scholarly journals Postoptimal analysis in the coefficients matrix piecewise linear fractional programming problems with non-degenerate optimal solution

2010 ◽  
Vol 30 (3) ◽  
pp. 281
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Fractional Programming ◽  
Piecewise Linear ◽  
Optimal Solution ◽  
Linear Fractional Programming

scholarly journals Ranking Function Application for Optimal Solution of Fractional programming problem

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Rasha Jalal
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fractional Programming ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Ranking Function ◽  
Linear Fractional Programming ◽  
Fractional Programming Problem ◽  
Linear Programming Problems

The aim of this paper is to suggest a solution procedure to fractional programming problem based on new ranking function (RF) with triangular fuzzy number (TFN) based on alpha cuts sets of fuzzy numbers. In the present procedure the linear fractional programming (LFP) problems is converted into linear programming problems. We concentrate on linear programming problem problems in which the coefficients of objective function are fuzzy numbers, the right- hand side are fuzzy numbers too, then solving these linear programming problems by using a new ranking function. The obtained linear programming problem can be solved using win QSB program (simplex method) which yields an optimal solution of the linear fractional programming problem. Illustrated examples and comparisons with previous approaches are included to evince the feasibility of the proposed approach.

scholarly journals Application of linear fractional programming problem with fuzzy nature in industry sector

Filomat ◽  
2020 ◽  
Vol 34 (15) ◽  
pp. 5073-5084
Author(s):  
Sapan Das ◽  
S.A. Edalatpanah ◽  
T. Mandal
Keyword(s):  
Fractional Programming ◽  
Simple Structure ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Linear Fractional Programming ◽  
Fuzzy Variables ◽  
Life Problems ◽  
Fuzzy Optimal Solution ◽  
Fuzzy Linear Fractional Programming

Several methods currently exist for solving fuzzy linear fractional programming problems under non negative fuzzy variables. However, due to the limitation of these methods, they cannot be applied for solving fully fuzzy linear fractional programming (FFLFP) problems where all the variables and parameters are fuzzy numbers. So, this paper is planning to fill in this gap and in order to obtain the fuzzy optimal solution we propose a new efficient method for FFLFP problems utilized in daily life circumstances. This proposed method is based on crisp linear fractional programming and has a simple structure. To show the efficiency of our proposed method some numerical and real life problems have been illustrated.

scholarly journals An Effective Branch and Bound Algorithm for Minimax Linear Fractional Programming

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hong-Wei Jiao ◽  
Feng-Hui Wang ◽  
Yong-Qiang Chen
Keyword(s):  
Branch And Bound ◽  
Fractional Programming ◽  
Optimal Solution ◽  
Branch And Bound Algorithm ◽  
Linear Relaxation ◽  
Feasible Region ◽  
Test Problems ◽  
Linear Fractional Programming ◽  
Successive Refinement ◽  
Global Optimal

An effective branch and bound algorithm is proposed for globally solving minimax linear fractional programming problem (MLFP). In this algorithm, the lower bounds are computed during the branch and bound search by solving a sequence of linear relaxation programming problems (LRP) of the problem (MLFP), which can be derived by using a new linear relaxation bounding technique, and which can be effectively solved by the simplex method. The proposed branch and bound algorithm is convergent to the global optimal solution of the problem (MLFP) through the successive refinement of the feasible region and solutions of a series of the LRP. Numerical results for several test problems are reported to show the feasibility and effectiveness of the proposed algorithm.

scholarly journals GOAL PROGRAMMING APPROACH TO CHANCE CONSTRAINED MULTI-OBJECTIVE LINEAR FRACTIONAL PROGRAMMING PROBLEM BASED ON TAYLOR’S SERIES APPROXIMATION

2012 ◽  
Vol 2 (2) ◽  
pp. 77-80
Author(s):  
Durga Banerjee ◽  
Surapati Pramanik
Keyword(s):  
Programming Problem ◽  
Goal Programming ◽  
Fractional Programming ◽  
Random Variables ◽  
Optimal Solution ◽  
Programming Approach ◽  
Objective Functions ◽  
Linear Fractional Programming ◽  
Multi Objective ◽  
Linear Fractional Programming Problem

This paper deals with goal programming approach to chance constrained multi-objective linear fractional programming problem based on Taylor’s series approximation. We consider the constraints with right hand parameters as the random variables of known mean and variance. The random variables are transformed into standard normal variables with zero mean and unit variance. We convert the chance constraints with known confidence level into equivalent deterministic constraints. The goals of linear fractional objective functions are determined by optimizing it subject to the equivalent deterministic system constraints. Then the fractional objective functions are transformed into equivalent linear functions at the optimal solution point by using first order Taylor polynomial series. In the solution process, we use three minsum goal programming models and identify the most compromise optimal solution by using Euclidean distance function.

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