scholarly journals An Achievement Rate Approach to Linear Programming Problems with an Interval Objective Function

1997 ◽  
Vol 48 (1) ◽  
pp. 25 ◽  
Author(s):  
M. Inuiguchi ◽  
M. Sakawa
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Achievement Rate ◽  
Linear Programming Problems

scholarly journals Modeling of Gauss Elimination Technique and AHA Simplex Algorithm for Multi-objective Linear Programming Problems

2020 ◽  
pp. 1-14
Author(s):  
Sanjay Jain ◽  
Adarsh Mangal
Keyword(s):  
Linear Programming ◽  
Numerical Solution ◽  
Objective Function ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Simplex Algorithm ◽  
Multi Objective ◽  
Linear Objective Function ◽  
Gauss Elimination ◽  
Linear Programming Problems

In this research paper, an effort has been made to solve each linear objective function involved in the Multi-objective Linear Programming Problem (MOLPP) under consideration by AHA simplex algorithm and then the MOLPP is converted into a single LPP by using various techniques and then the solution of LPP thus formed is recovered by Gauss elimination technique. MOLPP is concerned with the linear programming problems of maximizing or minimizing, the linear objective function having more than one objective along with subject to a set of constraints having linear inequalities in nature. Modeling of Gauss elimination technique of inequalities is derived for numerical solution of linear programming problem by using concept of bounds. The method is quite useful because the calculations involved are simple as compared to other existing methods and takes least time. The same has been illustrated by a numerical example for each technique discussed here.

scholarly journals Comparing different ranking functions for solving fuzzy linear programming problems with fuzzy cost coefficients

2021 ◽  
Vol 4 (2) ◽  
pp. 3-17
Author(s):  
Betsabé Pérez Garrido ◽  
Szabolcs Szilárd Sebrek ◽  
Viktoriia Semenova
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Programming ◽  
Ranking Functions ◽  
Statistical Software ◽  
Linear Programming Problems ◽  
Fuzzy Cost ◽  
The Cost ◽  
Cost Vector

In many applications of linear programming, the lack of exact information results in various problems. Nevertheless, these types of problems can be handled using fuzzy linear programming. This study aims to compare different ranking functions for solving fuzzy linear programming problems in which the coefficients of the objective function (the cost vector) are fuzzy numbers. A numerical example is introduced from the field of tourism and then solved using five ranking functions. Computations were carried out using the FuzzyLP package implemented in the statistical software R.

scholarly journals Two simple ways to find an efficient solution for a multiple objective linear programming problem

2018 ◽  
Vol 23 (1) ◽  
pp. 11-18
Author(s):  
Vasile Căruțașu
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Efficient Solution ◽  
Multiple Objective ◽  
Multiple Objective Linear Programming ◽  
Optimal Solutions ◽  
Nadir Point ◽  
Linear Programming Problems

Abstract A number of methods and techniques for determining “effective” solutions for multiple objective linear programming problems (MPP) have been developed. In this study, we will present two simple methods for determining an efficient solution for a MPP that reducing the given problem to a one-objective linear programming problem. One of these methods falls under the category of methods of weighted metrics, and the other is an approach similar to the ε- constraint method. The solutions determined by the two methods are not only effective and are found on the Pareto frontier, but are also “the best” in terms of distance to the optimal solutions for all objective function from the MPP. Obviously, besides the optimal solutions of linear programming problems in which we take each objective function, we can also consider the ideal point and Nadir point, in order to take into account all the notions that have been introduced to provide a solution to this problem

scholarly journals On multi-objective linear programming problems with inexact rough interval-fuzzy coefficients

2015 ◽  
Vol 14 (5) ◽  
pp. 5742-5758
Author(s):  
E. E. Ammar ◽  
M. L. Hussein ◽  
A. M. Khalifa
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Fuzzy Number ◽  
Linear Programming Problem ◽  
Solution Procedure ◽  
Modeling Framework ◽  
Multi Objective ◽  
Interval Solution ◽  
Linear Programming Problems ◽  
Rough Interval

This paper deals with a multi-objective linear programming problem with an inexact rough interval fuzzy coefficients IRFMOLP. This problem is considered by incorporating an inexact rough interval fuzzy number in both the objective function and constrains. The concept of "Rough interval" is introduced in the modeling framework to represent dualuncertain parameters. A suggested solution procedure is given to obtain rough interval solution for IRFLP(w) problem. Finally,two numerical example is given to clarify the obtained results in this paper.

scholarly journals Solving Linear Programming Problems with Grey Data

2018 ◽  
Vol 3 (1) ◽  
pp. 17-23 ◽  
Author(s):  
Michael Gr. Voskoglou
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Programming Problem ◽  
Standard Method ◽  
Linear Programming Problem ◽  
Real Life ◽  
Optimal Solution ◽  
Real Numbers ◽  
Decision Variables ◽  
Linear Programming Problems

A Grey Linear Programming problem differs from an ordinary one to the fact that the coefficients of its objective function and / or the technological coefficients and constants of its constraints are grey instead of real numbers. In this work a new method is developed for solving such kind of problems by the whitenization of the grey numbers involved and the solution of the obtained in this way ordinary Linear Programming problem with a standard method. The values of the decision variables in the optimal solution may then be converted to grey numbers to facilitate a vague expression of it, but this must be strictly checked to avoid non creditable such expressions. Examples are also presented to illustrate the applicability of our method in real life applications.

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