Advertisement

Concepts of the Reference Point Class of Methods of Interactive Multiple Objective Programming

  • R. E. Steuer
  • L. R. Gardiner
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 320)

Abstract

This paper discusses topics fundamental to the understanding of the reference point methods of interactive multiple objective programming (represented by the work of Benayoun, de Montgolfier, Tergny and Larichev (1971), Wierzbicki (1977, 1982 and 1986), Steuer and Choo (1983), Nakayama and Sawaragi (1984), Korhonen and Laakso (1986), and others [6, 11, 12, 13, 14 and 18] that has attracted considerable attention in the 1980s.

Keywords

Decision Maker Sampling Program Decision Space Criterion Space Criterion Vector 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Benayoun, R., J. de Montgolfier, J. Tergny, and O. Larichev (1971). “Linear Programming with Multiple Objective Functions: Step Method (STEM),” Mathematical Programming, Vol. 1, No. 3, pp. 366–375.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    Brockhoff, K. (1985). “Experimental Test of MCDM Algorithms in a Modular Approach,” European Journal of Operational Research, Vol. 22, No. 2, pp. 159–166.CrossRefMATHGoogle Scholar
  3. [3]
    Buchanan, J. T. and H. G. Daellenbach (1987). “A Comparative Evaluation of Interactive Solution Methods for Multiple Objective Decision Models,” European Journal of Operational Research, Vol. 29, No. 3, pp. 353–359.CrossRefGoogle Scholar
  4. [4]
    Chankong, V. and Y. Y. Haimes (1978). “The Interactive Surrogate Worth Trade-off (ISWT) Method for Multiobjective Decision-Making,” Lecture Notes in Economics and Mathematical Systems, Vol. 155, Springer-Verlag, pp. 42–67.Google Scholar
  5. [5]
    Chankong, V. and Y. Y. Haimes (1983). Multiobjective Decision Making: Theory and Methodology, New York: North-Holland.MATHGoogle Scholar
  6. [6]
    Franz, L. S. and S. M. Lee (1980). “A Coal Programming Based Interactive Decision Support System,” Lecture Notes in Economics and Mathematical Systems, Vol. 190, Springer-Verlag, pp. 110–115.Google Scholar
  7. [7]
    Gardiner, L. R. (1989). “Unified Interactive Multiple Objective Programming,” Ph.D. Dissertation, Department of Management Science & Information Technology, University of Georgia, Athens, Georgia, USA.Google Scholar
  8. [8]
    Geoffrion, A. M., J. S. Dyer, and A. Feinberg (1972). “An Interactive Approach for Multicriterion Optimization, with an Application to the Operation of an Academic Department,,” Management Science, Vol. 19, No. 4, pp. 357–368.CrossRefMATHGoogle Scholar
  9. [9]
    Kennington, J. and A. W. Whisman (1986). “NETSIDE Users Guide”, Technical Report 86–0R-01, Department of Operations Research, Southern Methodist University, Dallas, Texas 75275.Google Scholar
  10. [10]
    Korhonen, P. J. and J Laakso (1986). “A Visual Interactive Method for Solving the Multiple Criteria Problem,” European,Journal of Operational Research, Vol. 24, No. 2, pp. 277–287.MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    Korhonen, P. J. and J. Wallenius (1988). “A Pareto Race,” Naval Research Logistics, Vol. 35, No. 6, pp. 615–623.CrossRefMATHGoogle Scholar
  12. [12]
    Kreglewski, T., J. Paczynski, J. Granat, and A. P. Wierzbicki (1918). “IAC-DIDAS-N: A Dynamic Interactive Decision Analysis and Support System for Multicriteria Analysis of Nonlinear Models with Nonlinear Model Generator Supporting Model Analysis,” WP-88–112, International Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
  13. [13]
    Lewandowski, A. and M. Grauer (1982). “The Reference Point Approach: Methods of Efficient Implementation,” WP-82–26, International Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
  14. [14]
    Lewandowski, A., T. Kreglewski, T. Rogowski, and A. P. Wierzbicki (1987). “Decision Support Systems of DIDAS Family (Dynamic Interactive Decision Analysis and Support),” Archiwum Automatvki iTelemechaniki, Vol. 32, No. 4, pp. 221–246.MATHGoogle Scholar
  15. [15]
    Lieberman, E. R. (1990). Multi-Objective Programming in the USSR, book manuscript, School of Management, State University of New York at Buffalo, Buffalo, New York, USA.Google Scholar
  16. [16]
    Liou, F. H. (1984). “A Routine for Generating Grid Point Defined Weighting Vectors,” Masters Thesis, Department of Management Science & Information Technology, University of Georgia, Athens, Georgia, USA.Google Scholar
  17. [17]
    Nakayama, H. and Y. Sawaragi (1984). “Satisficing Trade-off Method for Multiobjective Programming.” Lecture Notes in Economics and Mathematical Systems, Vol. 229, Springer-Verlag, pp. 113–122.Google Scholar
  18. [18]
    Rogowski, T., J. Sobczyk, and A. P. Wierzbicki (1988). “IAC-DIDAS-L:, Dynamic Interactive Decision Analysis and Support System: Linear Version,” WP-88–110, International Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
  19. [19]
    Steuer, R. E. (1986). Multiple Criteria Optimization: Theory, Computation, and Application, (published by John Wiley & Sons, New York; republished by Krieger Publishing, Melbourne, Florida ), 546 ppGoogle Scholar
  20. [20]
    Steuer, R. E. (1990). “ADBASE Operating Mnaual,” Department of Management Science & Information Technology, University of Georgia, Athens, Georgia, USA.Google Scholar
  21. [21]
    Steuer, R. E. and E.-U. Choo (1983). “An Interactive Weighted Tchebycheff Procedure for Multiple Objective Programming,” Mathematical Programming, Vol. 26, No. 1, pp. 326–344.MathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    Wierzbicki, A. P. (1977). “Basic Properties of Scalarizing Functionals for Multiobjective Optimization,” Mathematische Operationsforschung und Statistik–Series Optimization, Vol. 8, No. 1, pp. 55–60.MathSciNetCrossRefGoogle Scholar
  23. [23]
    Wierzbicki, A. P. (1982). “A Mathematical Basis for Satisficing Decision Making,” Mathematical Modelling, Vol. 3, pp. 391–405.MathSciNetCrossRefMATHGoogle Scholar
  24. [24]
    Wierzbicki, A. P. (1986). “On the Completeness and Constructiveness of Parametric Characterizations to Vector Optimization Problems,” OR Spektrum, Vol. 8, No. 2, pp. 73–87.MathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    Zeleny, M. (1989). “Stable Patterns from Decision-Producing Networks: New Interfaces of DSS and MCDM,” MCDM WorldScan, Vol. 3, Nos. 23, pp. 6–7.Google Scholar
  26. [26]
    Zionts, S. and J. Wallenius (1976). “An Interactive Programming Method for Solving the Multiple Criteria Problem,” Management Science, Vol. 22, No. 6, pp. 652–663.CrossRefMATHGoogle Scholar
  27. [27]
    Zionts, S. and J. Wallenius (1983). “An Interactive Multiple Objective Linear Programming Method for a Class of Underlying Nonlinear Utility Functions,” Management Science, Vol. 29, No. 5, pp. 519–529.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 1991

Authors and Affiliations

  • R. E. Steuer
    • 1
  • L. R. Gardiner
    • 2
  1. 1.University of GeorgiaAthensUSA
  2. 2.Auburn UniversityAuburnUSA

Personalised recommendations