Abstract
The application of Data Envelopment Analysis (DEA) as an alternative multiple criteria decision making (MCDM) tool has been gaining more attentions in the literatures. Doyle (Organ. Behav. Hum. Decis. Process. 62(1):87–100, 1995) presents a method of multi-attribute choice based on an application of DEA. In the first part of his method, the straightforward DEA is considered as an idealized process of self-evaluation in which each alternative weighs the attributes in order to maximize its own score (or desirability) relative to the other alternatives. Then, in the second step, each alternative applies its own DEA-derived best weights to each of the other alternatives (i.e., cross-evaluation), then the average of the cross-evaluations that get placed on an alternative is taken as an index of its overall score. In some cases of multiple criteria decision making, direct or indirect competitions exist among the alternatives, while the factor of competition is usually ignored in most of MCDM settings. This paper proposes an approach to evaluate and rank alternatives in MCDM via an extension of DEA method, namely DEA game cross-efficiency model in Liang, Wu, Cook and Zhu (Oper. Res. 56(5):1278–1288, 2008b), in which each alternative is viewed as a player who seeks to maximize its own score (or desirability), under the condition that the cross-evaluation scores of each of other alternatives does not deteriorate. The game cross-evaluation score is obtained when the alternative’s own maximized scores are averaged. The obtained game cross-evaluation scores are unique and constitute a Nash equilibrium point. Therefore, the results and rankings based upon game cross-evaluation score analysis are more reliable and will benefit the decision makers.
Similar content being viewed by others
References
Anderson, T. R., Hollingsworth, K., & Inman, L. (2002). The fixed weighting nature of a cross-evaluation model. Journal of Productivity Analysis, 17(3), 249–255.
Bao, C. P., Chen, T. H., & Chang, S. Y. (2008). Slack-based ranking method: an interpretation to the cross-efficiency method in DEA. Journal of the Operational Research Society, 59(6), 860–862.
Behzadian, M., Kazemzadeh, R. B., Albadvi, A., & Aghdasi, M. (2010). PROMETHEE: a comprehensive literature review on methodologies and applications. European Journal of Operational Research, 200(1), 198–215.
Bouyssou, D., & Pirlot, M. (2008). On some ordinal models for decision making under uncertainty. Annals of Operations Research, 163(1), 19–48.
Brans, J. P., & Vincke, P. (1985). A preference ranking organisation method (the PROMETHEE method for multiple criteria decision-making). Management Science, 31(6), 647–656.
Brans, J. P., Vincke, P., & Mareschal, B. (1986). How to select and rank projects: the PROMETHEE method. European Journal of Operational Research, 24(2), 228–238.
Cook, W. D., & Kress, M. (1991). A multiple criteria decision model with ordinal preference data. European Journal of Operational Research, 54(2), 191–198.
Cook, W. D., Doyle, J., Green, R., & Kress, M. (1996a). Ranking players in multiple tournaments. Computers and Operations Research, 23(9), 869–880.
Cook, W. D., Kress, M., & Seiford, L. M. (1996b). Data envelopment analysis in the presence of both quantitative and qualitative factors. Journal of the Operational Research Society, 47(7), 945–953.
Doyle, J. R. (1995). Multi-attribute choice for the lazy decision maker: let the alternatives decide. Organizational Behavior and Human Decision Processes, 62(1), 87–100.
Doyle, J. R., & Green, R. H. (1993). Data envelopment analysis and multiple criteria decision making. Omega, 21(6), 713–715.
Ehrgott, M. (2006). A discussion of scalarization techniques for multiple objective integer programming. Annals of Operations Research, 147(1), 343–360.
Grabisch, M., & Labreuche, C. (2010). A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. Annals of Operations Research, 175(1), 247–286.
Green, R. H., Doyle, J. R., & Cook, W. D. (1996). Preference voting and project ranking using DEA and cross-evaluation. European Journal of Operational Research, 90(3), 461–472.
Liang, L., Wu, J., Cook, W. D., & Zhu, J. (2008a). Alternative secondary goals in DEA cross-efficiency evaluation. International Journal of Production Economics, 113(2), 1025–1030.
Liang, L., Wu, J., Cook, W. D., & Zhu, J. (2008b). The DEA game cross-efficiency model and its Nash equilibrium. Operations Research, 56(5), 1278–1288.
Peng, Y., Kou, G., Shi, Y., & Chen, Z. X. (2008). A descriptive framework for the field of data mining and knowledge discovery. International Journal of Information Technology & Decision Making, 7(4), 639–682.
Ralphs, T. K., Saltzman, M. J., & Wiecek, M. M. (2006). An improved algorithm for solving biobjective integer programs. Annals of Operations Research, 147(1), 43–70.
Roy, B. (1991). The outranking approach and the foundations of ELECTRE methods. Theory and Decision, 31(1), 49–73.
Sexton, T. R., Silkman, R. H., & Hogan, A. J. (1986). Data envelopment analysis: critique and extensions. In R. H. Silkman (Ed.), Measuring efficiency: an assessment of data envelopment analysis (pp. 73–105). San Francisco: Jossey-Bass.
Shi, Y. (2010). The research trend of information technology and decision making in 2009. International Journal of Information Technology & Decision Making, 9(1), 1–8.
Stewart, T. J. (1996). Relationships between data envelopment analysis and multicriteria decision analysis. Journal of the Operational Research Society, 47(5), 654–665.
Sun, S., & Lu, W. M. (2005). A cross-efficiency profiling for increasing discrimination in data envelopment analysis. INFOR, Information Systems and Operational Research, 43(1), 51–60.
Von Winderfelt, D., & Edwards, W. (1986). Decision analysis and behavioral research. Cambridge: Cambridge University Press.
Wallenius, J., Dyer, J. S., Fishburn, P. C., Steuer, R. E., Zionts, S., & Deb, K. (2008). Multiple criteria decision making, multi-attribute utility theory: recent accomplishments and what lies ahead. Management Science, 54(7), 1336–1349.
Weistroffer, H. R., & Narula, S. C. (1997). The state of multiple criteria decision support software. Annals of Operations Research, 72, 299–313.
Wu, D. (2009). Performance evaluation: an integrated method using data envelopment analysis and fuzzy preference relations. European Journal of Operational Research, 194(1), 227–235.
Wu, J., Liang, L., & Chen, Y. (2009a). DEA game cross-efficiency approach to Olympic rankings. Omega, 37(4), 909–918.
Wu, J., Liang, L., & Yang, F. (2009b). Determination of the weights for the ultimate cross-efficiency using Shapley value in cooperative game. Expert Systems with Applications, 36(1), 872–876.
Wu, J., Liang, L., Yang, F., & Yan, H. (2009c). Bargaining game model in the evaluation of decision making units. Expert Systems with Applications, 36(3), 4357–4362.
Wu, J., Liang, L., Zha, Y., & Yang, F. (2009d). Determination of cross-efficiency under the principle of rank priority in cross-evaluation. Expert Systems with Applications, 36(3), 4826–4829.
Yang, Y. P., Shieh, H. M., Leu, J. D., & Tzeng, G. H. (2009). A Vikor-based multiple criteria decision method for improving information security risk. International Journal of Information Technology & Decision Making, 8(2), 267–287.
Author information
Authors and Affiliations
Corresponding author
Additional information
The previous version of this paper was presented in the 20th International Conference on Multiple Criteria Decision Making held in Chengdu/Jiuzhaigou, China, 21–26 June 2009.
Rights and permissions
About this article
Cite this article
Wu, J., Liang, L. A multiple criteria ranking method based on game cross-evaluation approach. Ann Oper Res 197, 191–200 (2012). https://doi.org/10.1007/s10479-010-0817-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-010-0817-8