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A generalization of the Zionts-Wallenius multiple criteria decision making algorithm

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Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In multicriteria problem solving, much can be learned by observing the decision-making process. Some, if not many, of the theoretical constructs used in some academically-generated models are simply not necessary. Taking this into account, we generalize the Zionts-Wallenius Multiple Criteria Decision Making Algorithm. We generalize the approach so that it can solve general convex problems. We do this by drawing from other methods, and by incorporating what we have learned in our work. To deal with the class of convex problems we face, we broaden the concept of tradeoff, and use global tradeoffs. Theory is developed, and then a method incorporating the theory is presented. A small example is included. We discuss how our development enriches decision-making tools currently available. We discuss applications in finance and technology.
Rocznik
Strony
477--500
Opis fizyczny
Bibliogr. 35 poz.
Twórcy
  • Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
autor
  • School of Management, State University of New York Buffalo, NY 14260-4000, USA
Bibliografia
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  • Dahl, H., Meeraus, A. and Zenios, S. (1993) Some financial optimizationmodels: I Risk management. In: S. Zenios, ed.,Financial optimization, Cambridge University Press, 3–36.
  • Dell, R.F. and Karwan, M.H. (1990) An interactive MCDM weight space reduction method utilizing a Tchebycheff value function. Naval Research Logistics 37, 263–277.
  • Elton, E.J. and Gruber, M.J. (1995) Modern Portfolio Theory and Investment Analysis. John Wiley & Sons, New York.
  • Fliege, J. and Heseler, A. (2002) Constructing approximations to the efficient set of convex quadratic muliobjective problems. Universiẗat Dortmund, Ergebnisberichte Angewandte Mathematik 211.
  • Fortune Magazine (1999) Click Here for Decisions (by Brian Palmer). May 10, 153–155.
  • Geoffrion, A.M. (1968) Proper efficiency and the theory of vector maximization. Journal of Mathematical Analysis and its Applications 22, 618–630.
  • Halme M. (1992) Local characterizations of efficient solutions in interactive multiple objective programming. Acta Academiae Oeconomicae Helsingiesis, Series A:84.
  • Henig, M.I. and Buchanan, J. (1997) Tradeoff directions in multiobjective optimization problems. Mathematical Programming 78, 357–374.
  • Kaliszewski, I. (1987) A modified weighted Tchebycheff metric for multiple objective programming. Computers and Operations Research 14, 315–323.
  • Kaliszewski, I. (1993) Calculating tradeoffs by two step parametric programming. Central European Journal of Operational Research and Economics 2, 291–305.
  • Kaliszewski, I. (1994) Quantitative Pareto Analysis by Cone Separation Technique. Kluwer Academic Publishers, Boston.
  • Kaliszewski, I. (1998) Using tradeoff information in Zionts-Wallenius typedecision making algorithm. In: T. Trzaskalik, ed. Metody i Zastosowania Badan Operacyjnych, II, 265–278, Akademia Ekonomiczna, Katowice,1998, (in Polish). English version: Systems Research Institute Report PMMiO, 8/96, 1996.
  • Kaliszewski I. (2000) Using trade-off information in decision making algorithms. Computers and Operations Research 27 (2), 161–182.
  • Kaliszewski, I. and Michalowski, W. (1995) Generation of outcomes with selectively bounded tradeoffs. Foundations of Computing and DecisionSciences 20, 113–122.
  • Kaliszewski, I. and Michalowski, W. (1997) Efficient solutions and boundson tradeoffs. Journal of Optimization Theory and Applications 94, 381–394.
  • Kaliszewski, I. and Michalowski, W. (1999) Searching for psychologically stable solutions of multiple criteria decision problems. European Journalof Operational Research 118, 123–136.
  • Kaliszewski, I., Michalowski, W. and Kersten, G. (1997) A hybrid interactive technique for the MCDM problems. In: M. Karwan, J.Spronk,J. Wallenius, eds.,Essays in Decision Making, A Volume in Honour of Stanley Zionts. Springer, Heidelberg, 48-59.
  • K̈oksalan, M., Karwan, M.H. and Zionts, S.(1984) An Improved Method for Solving Multiple Criteria Problems Involving Discrete Alternatives. IEEE Transactions on Systems, Man, and Cybernetics 14, 24–34.
  • Kuhn, H.W. and Tucker, A. (1951) Nonlinear programming. In:Proceedings of the Second Berkeley Symposium on Mathematics, Statistics, and Probability, University of California Press, Berkeley.
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  • Markowitz, H.M. (1959) Portfolio Selection, Efficient Diversification of Investments. John Wiley, New York.
  • New Basel Capital Accord (2004) International Convergence of Capita lMeasurement and Capital Standards; a revised framework. Basel Committee on Banking Supervision, available from the Bank for International Settlements, www.bis.org.
  • Roy, A. and Wallenius, J. (1991) Nonlinear and unconstrained multipleobjective optimization: algorithm, computation and application. Naval Research Logistics 38, 623–635.
  • Roy, A. and Wallenius, J. (1992) Nonlinear multiple objective optimization: An algorithm and some theory. Mathematical Programming 55, 235–249.
  • Sakawa, M. and Yano, H. (1990) Tradeoff rates in the hyperplane method for multiple-objective optimization. European Journal of Operational Research 44, 105–118.
  • Steuer, R.E. (1986) Multiple Criteria Optimization: Theory, Computationand Application. John Wiley, New York.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0007-0064
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