Abstract
An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example.
Highlights
The transportation problem refers to a special case of linear programming problem
We proposed a new method to find the optimal solution of the fractional fuzzy transportation problem based on dual simplex approach
Fractional fuzzy transportation problem is a special type of linear programming problem and it is an active area of research
Summary
The transportation problem refers to a special case of linear programming problem. The basic transportation problem was developed by Hitchcock in 1941 [1]. When applying OR-methods to engineering problems, for instance, the problems to be modelled and solved are normally quite clear cut, well described, and crisp. They can generally be modelled and solved by using classical mathematics which is dichotomous in character. Chief among these limitations is the problem of dimensionality This suggests the idea of developing methods of solution that should not use simultaneously all the data of the problem; one such approach is the decomposition principle due to Dantzig [2] for linear programs. We proposed a new method to find the optimal solution of the fractional fuzzy transportation problem based on dual simplex approach. An illustrative example is provided to explain this proposed method and the conclusions are given in Sections 7 and 8, respectively
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