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Ogryczak Włodzimierz (Warsaw University of Technology, Poland)
On Robust Solutions to Multi-Objective Linear Programs
Multiple Criteria Decision Making / University of Economics in Katowice, 2010, vol. 5, s. 197-212, bibliogr. 19 poz.
Słowa kluczowe
Analiza wielokryterialna, Programowanie liniowe, Odporne metody statystyczne
Multicriteria analysis, Linear programming, Robust statistical methods
summ., Korespondencja z redakcją: numeracja wpisana za zgodą redakcji (wynika z ciągłości wydawniczej serii MCDM) - brak numeracji na stronie tytułowej
In multiple criteria linear programming (MOLP) any efficient solution can be found by the weighting approach with some positive weights allocated to several criteria. The weights settings represent preferences model thus involving impreciseness and uncertainties. The resulting weighted average performance may be lower than expected. Several approaches have been developed to deal with uncertain or imprecise data. In this paper we focus on robust approaches to the weighted averages of criteria where the weights are varying. Assume that the weights may be affected by perturbations varying within given intervals. Note that the weights are normalized and although varying independently they must total to 1. We are interested in the optimization of the worst case weighted average outcome with respect to the weights perturbation set. For the case of unlimited perturbations the worst case weighted average becomes the worst outcome (max-min solution). For the special case of proportional perturbation limits this becomes the conditional average. In general case, the worst case weighted average is a generalization of the conditional average. Nevertheless, it can be effectively reformulated as an LP expansion of the original problem.(original abstract)
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Biblioteka Główna Uniwersytetu Ekonomicznego w Krakowie
Biblioteka Szkoły Głównej Handlowej w Warszawie
Biblioteka Główna Uniwersytetu Ekonomicznego w Katowicach
Biblioteka Główna Uniwersytetu Ekonomicznego w Poznaniu
Biblioteka Główna Uniwersytetu Ekonomicznego we Wrocławiu
Pełny tekst
  1. Fernandez F.R., Nickel S., Puerto J., Rodriguez-Chia A.M.: Robustness in the Pareto Solutions for the Multi-Criteria Minisum Location Problem. "Journal of Multi-Criteria Decision Analysis" 2001, 10, pp. 191-203.
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  4. Kostreva M.M., Ogryczak W.: Linear Optimization with Multiple Equitable Criteria. "RAIRO Operations Research" 1999, 33, pp. 275-297.
  5. Kostreva M.M., Ogryczak W. and Wierzbicki A.: Equitable Aggregations and Multiple Criteria Analysis. "European Journal of Operational Research" 2004, 158, pp. 362-367.
  6. Kouvelis P., Yu G.: Robust Discrete Optimization and Its Applications. Kluwer, Dordrecht 1997.
  7. Miettinen K., Deb K., Jahn J., Ogryczak W., Shimoyama K., Vetchera R.: Future Chauenges (Chapter 16). In: Multi-Objective Optimization Evolutionary and Interactive Approaches. Lecture Notes in Computer Science, 5252, Springer 2008, pp. 435-461.
  8. Ogryczak W.: Linear and Discrete Optimization with Multiple Criteria: Preference Models and Applications to Decision Support (in Polish), Warsaw University Press 1997.
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  10. Ogryczak W.: Inequality Measures and Equitable Locations. "Annals of Operations Research" 2009, 167, pp. 61-86.
  11. Ogryczak W., Ruszczyński A.: Dual Stochastic Dominance and Quantile Risk Measures. "International Transactions on Operational Research" 2002, 9, pp. 661-680.
  12. Ogryczak W., Śliwiński T.: On Equitable Approaches to Resource Allocation Problems: the Conditional Minimax Solution. "Journal of Telecommunication and Information Technology" 2002, 3, pp. 40-48.
  13. Ogryczak W., Śliwiński T.: On Solving Linear Programs with the Ordered Weighted Averaging Objective. "European Journal of Operational Research" 2003, 148, pp. 80-91.
  14. Ogryczak W., Tamir A.: Minimizing the Sum of the k Largest Functions in Linear Time. "Information Processing Letters" 2003, 85, pp. 117-122.
  15. Ogryczak W., Zawadzki M.: Conditional Median: a Parametric Solution Concept for Location Problems. "Annals of Operations Research" 2002, 110, pp. 167-181.
  16. Perny P., Spanjaard O., Storme L.-X.: A Decision-Theoretic Approach to Robust Optimization in Multivalued Graphs. "Annals of Operations Research" 2006, 147, pp. 317 341.
  17. Pflug G.Ch.: Some Remarks on the Value-at-Risk and the Conditional Value-at-Risk. In: Probabilistic Constrained Optimization: Methodology and Applications. Ed. S. Uryasev. Kluwer, Dordrecht 2000.
  18. Roy B.: A Missing Link in Or-DA: Robustness Analysis. "Foundations of Computing and Decision Sciences" 1998, 23, pp. 141-160.
  19. Steuer R.E.: Multiple Criteria Optimization: Theory, Computation & Applications. Wiley, New York 1986.
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