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

An excellent research contribution was made by Sanjay and Adarsh in using Gauss Elimination Technique and AHA simplex method for solving multi-objective optimization (MOO) problems. The method was applied for solving MOO problems using Chandra Sen's technique and several other averaging techniques. The formulation of multi-objective function in the averaging techniques was not perfect. The example was also not appropriate.

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

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2020/v8i430211 ◽

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.

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

INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY ◽

10.24297/ijct.v14i5.3985 ◽

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.

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Generalised Single-Valued Neutrosophic Number and Its Application to Neutrosophic Linear Programming

Neutrosophic Sets in Decision Analysis and Operations Research - Advances in Logistics, Operations, and Management Science ◽

10.4018/978-1-7998-2555-5.ch009 ◽

2020 ◽

pp. 180-214

Author(s):

Nirmal Kumar Mahapatra ◽

Tuhin Bera

Keyword(s):

Linear Programming ◽

Objective Function ◽

Programming Problem ◽

Linear Programming Problem ◽

Simplex Method ◽

Real Life ◽

Simplex Algorithm ◽

Real Life Problem ◽

Crisp Linear Programming ◽

Neutrosophic Number

In this chapter, the concept of single valued neutrosophic number (SVN-Number) is presented in a generalized way. Using this notion, a crisp linear programming problem (LP-problem) is extended to a neutrosophic linear programming problem (NLP-problem). The coefficients of the objective function of a crisp LP-problem are considered as generalized single valued neutrosophic number (GSVN-Number). This modified form of LP-problem is here called an NLP-problem. An algorithm is developed to solve NLP-problem by simplex method. Finally, this simplex algorithm is applied to a real-life problem. The problem is illustrated and solved numerically.

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Solving Neutrosophic Linear Programming Problems With Two-Phase Approach

Neutrosophic Sets in Decision Analysis and Operations Research - Advances in Logistics, Operations, and Management Science ◽

10.4018/978-1-7998-2555-5.ch016 ◽

2020 ◽

pp. 391-412

Author(s):

Elsayed Metwalli Badr ◽

Mustafa Abdul Salam ◽

Florentin Smarandache

Keyword(s):

Linear Programming ◽

Programming Problem ◽

Linear Programming Problem ◽

Simplex Method ◽

Feasible Solution ◽

Simplex Algorithm ◽

Phase Method ◽

Basic Feasible Solution ◽

Two Phase ◽

Linear Programming Problems

The neutrosophic primal simplex algorithm starts from a neutrosophic basic feasible solution. If there is no such a solution, we cannot apply the neutrosophic primal simplex method for solving the neutrosophic linear programming problem. In this chapter, the authors propose a neutrosophic two-phase method involving neutrosophic artificial variables to obtain an initial neutrosophic basic feasible solution to a slightly modified set of constraints. Then the neutrosophic primal simplex method is used to eliminate the neutrosophic artificial variables and to solve the original problem.

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Application of Change of Basis in the Simplex Method

European Journal of Social Sciences Education and Research ◽

10.26417/ejser.v11i1.p41-49 ◽

2017 ◽

Vol 11 (1) ◽

pp. 41

Author(s):

Mehmet Hakan Özdemir

Keyword(s):

Linear Programming ◽

Iterative Method ◽

Objective Function ◽

Simplex Method ◽

Programming Model ◽

Feasible Region ◽

Optimal Value ◽

Linear Programming Problems ◽

Repeated Use ◽

Simplex Tableau

The simplex method is a very useful method to solve linear programming problems. It gives us a systematic way of examining the vertices of the feasible region to determine the optimal value of the objective function. It is executed by performing elementary row operations on a matrix that we call the simplex tableau. It is an iterative method that by repeated use gives us the solution to any n variable linear programming model. In this paper, we apply the change of basis to construct following simplex tableaus without applying elementary row operations on the initial simplex tableau.

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