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)

scholarly journals Algorithm to Perform a Complete RHS Parametric Analysis for LPP with Bounded Variables

2012 ◽  
Vol 60 (2) ◽  
pp. 217-222
Author(s):  
Sanwar Uddin Ahmad ◽  
M. Babul Hasan ◽  
M. Ainul Islam
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Simplex Method ◽  
Parametric Analysis ◽  
Bounded Variables ◽  
Explicit Consideration

Linear Programming problem (LPP)s with upper bounded variables can be solved using the Bounded Simplex method, without the explicit consideration of the upper bounded constraints. One can consider the upper bounded constraints explicitly and perform the regular righthand- side parametric analysis of LPPs with bounded variables. This paper develops a method to perform the parametric analysis where the upper bounded constraints are considered implicitly, thus reduce the size of the basis matrix.DOI: http://dx.doi.org/10.3329/dujs.v60i2.11521 Dhaka Univ. J. Sci. 60(2): 217-222, 2012 (July) 

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

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.

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 Strategizing for The Competitiveness of Branches and Enterprises of Industry in The Spatial Development of The Region

2020 ◽  
Vol 8 (15) ◽  
pp. 358-379
Author(s):  
Evgeny Vyacheslavovich Shcheglov ◽  
Anna Alexandrovna Urasova ◽  
Dmitry Arkadievich Balandin ◽  
Alexander Nikolaevich Pytkin Nikolaevich Pytkin
Keyword(s):  
Factor Analysis ◽  
Linear Programming ◽  
Initial Data ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Simplex Method ◽  
Industrial Complex ◽  
Data Sampling ◽  
Methodological Basis ◽  
Weighting Factors

The issues related to developing the industrial complex of a particular region or country in terms of the need to increase competitiveness in the modern conditions of economic instability have been discussed in the article. The synthesis of methods of strategic matrix and factor analysis with data sampling and consideration for the Kaiser normalization criterion is the methodological basis of the work. In particular, the methods include procedures for determining weighting factors based on the comprehensive ranking of expert estimates using the simplex method with bringing the initial data to the linear programming problem. The authors have made the conclusions that allow, using a specific example, to determine the strategic positions of enterprises and industries in the region, outlining possible paths to increase competitiveness.

AN UPPER BOUND FOR THE NUMBER OF DIFFERENT SOLUTIONS GENERATED BY THE PRIMAL SIMPLEX METHOD WITH ANY SELECTION RULE OF ENTERING VARIABLES

2013 ◽  
Vol 30 (03) ◽  
pp. 1340012 ◽  
Author(s):  
TOMONARI KITAHARA ◽  
SHINJI MIZUNO
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Upper Bound ◽  
Linear Programming Problem ◽  
Simplex Method ◽  
Selection Rule ◽  
Dual Simplex Method ◽  
Unimodular Matrix ◽  
Dual Simplex ◽  
Pivoting Rule

Recently, Kitahara, and Mizuno derived an upper bound for the number of different solutions generated by the primal simplex method with Dantzig's (the most negative) pivoting rule. In this paper, we obtain an upper bound with any pivoting rule which chooses an entering variable whose reduced cost is negative at each iteration. The upper bound is applied to a linear programming problem with a totally unimodular matrix. We also obtain a similar upper bound for the dual simplex method.

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