Efficient solution generation for multiple objective linear programming based on extreme ray generation method

2005 ◽  
Vol 160 (1) ◽  
pp. 242-251 ◽  
Author(s):  
Masaaki Ida
Keyword(s):  
Linear Programming ◽  
Efficient Solution ◽  
Multiple Objective ◽  
Multiple Objective Linear Programming ◽  
Solution Generation

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

SENSITIVITY ANALYSIS OF WEAK EFFICIENCY IN MULTIPLE OBJECTIVE LINEAR PROGRAMMING

2011 ◽  
Vol 28 (04) ◽  
pp. 445-455 ◽  
Author(s):  
SEBASTIAN SITARZ
Keyword(s):  
Sensitivity Analysis ◽  
Linear Programming ◽  
Extreme Point ◽  
Efficient Solution ◽  
Multiple Objective ◽  
Weak Efficiency ◽  
Multiple Objective Linear Programming ◽  
Weakly Efficient Solution ◽  
Extreme Solutions

This paper, studies the sensitivity analysis of weakly efficient extreme solutions in multiple objective linear programming (MOLP). The aim of the paper is to compute the set of the parameters (corresponding to one coefficient) for which a given extreme point is a weakly efficient solution. We also focus on the properties of the parameters set by proving convexity and closeness of this set. Moreover, we compare the results of the sensitivity analysis of efficiency and of weak efficiency in MOLP.

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