Solving bilevel programming problem with interval coefficients at the lower level : a fuzzy approach
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Bilevel programming has been proposed for dealing with decision processes involving two decision makers with a hierarchical structure.This paper presents a procedure for solving bilevel programming problem (BLPP) with interval coefficients at the lower level. In the proposed procedure, this problem is transformed into a classical BLPP with two objective functions at the lower level by considering order relations on the class of all closed intervals. Then, the obtained problem is converted into an ordinary BLPP with a single objective function at each level by use of fuzzy programming technique. Finally, a numerical example is given to illustrate this approach.
Abstract
Bilevel programming has been proposed for dealing with decision processes involving two decision makers with a hierarchical structure.This paper presents a procedure for solving bilevel programming problem (BLPP) with interval coefficients at the lower level. In the proposed procedure, this problem is transformed into a classical BLPP with two objective functions at the lower level by considering order relations on the class of all closed intervals. Then, the obtained problem is converted into an ordinary BLPP with a single objective function at each level by use of fuzzy programming technique. Finally, a numerical example is given to illustrate this approach.
참고문헌 (8)
- G. Alefeld, "Introduction to Interval Computations" (1983), Academic Press
- W. Bialas, "Two-level linear programming", Management Science, 30, pp.1004~1020 (1984)
- J.F. Bard, "Practical Bilevel Optimization: Algorithms and Applications" (1998), Kluwer Academic Publishers
- S. Dempe, "Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints", Optimization, 52, pp.333~359 (2003)
- S. Dempe, "Foundations of Bilevel Programming" (2002), Kluwer Academic Publishers
- H. Ishibuchi, "Multiobjective programming in optimization of the interval objective function", European Journal of Operational Research, 48, pp.219~225 (1990)
- L. N. Vicente, "Bilevel and multilevel programming: A bibliography review", Journal of Global Optimization, 5, pp.291~306 (1994)
- H.J. Zimmermann, "Fuzzy programming and linear programming with several objective functions", Fuzzy Sets and Systems, 1, pp.45~55 (1978)