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Robust optimization analysis for multiple attribute decision making problems with imprecise information

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  • Jiamin Wang

Abstract

This paper considers ranking decision alternatives under multiple attributes with imprecise information on both attribute weights and alternative ratings. It is demonstrated that regret results from the decision maker’s inadequate knowledge about the true scenario to occur. Potential optimality analysis is a traditional method to evaluate alternatives with imprecise information. The essence of this approach is to identify any alternative that outperforms the others in its best-case scenario. Our analysis shows that potential optimality analysis is optimistic in nature and may lead to a significant loss if an unfavorable scenario occurs. We suggest a robust optimization analysis approach that ranks alternatives in terms of their worst-case absolute or relative regret. A robust optimal alternative performs reasonably well in all scenarios and is shown to be desirable for a risk-concerned decision maker. Linear programming models are developed to check robust optimality. Copyright Springer Science+Business Media, LLC 2012

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  • Jiamin Wang, 2012. "Robust optimization analysis for multiple attribute decision making problems with imprecise information," Annals of Operations Research, Springer, vol. 197(1), pages 109-122, August.
    • Handle: RePEc:spr:annopr:v:197:y:2012:i:1:p:109-122:10.1007/s10479-010-0734-x
    DOI: 10.1007/s10479-010-0734-x
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    1. Deng-Feng Li, 2009. "Relative Ratio Method For Multiple Attribute Decision Making Problems," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 289-311.
    2. Zeelenberg, M., 1999. "Anticipated regret, expected feedback and behavioral decision-making," Other publications TiSEM 38371d1b-31fd-45b0-860f-b, Tilburg University, School of Economics and Management.
    3. Saaty, Thomas L. & Vargas, Luis G., 1987. "Uncertainty and rank order in the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 32(1), pages 107-117, October.
    4. David E. Bell, 1985. "Disappointment in Decision Making Under Uncertainty," Operations Research, INFORMS, vol. 33(1), pages 1-27, February.
    5. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    6. Gordon B. Hazen, 1986. "Partial Information, Dominance, and Potential Optimality in Multiattribute Utility Theory," Operations Research, INFORMS, vol. 34(2), pages 296-310, April.
    7. Murat Köksalan & Ceren Tuncer, 2009. "A Dea-Based Approach To Ranking Multi-Criteria Alternatives," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 29-54.
    8. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    9. Craig W. Kirkwood & Rakesh K. Sarin, 1985. "Ranking with Partial Information: A Method and an Application," Operations Research, INFORMS, vol. 33(1), pages 38-48, February.
    10. Weber, Martin, 1987. "Decision making with incomplete information," European Journal of Operational Research, Elsevier, vol. 28(1), pages 44-57, January.
    11. Stewart, TJ, 1992. "A critical survey on the status of multiple criteria decision making theory and practice," Omega, Elsevier, vol. 20(5-6), pages 569-586.
    12. Han-Lin Li & Li-Ching Ma, 2008. "Ranking Decision Alternatives By Integrated Dea, Ahp And Gower Plot Techniques," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 241-258.
    13. Peter C. Fishburn, 1965. "Analysis of Decisions with Incomplete Knowledge of Probabilities," Operations Research, INFORMS, vol. 13(2), pages 217-237, April.
    14. Sam Park, Kyung & Sang Lee, Kyung & Seong Eum, Yun & Park, Kwangtae, 2001. "Extended methods for identifying dominance and potential optimality in multi-criteria analysis with imprecise information," European Journal of Operational Research, Elsevier, vol. 134(3), pages 557-563, November.
    15. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    16. Yu-Ping Ou Yang & How-Ming Shieh & Jun-Der Leu & Gwo-Hshiung Tzeng, 2009. "A Vikor-Based Multiple Criteria Decision Method For Improving Information Security Risk," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 267-287.
    17. Ayeley P. Tchangani, 2009. "Evaluation Model For Multiattributes–Multiagents Decision Making: Satisficing Game Approach," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 73-91.
    18. L C Dias & J N Clímaco, 2000. "Additive aggregation with variable interdependent parameters: the VIP analysis software," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(9), pages 1070-1082, September.
    19. John M. Mulvey & Robert J. Vanderbei & Stavros A. Zenios, 1995. "Robust Optimization of Large-Scale Systems," Operations Research, INFORMS, vol. 43(2), pages 264-281, April.
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