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Modifying olympics medal table via a stochastic multicriteria acceptability analysis. (English) Zbl 1427.90174

Summary: This paper addresses the issue of developing a widely accepted Olympics ranking scheme based upon the Olympic Game medal table published by the International Olympic Committee, since the existing lexicographic ranking and sum ranking systems are both criticized as biases. More specifically, the lexicographic ranking system is deemed as overvaluing gold medals, while the sum ranking system fails to reveal the real value of gold medals and fails to discriminate National Olympic Committees that won equal number of medals. To start, we employ a sophisticated mathematical method based upon the incenter of a convex cone to aggregate the lexicographic ranking system. Then, we consider the fact that the preferences between the lexicographic and the sum ranking systems may not be consistent across National Olympic Committees and develop a well-designed mathematical transformation to obtain interval assessment results under typical preference. The formulation of intervals is inspired by the observation that it is extremely difficult to achieve a group consensus on the exact value of weights with respect to each ranking system, since different weight elicitation methods may produce different weight schemes. Finally, regarding the derived decision making problem involving interval-valued data, this paper utilizes the Stochastic Multicriteria Acceptability Analysis to obtain a comprehensive ranking of all National Olympic Committees. Instead of determining precise weights, this work probes the weight space to guarantee each alternative getting the most preferred one. The proposed method is illustrated by presenting a new ranking of 12 National Olympic Committees participating in the London 2012 Summer Olympic Games.

MSC:

90B50 Management decision making, including multiple objectives
90B90 Case-oriented studies in operations research
90C15 Stochastic programming

Software:

JSMAA
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Full Text: DOI

References:

[1] Sitarz, S., Mean value and volume-based sensitivity analysis for Olympic rankings, European Journal of Operational Research, 216, 1, 232-238 (2012) · Zbl 1237.90122 · doi:10.1016/j.ejor.2011.07.010
[2] Sitarz, S., The medal points’ incenter for rankings in sport, Applied Mathematics Letters, 26, 4, 408-412 (2013) · Zbl 1269.90110 · doi:10.1016/j.aml.2012.10.014
[3] Cao, X.; Fu, Y.; Du, J.; Sun, J.; Wang, M., Measuring Olympics performance based on a distance-based approach, International Transactions in Operational Research, 23, 5, 979-990 (2016) · Zbl 1348.90512 · doi:10.1111/itor.12225
[4] Lahdelma, R.; Salminen, P., SMAA-2: stochastic multicriteria acceptability analysis for group decision making, Operations Research, 49, 3, 444-454 (2001) · Zbl 1163.90552 · doi:10.1287/opre.49.3.444.11220
[5] Song, L.; Fu, Y.; Zhou, P.; Lai, K. K., Measuring national energy performance via Energy Trilemma Index: A Stochastic Multicriteria Acceptability Analysis, Energy Economics, 66, 313-319 (2017) · doi:10.1016/j.eneco.2017.07.004
[6] Lozano, S.; Villa, G.; Guerrero, F.; Cortés, P., Measuring the performance of nations at the summer olympics using data envelopment analysis, Journal of the Operational Research Society, 53, 5, 501-511 (2002) · Zbl 1130.90343 · doi:10.1057/palgrave.jors.2601327
[7] Lins, M. P. E.; Gomes, E. G.; Soares de Mello, J. C. C. B.; Soares de Mello, A. J. R., Olympic ranking based on a zero sum gains DEA model, European Journal of Operational Research, 148, 2, 312-322 (2003) · Zbl 1137.91358 · doi:10.1016/S0377-2217(02)00687-2
[8] Li, Y.; Liang, L.; Chen, Y.; Morita, H., Models for measuring and benchmarking olympics achievements, Omega, 36, 6, 933-940 (2008) · doi:10.1016/j.omega.2007.05.003
[9] De Mello, J. C. C. B. S.; Angulo-Meza, L.; Branco Da Silva, B. P., A ranking for the Olympic Games with unitary input DEA models, IMA Journal of Management Mathematics, 20, 2, 201-211 (2009) · Zbl 1169.90495
[10] Wu, J.; Liang, L.; Chen, Y., DEA game cross-efficiency approach to Olympic rankings, Omega, 37, 4, 909-918 (2009) · doi:10.1016/j.omega.2008.07.001
[11] Wu, J.; Liang, L.; Yang, F., Achievement and benchmarking of countries at the Summer Olympics using cross efficiency evaluation method, European Journal of Operational Research, 197, 2, 722-730 (2009) · Zbl 1159.90453 · doi:10.1016/j.ejor.2008.06.030
[12] Zhang, D.; Li, X.; Meng, W.; Liu, W., Measuring the performance of nations at the olympic games using DEA models with different preferences, Journal of the Operational Research Society, 60, 7, 983-990 (2009) · Zbl 1168.90552 · doi:10.1057/palgrave.jors.2602638
[13] Lei, X.; Li, Y.; Xie, Q.; Liang, L., Measuring Olympics achievements based on a parallel DEA approach, Annals of Operations Research, 226, 1, 1-18 (2015) · Zbl 1315.90065 · doi:10.1007/s10479-014-1708-1
[14] Li, Y.; Lei, X.; Dai, Q.; Liang, L., Performance evaluation of participating nations at the 2012 London Summer Olympics by a two-stage data envelopment analysis, European Journal of Operational Research, 243, 3, 964-973 (2015) · Zbl 1346.90850 · doi:10.1016/j.ejor.2014.12.032
[15] Bergiante, N. C. R.; Soares de Mello, J. C. C. B., A ranking for the Vancouver 2010 winter Olympic Games based on the Copeland method, Proceedings of the 3rd IMA International Conference on Mathematics in Sports, The Lowry
[16] Gomes, S. F.; Soares De Mello, J. C. C. B.; Meza, L. A., Sequential use of ordinal multicriteria methods to obtain a ranking for the 2012 Summer Olympic Games, WSEAS Transactions on Systems, 13, 1, 223-230 (2014)
[17] Lahdelma, R.; Hokkanen, J.; Salminen, P., SMAA—stochastic multiobjective acceptability analysis, European Journal of Operational Research, 106, 1, 137-143 (1998) · doi:10.1016/s0377-2217(97)00163-x
[18] Durbach, I., A simulation-based test of stochastic multicriteria acceptability analysis using achievement functions, European Journal of Operational Research, 170, 3, 923-934 (2006) · Zbl 1091.90511 · doi:10.1016/j.ejor.2004.06.031
[19] Lahdelma, R.; Salminen, P., Classifying efficient alternatives in SMAA using cross confidence factors, European Journal of Operational Research, 170, 1, 228-240 (2005) · Zbl 1079.90555 · doi:10.1016/j.ejor.2004.07.039
[20] Lahdelma, R.; Salminen, P., Stochastic multicriteria acceptability analysis using the data envelopment model, European Journal of Operational Research, 170, 1, 241-252 (2005) · Zbl 1079.90556
[21] Lahdelma, R.; Salminen, P., Prospect theory and stochastic multicriteria acceptability analysis (SMAA), Omega, 37, 5, 961-971 (2009) · doi:10.1016/j.omega.2008.09.001
[22] Lahdelma, R.; Makkonen, S.; Salminen, P., Multivariate Gaussian criteria in SMAA, European Journal of Operational Research, 170, 3, 957-970 (2006) · Zbl 1091.90030 · doi:10.1016/j.ejor.2004.08.022
[23] Lahdelma, R.; Makkonen, S.; Salminen, P., Two ways to handle dependent uncertainties in multi-criteria decision problems, Omega, 37, 1, 79-92 (2009) · doi:10.1016/j.omega.2006.08.005
[24] Tervonen, T.; Lahdelma, R., Implementing stochastic multicriteria acceptability analysis, European Journal of Operational Research, 178, 2, 500-513 (2007) · Zbl 1107.90026 · doi:10.1016/j.ejor.2005.12.037
[25] Corrente, S.; Figueira, J. R.; Greco, S., The SMAA-PROMETHEE method, European Journal of Operational Research, 239, 2, 514-522 (2014) · Zbl 1339.90167 · doi:10.1016/j.ejor.2014.05.026
[26] Angilella, S.; Corrente, S.; Greco, S., Stochastic multiobjective acceptability analysis for the Choquet integral preference model and the scale construction problem, European Journal of Operational Research, 240, 1, 172-182 (2015) · Zbl 1339.90163 · doi:10.1016/j.ejor.2014.06.031
[27] Angilella, S.; Corrente, S.; Greco, S.; Słowiński, R., Robust Ordinal Regression and Stochastic Multiobjective Acceptability Analysis in multiple criteria hierarchy process for the Choquet integral preference model, OMEGA - The International Journal of Management Science, 63, 154-169 (2016)
[28] Durbach, I. N.; Calder, J. M., Modelling uncertainty in stochastic multicriteria acceptability analysis, OMEGA - The International Journal of Management Science, 64, 13-23 (2016)
[29] Lahdelma, R.; Salminen, P.; Hokkanen, J., Locating a waste treatment facility by using stochastic multicriteria acceptability analysis with ordinal criteria, European Journal of Operational Research, 142, 2, 345-356 (2002) · Zbl 1082.90536 · doi:10.1016/s0377-2217(01)00303-4
[30] Kangas, A. S.; Kangas, J.; Lahdelma, R.; Salminen, P., Using SMAA-2 method with dependent uncertainties for strategic forest planning, Forest Policy and Economics, 9, 2, 113-125 (2006) · doi:10.1016/j.forpol.2005.03.012
[31] Tervonen, T.; Hakonen, H.; Lahdelma, R., Elevator planning with stochastic multicriteria acceptability analysis, Omega, 36, 3, 352-362 (2008) · doi:10.1016/j.omega.2006.04.017
[32] Durbach, I. N., The use of the SMAA acceptability index in descriptive decision analysis, European Journal of Operational Research, 196, 3, 1229-1237 (2009) · Zbl 1176.90284 · doi:10.1016/j.ejor.2008.05.021
[33] Durbach, I., On the estimation of a satisficing model of choice using stochastic multicriteria acceptability analysis, Omega, 37, 3, 497-509 (2009) · doi:10.1016/j.omega.2007.09.001
[34] Yang, F.; Ang, S.; Xia, Q.; Yang, C., Ranking DMUs by using interval DEA cross efficiency matrix with acceptability analysis, European Journal of Operational Research, 223, 2, 483-488 (2012) · Zbl 1292.90204 · doi:10.1016/j.ejor.2012.07.001
[35] Babalos, V.; Philippas, N.; Doumpos, M.; Zopounidis, C., Mutual funds performance appraisal using stochastic multicriteria acceptability analysis, Applied Mathematics and Computation, 218, 9, 5693-5703 (2012) · Zbl 1239.90056 · doi:10.1016/j.amc.2011.11.066
[36] Yang, F.; Song, S.; Huang, W.; Xia, Q., SMAA-PO: project portfolio optimization problems based on stochastic multicriteria acceptability analysis, Annals of Operations Research, 233, 1, 535-547 (2015) · Zbl 1358.90062 · doi:10.1007/s10479-014-1583-9
[37] Hai, H. L., Using vote-ranking and cross-evaluation methods to assess the performance of nations at the Olympics, WSEAS Transactions on Systems, 6, 6, 1196-1205 (2007) · Zbl 1126.90353
[38] de Mello, J. C. C. B. S.; Gomes, E. G.; Meza, L. A.; Neto, L. B., Cross evaluation using weight restrictions in unitary input DEA models: Theoretical aspects and application to Olympic Games ranking, WSEAS Transactions on Systems, 7, 1, 31-39 (2008)
[39] Henrion, R.; Seeger, A., On properties of different notions of centers for convex cones, Set-Valued and Variational Analysis, 18, 2, 205-231 (2010) · Zbl 1198.46011 · doi:10.1007/s11228-009-0131-2
[40] Henrion, R.; Seeger, A., Inradius and circumradius of various convex cones arising in applications, Set-Valued and Variational Analysis, 18, 3-4, 483-511 (2010) · Zbl 1217.46047 · doi:10.1007/s11228-010-0150-z
[41] Wang, Y.-M.; Luo, Y., Integration of correlations with standard deviations for determining attribute weights in multiple attribute decision making, Mathematical and Computer Modelling, 51, 1-2, 1-12 (2010) · Zbl 1190.90082 · doi:10.1016/j.mcm.2009.07.016
[42] Barron, F. H.; Barrett, B. E., Decision quality using ranked attribute weights, Management Science, 42, 11, 1515-1523 (1996) · Zbl 0879.90002 · doi:10.1287/mnsc.42.11.1515
[43] Tervonen, T., JSMAA: Open source software for SMAA computations, International Journal of Systems Science, 45, 1, 69-81 (2014) · Zbl 1307.93006 · doi:10.1080/00207721.2012.659706
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