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Abstract

Yu (1973) and Zeleny (1974) define the ideal solution (Yu describes this solution as the “utopia point”) as any solution that would simultaneously optimize each individual objective. In objective function space this point has the coordinates Z(x*) = [Z1(x*), ..., Zk(x*)], where x* optimizes every Zh(x). It is an unusual case where there is a single solution wh ich simultaneously optimizes all of the objectives. However, a representation of the unobtainable ideal solution can be obtained for any properly bounded set of alternatives by optimizing each Zh(x) separately. The coordinates of this representation are then given by [Z1(x1 *), ..., Zk(xk *)], where xh * optimizes the hth objective. Should any Zh be unbounded, Zh * cannot be precisely specified. This case will be discussed in greater detail in Section 10.4. If the ideal solution is obtainable (x1 * = ... = xk *) it is dearly the solution to the multiobjective linear program.

Keywords

MULTIOBJECTIVE Optimization Ideal Solution Ideal Point Compromise Solution Multiple Criterion Decision 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Ackoff, R. L., A Concept of Corporate Planning, Wiley, New York, 1970.Google Scholar
  2. Ackoff, R. L., The Art of Problem Solving, Wiley, New York, 1978.Google Scholar
  3. Chankong, V. and Y. Y. Haimes Multiobjective Decision Maldng: Theory and Methodology, North-Holland, New York, 1983.Google Scholar
  4. Yu, P. L., “A Class of Solutions for Group Decision Problems,” Management Science, 19 (1973), 936–946.CrossRefGoogle Scholar
  5. Yu, P. L., Multiple-Criteria Decision Making, Plenum Press, New York, 1985.CrossRefGoogle Scholar
  6. Zeleny, M., “A Concept of Compromise Solutions and the Method of the Displaced Ideal,” Computers and Operations Research, 1 (1974), 479–496.CrossRefGoogle Scholar
  7. Zeleny, M., “The Theory of the Displaced Ideal,” in M. Zeleny (Ed.) Multiple Criteria Decision Making: Kyoto 1975, Springer-Verlag, Berlin, 1975.Google Scholar
  8. Zeleny, M., “The Attribute-Dynamic Attitude Model (ADAM),” Management Science, 23 (1976), 12–26.CrossRefGoogle Scholar
  9. Zeleny, M., “Adaptive Displacement of Preferences in Decision Making,” in M. K. Starr, and M. Zeleny (Eds.) Multiple Criteria Decision Making-TIMS Studies in Management Science, North-Holland, Amsterdam, 1977.Google Scholar
  10. Zeleny, M., Multiple Criteria Decision Making, McGraw-Hill, New York, 1982.Google Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Jeffrey L. Ringuest
    • 1
  1. 1.Operations Research and Strategic Management, Wallace Carroll School of ManagementBoston CollegeChestnut HillUSA

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