An Approach for Solving Multi-Objective Linear Fractional Programming Problem with fully Rough Interval Coefficients

In this paper, a multi-objective linear fractional programming (MOLFP) problem is considered where all of its coefficients in the objective function and constraints are rough intervals (RIs). At first, to solve this problem, we will construct two MOLFP problems with interval coefficients. One of these problems is a MOLFP where all of its coefficients are upper approximations of RIs and the other is a MOLFP where all of its coefficients are lower approximations of RIs. Second, the MOLFP problems are transformed into a single objective linear programming (LP) problem using a proposal given by Nuran Guzel. Finally, the single objective LP problem is solved by a regular simplex method which yields an efficient solution of the original MOLFP problem. A numerical example is given to demonstrate the results.

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An Approach for Solving Fuzzy Multi-Objective Linear Fractional Programming Problems

International Journal of Mathematical Engineering and Management Sciences ◽

10.33889/ijmems.2018.3.3-020 ◽

2018 ◽

Vol 3 (3) ◽

pp. 280-293 ◽

Cited By ~ 2

Author(s):

Farhana Akond Pramy

Keyword(s):

Linear Programming ◽

Fractional Programming ◽

Simplex Method ◽

Efficient Solution ◽

Regular Simplex ◽

Linear Fractional Programming ◽

Numerical Examples ◽

Multi Objective ◽

Fuzzy Parameters ◽

Single Objective

In this paper, an attempt has been taken to develop a method for solving fuzzy multi-objective linear fractional programming (FMOLFP) problem. Here, at first the FMOLFP problem is converted into (crisp) multi-objective linear fractional programming (MOLFP) problem using the graded mean integration representation (GMIR) method proposed by Chen and Hsieh. That is, all the fuzzy parameters of FMOLFP problem are converted into crisp values. Then the MOLFP problem is transformed into a single objective linear programming (LP) problem using a proposal given by Nuran Guzel. Finally the single objective LP problem is solved by regular simplex method which yields an efficient solution of the original FMOLFP problem. To show the efficiency of our proposed method, three numerical examples are illustrated and also for each example, a comparison is drawn between our proposed method and the respected existing method.

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A Proposal to the Solution of Multiobjective Linear Fractional Programming Problem

Abstract and Applied Analysis ◽

10.1155/2013/435030 ◽

2013 ◽

Vol 2013 ◽

pp. 1-4 ◽

Cited By ~ 13

Author(s):

Nuran Güzel

Keyword(s):

Programming Problem ◽

Fractional Programming ◽

Software Package ◽

Efficient Solution ◽

Optimal Solution ◽

Linear Fractional Programming ◽

Fractional Programming Problem ◽

Nonlinear Fractional Programming ◽

Single Objective ◽

Linear Fractional Programming Problem

We have proposed a new solution to the Multiobjective Linear Fractional Programming Problem (MOLFPP). The proposed solution is based on a theorem that deals with nonlinear fractional programming with single objective function and studied in the work by Dinkelbach, 1967. As a new contribution, we have proposed that is an efficient solution of MOLFPP if is an optimal solution of problem , where is for all . Hence, MOLFPP is simply reduced to linear programming problem (LPP). Some numerical examples are provided in order to illustrate the applications of the proposed method. The optimization software package, namely, WinQSB (Chang, 2001), has been employed in the computations.

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