The Simplex Method Using Pseudo-Basic Variables for Structured Linear Programming Problems

10.7249/p2405 ◽  
1961 ◽  
Author(s):  
E. Beale
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Linear Programming Problems

scholarly journals A Simplified Novel Technique for Solving Linear Programming Problems with Triangular Fuzzy Variables via Interval Linear Programming Problems

2021 ◽  
pp. 82-93
Author(s):  
Ladji Kané ◽  
Lassina Diabaté ◽  
Daouda Diawara ◽  
Moussa Konaté ◽  
Souleymane Kané
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Real Problem ◽  
Interval Linear Programming ◽  
Numerical Examples ◽  
Fuzzy Variables ◽  
Novel Technique ◽  
Interval Linear ◽  
Linear Programming Problems

This study proposes a novel technique for solving Linear Programming Problems with triangular fuzzy variables. A modified version of the well-known simplex method and the Existing Method for Solving Interval Linear Programming problems are used for solving linear programming problems with triangular fuzzy variables. Furthermore, for illustration, some numerical examples and one real problem are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy, and reasonable.

A New Dynamic Basis Algorithm for Solving Linear Programming Problems for Engineering Design

1988 ◽  
Author(s):  
Y. Wang ◽  
E. Sandgren
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Inequality Constraints ◽  
Upper And Lower Bounds ◽  
Programming Algorithm ◽  
Active Constraint ◽  
Design Variables ◽  
Artificial Variable ◽  
Linear Programming Problems ◽  
Revised Simplex Method

Abstract A new linear programming algorithm is proposed which has significant advantages compared to the traditional simplex method. The search direction generated which is always along a common edge of the active constraint set, is used to locate candidate constraints, and can be used to modify the current basis. The dimension of the basis begins at one and dynamically increases but remains less than or equal to the number of design variables. This is true regardless of the number of inequality constraints present including upper and lower bounds. The proposed method can operate equally well from a feasible or infeasible point. The pivot operation and artificial variable strategy of the simplex method are not used. Examples are presented and results are compared with a traditional revised simplex method.

Reduction-by-Projection Method for Linear Programming Problems

2014 ◽  
Vol 672-674 ◽  
pp. 1968-1971
Author(s):  
Xue Tong ◽  
Jun Qiang Wei
Keyword(s):  
Linear Programming ◽  
Linear Systems ◽  
Integer Linear Programming ◽  
Projection Method ◽  
Simplex Method ◽  
New Method ◽  
Linear Programming Problems

This paper defines the projection of algebic systems, and studies the projecting algorithm for linear systems. As its application, a new method is given to solve linear programming problems, which is called reduction-by-projection method. For many problems, especially when the problems have many constraint conditions in comparison with the number of their variables, the method needs less computation than simplex method and others. The great advantage of the method is shown when solving the integer linear programming problems.

A dual simplex method for grey linear programming problems based on duality results

2020 ◽  
Vol 10 (2) ◽  
pp. 145-157
Author(s):  
Davood Darvishi Salookolaei ◽  
Seyed Hadi Nasseri
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Simplex Method ◽  
Dual Problem ◽  
Complementary Slackness ◽  
Dual Simplex Method ◽  
Content Type ◽  
Dual Simplex ◽  
Linear Programming Problems

PurposeFor extending the common definitions and concepts of grey system theory to the optimization subject, a dual problem is proposed for the primal grey linear programming problem.Design/methodology/approachThe authors discuss the solution concepts of primal and dual of grey linear programming problems without converting them to classical linear programming problems. A numerical example is provided to illustrate the theory developed.FindingsBy using arithmetic operations between interval grey numbers, the authors prove the complementary slackness theorem for grey linear programming problem and the associated dual problem.Originality/valueComplementary slackness theorem for grey linear programming is first presented and proven. After that, a dual simplex method in grey environment is introduced and then some useful concepts are presented.

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.

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