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

Abstract

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.

Uncertain Multi Level Four Dimensional Multi Item Fractional Transportation Problem

“…Dheyab [16] developed a solving procedure for fuzzy linear fractional programming problem using linear ranking function. Jain [17] introduced a method for solving multi objective fractional programming problem by using the Gauss elimination method. Viwas [18] discussed the more for less paradox suitation which occurs in multi objective fractional transportation problem (MOFTP).…”

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

“…Finally the single objective LP problem is solved by a regular simplex method which yields an efficient solution of the original FMOLFP problem. Jain [22] proposed a method using Gauss elimination technique to derive a numerical solution of multi-objective linear programming (MOLP) problem. Then Jain [23] extended his work for MOLFP problem.…”

“…Jain [22] proposed a method using Gauss elimination technique to derive a numerical solution of multi-objective linear programming (MOLP) problem. Then Jain [23] extended his work for MOLFP problem. Porchelvi et al [20] presented procedures for solving both MOLFP problem and FMOLFP problem using the complementary development method of Dheyab [1], where the fractional linear programming is transformed into a linear programming problem.Guzel and Sivri [19] presented a method for finding an efficient solution of MOLFP problem using goal programming.…”

Comments on Modeling of Gauss Elimination Technique and AHA Simplex Algorithm for Multi-objective Linear Programming Problems by Sanjay Jain and Adarsh Mangal

“…The linear programming problems can be solved using various methods. The Gauss Elimination Technique and AHA simplex method was used by Sanjay and Adarsh [1] in solving MOO problems. The method has been applied to solve an example using Chandra Sen's MOO technique [2] and other averaging techniques [3]- [18].…”