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

2018 ◽  
Vol 3 (3) ◽  
pp. 280-293 ◽  
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.

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

2021 ◽  
Vol 23 (07) ◽  
pp. 94-109
Author(s):  
Mohamed Solomon ◽  
◽  
Hegazy Zaher ◽  
Naglaa Ragaa ◽  
◽  
...  
Keyword(s):  
Fractional Programming ◽  
Efficient Solution ◽  
The Other ◽  
Regular Simplex ◽  
Linear Fractional Programming ◽  
Multi Objective ◽  
Interval Coefficients ◽  
Rough Interval ◽  
Single Objective ◽  
Linear Fractional Programming Problem

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.

scholarly journals A linear programming approach to test efficiency in multi-objective linear fractional programming problems

2010 ◽  
Vol 34 (12) ◽  
pp. 4179-4183 ◽  
Author(s):  
Farhad Hosseinzadeh Lotfi ◽  
Abbas Ali Noora ◽  
Gholam Reza Jahanshahloo ◽  
Mohammad Khodabakhshi ◽  
Ali Payan
Keyword(s):  
Linear Programming ◽  
Fractional Programming ◽  
Programming Approach ◽  
Linear Fractional Programming ◽  
Multi Objective ◽  
Linear Programming Approach ◽  
Test Efficiency

scholarly journals Evaluating fuzzy inequalities and solving fully fuzzified linear fractional programs

2012 ◽  
Vol 22 (1) ◽  
pp. 41-50 ◽  
Author(s):  
B. Stanojevic ◽  
I.M. Stancu-Minasian
Keyword(s):  
Linear Programming ◽  
Fractional Programming ◽  
Fuzzy Numbers ◽  
Multiple Objective ◽  
Multiple Objective Linear Programming ◽  
Triangular Fuzzy Numbers ◽  
Linear Fractional Programming ◽  
Numerical Examples ◽  
Fractional Programs ◽  
Linear Fractional Programming Problem

In our earlier articles, we proposed two methods for solving the fully fuzzified linear fractional programming (FFLFP) problems. In this paper, we introduce a different approach of evaluating fuzzy inequalities between two triangular fuzzy numbers and solving FFLFP problems. First, using the Charnes-Cooper method, we transform the linear fractional programming problem into a linear one. Second, the problem of maximizing a function with triangular fuzzy value is transformed into a problem of deterministic multiple objective linear programming. Illustrative numerical examples are given to clarify the developed theory and the proposed algorithm.

scholarly journals A Proposal to the Solution of Multiobjective Linear Fractional Programming Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
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.

scholarly journals A Computer Technique for Solving Linear Fractional Programming Problems by Using Dinkelbach’s Algorithm

2016 ◽  
Vol 64 (2) ◽  
pp. 121-125
Author(s):  
Sajal Chakroborty ◽  
Md Babul Hasan
Keyword(s):  
Linear Programming ◽  
Mathematical Programming ◽  
Programming Language ◽  
Fractional Programming ◽  
Computer Code ◽  
Linear Fractional Programming ◽  
Computer Technique ◽  
Numerical Examples

In this paper, we introduce a computer oriented technique for solving linear fractional programming (LFP) problems by converting it into a single linear programming (LP) problem. We have used the idea of Dinkelbach’s algorithm. We use a mathematical programming language (AMPL) to develop computer code. A number of numerical examples are used to demonstrate the technique. Dhaka Univ. J. Sci. 64(2): 121-125, 2016 (July)

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