Solving Fuzzy Linear Programming Problems Using Two-Level Programming Approach

H. A. Khalifa

doi:https://doi.org/10.14445/22315373/IJMTT-V17P507

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 17 | Number 1 | Year 2015 | Article Id. IJMTT-V17P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V17P507

Solving Fuzzy Linear Programming Problems Using Two-Level Programming Approach

H. A. Khalifa

Citation :

H. A. Khalifa, "Solving Fuzzy Linear Programming Problems Using Two-Level Programming Approach," International Journal of Mathematics Trends and Technology (IJMTT), vol. 17, no. 1, pp. 36-50, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V17P507

Abstract

Linear programming (LP) has been widely applied to solving real world problems. The conventional LP model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This paper deals a linear programming (FLP) problem with fuzzy parameters. The problem is considered by incorporating fuzzy numbers in the cost coefficients, required coefficients, and technological coefficients. Through the use of the -level sets of fuzzy numbers, the FLP problem is converted to the corresponding -parametric LP problem ( -PLP) and hence to interval linear programming (ILP) problem. A pair of two-level mathematical programs is formulated to calculate the lower bound (Lb) and upper bound (Ub) of the objective values of ILP problem. The two-level mathematical programs are then transformed into one-level nonlinear programs. Solving the pair of nonlinear programs produces the interval of the objective values of the problem. An illustrative numerical example is provided in the sake of the paper to clarify the proposed approach.

Keywords

Linear programming problem, Fuzzy numbers, Cut; Interval confidence, Two-level programming approach, Optimal solution.

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