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A revised simplex algorithm for fuzzy number linear programming problems using linear ranking functions

S. H. Nasseri, B. Khabiri

Abstract


Recently, fuzzy simplex algorithms have been proposed for two kinds of fuzzy linear programming problems such as: 1) linear programming problems with fuzzy variables and 2) fuzzy number linear programming problems. In our recent paper, we proposed a revised fuzzy simplex algorithm to solve the problems in the first type of these problems using linear ranking functions. In this paper, we focus on the second type of problems and propose a revised simplex algorithm for solving these problems using linear ranking functions. It is simple to see that this method proceeds through the same steps as the simplex method but keeps all pertinent information in a smaller array. Furthermore, we emphasize that the new algorithm will be useful for sensitivity analysis on fuzzy number linear programming problems when using the primal simplex tableau. Finally, we also give an illustrative example to show the advantage of the proposed method. We emphasize that the mentioned algorithm will be useful for solving the dual of the linearprogramming problems with fuzzy variables (FVLP) which is a fuzzy number linear programming (FNLP) and also the sensitivity analysis on the FNLP or FVLP problems.

Keywords


Fuzzy number linear programming, fuzzy simplex algorithm, ranking function, revised simplex algorithm, trapezoidal fuzzy number.

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