scholarly journals Comparative Study of Efficiency of Integer Programming, Simplex Method and Transportation Method in Linear Programming Problem (LPP)

2015 ◽  
Vol 4 (3) ◽  
pp. 85
Author(s):  
Ayansola Olufemi Aderemi
Keyword(s):  
Linear Programming ◽  
Integer Programming ◽  
Comparative Study ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Simplex Method

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 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 A comparative study of the methods of solving non-linear programming problem

1970 ◽  
Vol 4 (1) ◽  
pp. 28-34
Author(s):  
Bimal Chandra Das
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Comparative Study ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Feasible Region ◽  
Non Linear Programming ◽  
Condition Method ◽  
Non Linear ◽  
Matlab Programming

The work present in this paper is based on a comparative study of the methods of solving Non-linear programming (NLP) problem. We know that Kuhn-Tucker condition method is an efficient method of solving Non-linear programming problem. By using Kuhn-Tucker conditions the quadratic programming (QP) problem reduced to form of Linear programming(LP) problem, so practically simplex type algorithm can be used to solve the quadratic programming problem (Wolfe's Algorithm).We have arranged the materials of this paper in following way. Fist we discuss about non-linear programming problems. In second step we discuss Kuhn- Tucker condition method of solving NLP problems. Finally we compare the solution obtained by Kuhn- Tucker condition method with other methods. For problem so consider we use MATLAB programming to graph the constraints for obtaining feasible region. Also we plot the objective functions for determining optimum points and compare the solution thus obtained with exact solutions. Keywords: Non-linear programming, objective function ,convex-region, pivotal element, optimal solution. DOI: 10.3329/diujst.v4i1.4352 Daffodil International University Journal of Science and Technology Vol.4(1) 2009 pp.28-34

scholarly journals Comparative Study of AMPL, Pyomo and JuMP Optimization Modeling Languages on a Network Linear Programming Problem Example

2021 ◽  
Vol 25 (3) ◽  
pp. 23-30
Author(s):  
Andrzej Karbowski ◽  
Krzysztof Wyskiel
Keyword(s):  
Linear Programming ◽  
Comparative Study ◽  
Programming Problem ◽  
Data Structures ◽  
Shortest Path ◽  
Linear Programming Problem ◽  
Modeling Languages ◽  
Specific Data ◽  
Optimization Modeling ◽  
Network Problems

The purpose of this work is a comparative study of three languages (environments) of optimization modeling: AMPL, Pyomo and JuMP. The comparison will be based on three implementations of the shortest path problem formulated as a linear programming problem. The codes for individual models and differences between them will be presented and discussed. Various aspects will be taken into account, such as: simplicity and intuitiveness of implementation, availability of specific data structures for a LP network problems, etc.

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 Maximum likelihood pedigree reconstruction using integer programming

10.29007/sghd ◽  
2018 ◽  
Author(s):  
James Cussens
Keyword(s):  
Linear Programming ◽  
Integer Programming ◽  
Maximum Likelihood ◽  
Programming Problem ◽  
Allele Frequency ◽  
Integer Linear Programming ◽  
Linear Programming Problem ◽  
Pedigree Reconstruction ◽  
Integer Linear Programming Problem ◽  
Family Trees

Pedigrees are `family trees' relating groups of individuals which can usefully be seen as Bayesian networks. The problem of finding a maximum likelihood pedigree from genotypic data is encoded as an integer linear programming problem. Two methods of ensuring that pedigrees are acyclic are considered. Results on obtaining maximum likelihood pedigrees relating 20, 46 and 59 individuals are presented. Running times for larger pedigrees depend strongly on the data used but generally compare well with those in the literature. Solving is particularly fast when allele frequency is uniform.

scholarly journals A Comparative Study of Solving Methods of Transportation Problem in Linear Programming Problem

2020 ◽  
pp. 45-67
Author(s):  
Farzana Sultana Rafi ◽  
Safiqul Islam
Keyword(s):  
Linear Programming ◽  
Comparative Study ◽  
Programming Problem ◽  
Approximation Method ◽  
Linear Programming Problem ◽  
Transportation Problem ◽  
Optimal Result ◽  
North West ◽  
C Programming

The paper is related with the basic transportation problem (TP)which is one kind of linear programming problem (LPP). There are some existing methods for solving transportation problem and in this paper all the standard existing methods has been discussed to understand which one is the best method among them. Among all of existing methods, the Vogel’s Approximation Method (VAM) is considered the best method which gives the better optimal result then other methods and North-West Corner Rule is considered as simplest but gives worst result. A C programming code for Vogel’s Approximation Method have been added in the appendix.

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