An exterior point simplex algorithm for (general) linear programming problems

1993 ◽  
Vol 46-47 (2) ◽  
pp. 497-508 ◽  
Author(s):  
Konstantinos Paparrizos
Keyword(s):  
Linear Programming ◽  
Simplex Algorithm ◽  
General Linear ◽  
Linear Programming Problems

Sensitivity Analysis on Linear Programming Problems with Trapezoidal Fuzzy Variables

2013 ◽  
pp. 64-82
Author(s):  
Seyed Hadi Nasseri ◽  
Ali Ebrahimnejad
Keyword(s):  
Linear Programming ◽  
Simplex Algorithm ◽  
Programming Models ◽  
Fuzzy Data ◽  
Fuzzy Variables ◽  
Fuzzy Environment ◽  
Dual Simplex ◽  
Linear Programming Problems ◽  
Simplex Tableau ◽  
Dual Simplex Algorithm

In the real word, there are many problems which have linear programming models and sometimes it is necessary to formulate these models with parameters of uncertainty. Many numbers from these problems are linear programming problems with fuzzy variables. Some authors considered these problems and have developed various methods for solving these problems. Recently, Mahdavi-Amiri and Nasseri (2007) considered linear programming problems with trapezoidal fuzzy data and/or variables and stated a fuzzy simplex algorithm to solve these problems. Moreover, they developed the duality results in fuzzy environment and presented a dual simplex algorithm for solving linear programming problems with trapezoidal fuzzy variables. Here, the authors show that this presented dual simplex algorithm directly using the primal simplex tableau algorithm tenders the capability for sensitivity (or post optimality) analysis using primal simplex tableaus.

A Decision Support System for Solving Linear Programming Problems

2014 ◽  
Vol 6 (2) ◽  
pp. 46-62
Author(s):  
Nikolaos Ploskas ◽  
Nikolaos Samaras ◽  
Jason Papathanasiou
Keyword(s):  
Linear Programming ◽  
Decision Support ◽  
Simplex Algorithm ◽  
Decision Makers ◽  
Web Interface ◽  
Web Based ◽  
Linear Programming Problems ◽  
Revised Simplex Algorithm ◽  
The Given ◽  
Programming Algorithms

Linear programming algorithms have been widely used in Decision Support Systems. These systems have incorporated linear programming algorithms for the solution of the given problems. Yet, the special structure of each linear problem may take advantage of different linear programming algorithms or different techniques used in these algorithms. This paper proposes a web-based DSS that assists decision makers in the solution of linear programming problems with a variety of linear programming algorithms and techniques. Two linear programming algorithms have been included in the DSS: (i) revised simplex algorithm and (ii) exterior primal simplex algorithm. Furthermore, ten scaling techniques, five basis update methods and eight pivoting rules have been incorporated in the DSS. All linear programming algorithms and methods have been implemented using MATLAB and converted to Java classes using MATLAB Builder JA, while the web interface of the DSS has been designed using Java Server Pages.

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.

Sensitivity Analysis on Linear Programming Problems with Trapezoidal Fuzzy Variables

2011 ◽  
Vol 2 (2) ◽  
pp. 22-39 ◽  
Author(s):  
Seyed Hadi Nasseri ◽  
Ali Ebrahimnejad
Keyword(s):  
Linear Programming ◽  
Simplex Algorithm ◽  
Fuzzy Data ◽  
Fuzzy Variables ◽  
Fuzzy Environment ◽  
Tableau Algorithm ◽  
Dual Simplex ◽  
Linear Programming Problems ◽  
Simplex Tableau ◽  
Dual Simplex Algorithm

In the real word, there are many problems which have linear programming models and sometimes it is necessary to formulate these models with parameters of uncertainty. Many numbers from these problems are linear programming problems with fuzzy variables. Some authors considered these problems and have developed various methods for solving these problems. Recently, Mahdavi-Amiri and Nasseri (2007) considered linear programming problems with trapezoidal fuzzy data and/or variables and stated a fuzzy simplex algorithm to solve these problems. Moreover, they developed the duality results in fuzzy environment and presented a dual simplex algorithm for solving linear programming problems with trapezoidal fuzzy variables. Here, the authors show that this presented dual simplex algorithm directly using the primal simplex tableau algorithm tenders the capability for sensitivity (or post optimality) analysis using primal simplex tableaus.

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

2020 ◽  
Vol 06 (09) ◽  
pp. 94-96
Author(s):  
Chandra Sen
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Simplex Method ◽  
Simplex Algorithm ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Excellent Research ◽  
Gauss Elimination ◽  
Linear Programming Problems ◽  
Averaging Techniques

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.

Solving Neutrosophic Linear Programming Problems With Two-Phase Approach

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.

scholarly journals A comparative study of two key algorithms in multiple objective linear programming

2019 ◽  
Vol 13 ◽  
pp. 174830261987042
Author(s):  
Paschal B Nyiam ◽  
Abdellah Salhi
Keyword(s):  
Linear Programming ◽  
Simplex Algorithm ◽  
Multiple Objective ◽  
Multiple Objective Linear Programming ◽  
Objective Space ◽  
Linear Programming Problems ◽  
Outer Approximation Algorithm ◽  
Parametric Simplex Algorithm ◽  
Problem Instances ◽  
Comparative Results

Multiple objective linear programming problems are solved with a variety of algorithms. While these algorithms vary in philosophy and outlook, most of them fall into two broad categories: those that are decision space-based and those that are objective space-based. This paper reports the outcome of a computational investigation of two key representative algorithms, one of each category, namely the parametric simplex algorithm which is a prominent representative of the former and the primal variant of Bensons Outer-approximation algorithm which is a prominent representative of the latter. The paper includes a procedure to compute the most preferred nondominated point which is an important feature in the implementation of these algorithms and their comparison. Computational and comparative results on problem instances ranging from small to medium and large are provided.

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