C., & Lin, P. H. (2012). Efficiency of parallel production systems with fuzzy data. Fuzzy Sets and Systems, 198, 83–98.

    Article  Google Scholar 

  • Khodabakhshi, M., & Aryavash, K. (2014). The fair allocation of common fixed cost or revenue using DEA concept. Annals of Operations Research, 214(1), 187–194.

  • Li, Y., Chen, Y., Liang, L., & Xie, J. (2012). DEA models for extended two-stage network structures. Omega, 40(5), 611–618.

    Article  Google Scholar 

  • Li, Y., Liang, L., Chen, Y., & Morita, H. (2008). Models for measuring and benchmarking olympics achievements. Omega, 36(6), 933–940.

    Article  Google Scholar 

  • Liang, L., Cook, W. D., & Zhu, J. (2008). DEA models for two-stage processes: Game approach and efficiency decomposition. Naval Research Logistics (NRL), 55(7), 643–653.

    Article  Google Scholar 

  • Lins, M. P. E., Gomes, E. G., Soares de Mello, J. C. C., & Soares de Mello, A. J. R. (2003). Olympic ranking based on a zero sum gains DEA model. European Journal of Operational Research, 148(2), 312–322.

    Article  Google Scholar 

  • Lozano, S., Villa, G., Guerrero, F., & Cortés, P. (2002). Measuring the performance of nations at the Summer Olympics using data envelopment analysis. Journal of the Operational Research Society, 53(5), 501–511.

    Article  Google Scholar 

  • Molinero, C. M. (1996). On the joint determination of efficiencies in a data envelopment analysis context. Journal of the Operational Research Society, 47(10), 1273–1279.

    Article  Google Scholar 

  • Moreno, P., & Lozano, S. (2014). A network DEA assessment of team efficiency in the NBA. Annals of Operations Research, 214(1), 99–124.

  • Prior, D. (2006). Efficiency and total quality management in health care organizations: A dynamic frontier approach. Annals of Operations Research, 145(1), 281–299.

    Article  Google Scholar 

  • Soares de Mello, J. C. C. B., Angulo-Meza, L., & Da Silva, B. P. B. (2009). A ranking for the Olympic Games with unitary input DEA models. IMA Journal of Management Mathematics, 20(2), 201–211.

    Article  Google Scholar 

  • Soares de Mello, J. C. C. B., Angulo-Meza, L., & Lacerda, F. G. (2012). A dea model with a non discritionary variable for olympic evaluation. Pesquisa Operacional, 32(1), 21–30.

    Article  Google Scholar 

  • Tsai, P. F., & Mar Molinero, C. (2002). A variable returns to scale data envelopment analysis model for the joint determination of efficiencies with an example of the UK health service. European Journal of Operational Research, 141(1), 21–38.

    Article  Google Scholar 

  • Wu, J., Liang, L., & Chen, Y. (2009). DEA game cross-efficiency approach to Olympic rankings. Omega, 37(4), 909–918.

    Article  Google Scholar 

  • Wu, J., Liang, L., & Yang, F. (2009). Achievement and benchmarking of countries at the Summer Olympics using cross efficiency evaluation method. European Journal of Operational Research, 197(2), 722–730.

    Article  Google Scholar 

  • Wu, J., Zhou, Z. X., & Liang, L. (2010). Measuring the performance of nations at Beijing Summer Olympics using integer-valued DEA model. Journal of Sports Economics, 11(5), 549–566.

    Article  Google Scholar 

  • Yang, C. C. (2014). An enhanced DEA model for decomposition of technical efficiency in banking. Annals of Operations Research, 214, 167–185.

    Article  Google Scholar 

  • Yang, C. H., Lin, H. Y., & Chen, C. P. (2014). Measuring the efficiency of NBA teams: Additive efficiency decomposition in two-stage DEA. Annals of Operations Research, 217(1), 565–589.

  • Yang, Y., Ma, B., & Koike, M. (2000). Efficiency-measuring DEA model for production system with k independent subsystems. Journal of the Operations Research Society of Japan-Keiei Kagaku, 43(3), 343–354.

    Google Scholar 

  • Yu, M. M. (2008). Measuring the efficiency and return to scale status of multi-mode bus transit-evidence from Taiwan’s bus system. Applied Economics Letters, 15(8), 647–653.

    Article  Google Scholar 

  • Zhang, D., Li, X., Meng, W., & Liu, W. (2009). Measuring the performance of nations at the Olympic Games using DEA models with different preferences & star. Journal of the Operational Research Society, 60(7), 983–990.

    Article  Google Scholar 

  • Zha, Y., & Liang, L. (2010). Two-stage cooperation model with input freely distributed among the stages. European Journal of Operational Research, 205(2), 332–338.

    Article  Google Scholar 

  • Zhou, Z., Wang, M., Ding, H., Ma, C., & Liu, W. (2013). Further study of production possibility set and performance evaluation model in supply chain DEA. Annals of Operations Research, 206(1), 585–592.

    Article  Google Scholar 

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Acknowledgments

The authors thank the editor-in-chief Professor Endre Boros and the reviewers for their constructive comments and suggestions, which have helped to improve the quality of this paper. The authors also thank Professor Alec Morton for his valuable suggestions and his technical check on this paper. This research is supported by National Natural Science Foundation of China under Grants (No. 61101219, 71271196), the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (No. 71121061), the Fund for International Cooperation and Exchange of the National Natural Science Foundation of China (No. 71110107024) and the Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. School of Management, University of Science and Technology of China, Hefei, 230026, Anhui Province, People’s Republic of China

    Xiyang Lei, Yongjun Li & Liang Liang

  2. Department of Electronics and Information, Toyota Technological Institute, Nagoya, 450-0002, Japan

    Qiwei Xie

  3. Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Qiwei Xie

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  1. Xiyang Lei
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  2. Yongjun Li
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  4. Liang Liang
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Correspondence to Yongjun Li or Qiwei Xie.

Appendices

Appendix 1

Theorem 1

If the overall Olympic Games system of \(DMU_{0}\) is efficient, then its each subsystem is efficient, namely \(e_{0}^{1} =e_{0}^{2} =1\).

Proof

Since we have \(\theta _0 =\lambda _0^1 \theta _0^1 +\lambda _0^2 \theta _0^2 \) which is a convex combination of \(\theta _0^1 \) and \(\theta _0^2 \). It is apparently that \(\theta _0 =1\) if and only if \(\theta _0^{1} =\theta _0^2 =1\). Hence, the overall Olympic parallel system of the given \(DMU_0 \) is efficient due to \(e_0 =1/\theta _0 =1\), and meanwhile, the two Olympic subsystems are also efficient due to \(e_0^1 =1/\theta _0^1 =1\) and \(e_0^2 =1/\theta _0^2 =1\). In other words, the overall Olympic parallel system is efficient, then its two Olympic subsystems are efficient. Thus, Theorem 1 has been completely proven. \(\square \)

Appendix 2

Theorem 2

If the overall Olympic Games system of \(DMU_{0}\) is efficient, then \(\underline{E_0^k }=\overline{E_0^k } =1,\forall k\)

Proof

Theorem 1 has proved that the overall Olympic Games system of \(DMU_{0}\) is efficient, then its each subsystem is efficient, namely \(e_{0}^{1} =e_{0}^{2} =1\). In other words, the subsystem has a unique solution equals to 1, thus, the maximum and minimum efficiencies were only identified, namely \(\underline{E_0^k }=\overline{E_0^k } =1,\forall k\). Then Theorem 2 has been proved. \(\square \)

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Lei, X., Li, Y., Xie, Q. et al. Measuring Olympics achievements based on a parallel DEA approach. Ann Oper Res 226, 379–396 (2015). https://doi.org/10.1007/s10479-014-1708-1

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