Interactive Decision Making for Hierarchical Multiobjective Linear Programming Problems

  • Hitoshi Yano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5861)


In this paper, we focus on hierarchical multiobjective linear programming problems where multiple decision makers in a hierarchical organization have their own multiple objective linear functions together with common linear constraints, and propose an interactive decision making method to obtain the satisfactory solution which reflects not only the hierarchical relationships between multiple decision makers but also their own preferences for their objective functions. In the proposed method, instead of Pareto optimal concept, the generalized Λ-extreme point concept is introduced. In order to obtain the satisfactory solution from among the generalized Λ-extreme point set, an interactive decision making method based on the linear programming is proposed, and an interactive processes are demonstrated by means of an illustrative numerical example.


Decision Maker Decision Power Satisfactory Solution Multiobjective Optimization Problem Unique Optimal Solution 
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  1. 1.
    Anandalingam, G.: A mathematical programming model of decentralized multi-Level systems. Journal of Operational Research Society 39, 1021–1033 (1988)CrossRefzbMATHGoogle Scholar
  2. 2.
    Fiacco, A.V.: Introduction to Sensitivity and Stability Analysis in Nonlinear Programming. Academic Press, New York (1983)zbMATHGoogle Scholar
  3. 3.
    Lai, Y.-J.: Hierarchical optimization: a satisfactory solution. Fuzzy Sets and Systems 77, 321–335 (1996)CrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    Sakawa, M.: Fuzzy Sets and Interactive Multiobjective Optimization. Plenum Press, New York (1993)zbMATHGoogle Scholar
  5. 5.
    Sakawa, M., Yano, H.: Generalized hyperplane methods for characterizing Λ-extreme points and trade-off rates for multiobjective optimization problems. European Journal of Operational Research 57, 368–380 (1992)CrossRefzbMATHGoogle Scholar
  6. 6.
    Shih, H.: An interactive approach for integrated multilevel systems in a fuzzy environment. Mathematical and Computer Modelling 36, 569–585 (2002)CrossRefzbMATHGoogle Scholar
  7. 7.
    Shih, H.: Fuzzy approach to multilevel knapsack problems. Computers and Mathematics with Applications 49, 1157–1176 (2005)CrossRefMathSciNetzbMATHGoogle Scholar
  8. 8.
    Shih, H., Lai, Y.-J., Lee, E.S.: Fuzzy approach for multi-level programming problems. Computers and Operations Research 23, 73–91 (1996)CrossRefMathSciNetzbMATHGoogle Scholar
  9. 9.
    Wen, U.-P., Hsu, S.-T.: Linear bi-level programming problems - a review. Journal of Operational Research Society 42, 125–133 (1991)CrossRefzbMATHGoogle Scholar
  10. 10.
    Yano, H., Sakawa, M.: A unified approach for characterizing Pareto optimal solutions of multiobjective optimization problems: The hyperplane method. European Journal of Operational Research 39, 61–70 (1989)CrossRefMathSciNetzbMATHGoogle Scholar
  11. 11.
    Yu, P.-L.: Cone convexity, cone extreme points, and nondominated solution in decision problems with multiple objective. Journal of Optimization Theory and Applications 14, 319–377 (1974)CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Hitoshi Yano
    • 1
  1. 1.Nagoya City UniversityNagoyaJapan

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