Computational Aspects of the Simplex Method: Revised Simplex Algorithm; Bounded Variables

1983 ◽  
pp. 109-123
Author(s):  
Michel Sakarovitch
Keyword(s):  
Simplex Method ◽  
Simplex Algorithm ◽  
Bounded Variables ◽  
Computational Aspects ◽  
Revised Simplex Algorithm

Computational aspects of linear programming Simplex method

2000 ◽  
Vol 31 (8-9) ◽  
pp. 539-545 ◽  
Author(s):  
D.T. Nguyen ◽  
Y. Bai ◽  
J. Qin ◽  
B. Han ◽  
Y. Hu
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Computational Aspects

Revised simplex algorithm for linear programming on GPUs with CUDA

2018 ◽  
Vol 77 (22) ◽  
pp. 30035-30050 ◽  
Author(s):  
Lili He ◽  
Hongtao Bai ◽  
Yu Jiang ◽  
Dantong Ouyang ◽  
Shanshan Jiang
Keyword(s):  
Linear Programming ◽  
Simplex Algorithm ◽  
Revised Simplex Algorithm

scholarly journals A Computer Technique for Solving LP Problems with Bounded Variables

2012 ◽  
Vol 60 (2) ◽  
pp. 163-168 ◽  
Author(s):  
S. M. Atiqur Rahman Chowdhury ◽  
Sanwar Uddin Ahmad
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Simplex Method ◽  
Basis Matrix ◽  
Computer Technique ◽  
Numerical Example ◽  
Bounded Variables ◽  
Explicit Consideration

Linear Programming problem (LPP)s with upper bounded variables can be solved using the Bounded Simplex method (BSM),without the explicit consideration of the upper bounded constraints. The upper bounded constraints are considered implicitly in this method which reduced the size of the basis matrix significantly. In this paper, we have developed MATHEMATICA codes for solving such problems. A complete algorithm of the program with the help of a numerical example has been provided. Finally a comparison with the built-in code has been made for showing the efficiency of the developed code.DOI: http://dx.doi.org/10.3329/dujs.v60i2.11487 Dhaka Univ. J. Sci. 60(2): 163-168, 2012 (July)

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.

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

1990 ◽  
Vol 112 (2) ◽  
pp. 208-214 ◽  
Author(s):  
Y. Wang ◽  
E. Sandgren
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Inequality Constraints ◽  
Simplex Algorithm ◽  
Upper And Lower Bounds ◽  
Programming Algorithm ◽  
Single Element ◽  
Basis Matrix ◽  
Active Constraint ◽  
Design Variables

A new linear programming algorithm is proposed which has significant advantages compared to a traditional simplex method. A search direction is generated along a common edge of the active constraint set. This direction is followed in order to identify candidate constraints and to modify the current basis. The dimension of the basis matrix begins with a single element 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 to those generated by a traditional revised simplex algorithm. Extensions are presented for both exterior and interior versions of the approach.

An Extended Simplex Algorithm for Linear Programming

2012 ◽  
Vol 532-533 ◽  
pp. 1626-1630
Author(s):  
Guo Guang Zhang
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Feasible Solution ◽  
Simplex Algorithm ◽  
Linear Program ◽  
Problem Solution ◽  
Test Number ◽  
The Times ◽  
Definition Of

Simplex method is one of the most useful methods to solve linear program. However, before using the simplex method, it is required to have a base feasible solution of linear program and the linear program is changed to thetypical form. Although there are some methods to gain the base feasible solution of linear program, artificial variablesare added and the times of calculating are increased with these calculations. In this paper, an extended algorithm of the simplex algorithm is established, the definition of feasible solution in the new algorithm is expended, the test number is not the same sign in the process of finding problem solution. Explained the principle of the new algorithm and showed results of LP problems calculated by the new algorithm.

scholarly journals Self-Regulating Artificial-Free Linear Programming Solver Using a Jump and Simplex Method

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 356
Author(s):  
Rujira Visuthirattanamanee ◽  
Krung Sinapiromsaran ◽  
Aua-aree Boonperm
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Phase 1 ◽  
Simplex Algorithm ◽  
Linear Programs ◽  
Feasible Point ◽  
Optimal Point ◽  
Dual Simplex Method ◽  
Feasible Points ◽  
Initial Starting

An enthusiastic artificial-free linear programming method based on a sequence of jumps and the simplex method is proposed in this paper. It performs in three phases. Starting with phase 1, it guarantees the existence of a feasible point by relaxing all non-acute constraints. With this initial starting feasible point, in phase 2, it sequentially jumps to the improved objective feasible points. The last phase reinstates the rest of the non-acute constraints and uses the dual simplex method to find the optimal point. The computation results show that this method is more efficient than the standard simplex method and the artificial-free simplex algorithm based on the non-acute constraint relaxation for 41 netlib problems and 280 simulated linear programs.

scholarly journals A Two-Phase Support Method for Solving Linear Programs: Numerical Experiments

2012 ◽  
Vol 2012 ◽  
pp. 1-28 ◽  
Author(s):  
Mohand Bentobache ◽  
Mohand Ouamer Bibi
Keyword(s):  
Real Life ◽  
Simplex Algorithm ◽  
Oil Refinery ◽  
Test Problems ◽  
Large Set ◽  
Linear Programs ◽  
Two Phase ◽  
Life Problems ◽  
Bounded Variables ◽  
Matlab Programming

We develop a single artificial variable technique to initialize the primal support method for solving linear programs with bounded variables. We first recall the full artificial basis technique, then we will present the proposed algorithm. In order to study the performances of the suggested algorithm, an implementation under the MATLAB programming language has been developed. Finally, we carry out an experimental study about CPU time and iterations number on a large set of the NETLIB test problems. These test problems are practical linear programs modelling various real-life problems arising from several fields such as oil refinery, audit staff scheduling, airline scheduling, industrial production and allocation, image restoration, multisector economic planning, and data fitting. It has been shown that our approach is competitive with our implementation of the primal simplex method and the primal simplex algorithm implemented in the known open-source LP solver LP_SOLVE.

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