scholarly journals A Computer Program for Solving LP Problems by 2-Basic Variables Replacement at Each Simplex Iteration

2013 ◽  
Vol 61 (1) ◽  
pp. 13-18
Author(s):  
M Babul Hasan ◽  
SM Asaduzzaman
Keyword(s):  
Linear Programming ◽  
Computer Program ◽  
Linear Programs ◽  
Basic Variable ◽  
Computer Technique ◽  
Numerical Examples ◽  
Replacement Method

In this paper, we develop a computer technique to implement the existing 2-basic variable replacement method of Paranjape for solving linear programming (LP) problems. To our knowledge there is no such computer oriented program which implemented Paranjape’s method. Our computer oriented program is a faster method for solving linear programs. A number of numerical examples are illustrated to demonstrate our algorithm. Dhaka Univ. J. Sci. 61(1): 13-18, 2013 (January) DOI: http://dx.doi.org/10.3329/dujs.v61i1.15090

Decomposition Procedure for Solving NLP and QP Problems based on Lagrange and Sander's Method

2016 ◽  
Vol 7 (4) ◽  
pp. 67-93
Author(s):  
H. K. Das
Keyword(s):  
Linear Programming ◽  
Optimal Solution ◽  
Computational Technique ◽  
Lagrange Method ◽  
Computer Technique ◽  
Numerical Examples ◽  
Non Linear Programming ◽  
Decomposition Procedure ◽  
Concave Quadratic Programming ◽  
Modified Algorithm

This paper develops a decompose procedure for finding the optimal solution of convex and concave Quadratic Programming (QP) problems together with general Non-linear Programming (NLP) problems. The paper also develops a sophisticated computer technique corresponding to the author's algorithm using programming language MATHEMATICA. As for auxiliary by making comparison, the author introduces a computer-oriented technique of the traditional Karush-Kuhn-Tucker (KKT) method and Lagrange method for solving NLP problems. He then modify the Sander's algorithm and develop a new computational technique to evaluate the performance of the Sander's algorithm for solving NLP problems. The author observe that the technique avoids some certain numerical difficulties in NLP and QP. He illustrates a number of numerical examples to demonstrate his method and the modified algorithm.

scholarly journals A Technique for Solving Special Type Quadratic Programming Problems

2012 ◽  
Vol 60 (2) ◽  
pp. 209-215
Author(s):  
M. Babul Hasan
Keyword(s):  
Quadratic Programming ◽  
Simplex Method ◽  
Linear Functions ◽  
Hospital Planning ◽  
Basic Variable ◽  
Computer Technique ◽  
Corporate Planning ◽  
Numerical Examples ◽  
Considerable Research ◽  
Quadratic Programming Problems

Because of its usefulness in production planning, financial and corporate planning, health care and hospital planning, quadratic programming (QP) problems have attracted considerable research and interest in recent years. In this paper, we first extend the simplex method for solving QP problems by replacing one basic variable at an iteration of simplex method. We then develop an algorithm and a computer technique for solving quadratic programming problem involving the product of two indefinite factorized linear functions. For developing the technique, we use programming language MATHEMATICA. We also illustrate numerical examples to demonstrate our technique.DOI: http://dx.doi.org/10.3329/dujs.v60i2.11520 Dhaka Univ. J. Sci. 60(2): 209-215, 2012 (July)

scholarly journals A Computer Oriented Method for Solving Transportation Problem

2015 ◽  
Vol 63 (1) ◽  
pp. 1-7
Author(s):  
Sharmin Afroz ◽  
M Babul Hasan
Keyword(s):  
Linear Programming ◽  
Computer Program ◽  
Simplex Method ◽  
Transportation Problem ◽  
Linear Program ◽  
Numerical Examples ◽  
Linear Programming Problems

In this paper, an algorithm and its computer oriented program have been developed for solving transportation programming (TP) reducing it into a linear program (LP). After formulating it into linear programming problems the number of variables becomes large. It then, becomes more difficult and time-consuming if it is done manually with simplex method. By using the computer program the solution can be found in a shorter time. It will be shown that a TP with a large number of variables can be solved in few seconds by using this method. A number of numerical examples are presented to demonstrate the method developed in this research. DOI: http://dx.doi.org/10.3329/dujs.v63i1.21758 Dhaka Univ. J. Sci. 63(1): 1-7, 2015 (January)

scholarly journals An Algorithmic Technique for Solving Non-Linear Programming and Quadratic Programming Problems

2016 ◽  
Vol 35 ◽  
pp. 41-55
Author(s):  
HK Das ◽  
M Babul Hasan
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Graphical Representations ◽  
Computer Technique ◽  
Numerical Examples ◽  
Non Linear Programming ◽  
Non Linear ◽  
Quadratic Programming Problems ◽  
Algorithmic Technique ◽  
Combined Algorithm

In this paper, we improve a combined algorithm and develop a uniform computer technique for solving constrained, unconstrained Non Linear Programming (NLP) and Quadratic Programming (QP) problems into a single framework. For this, we first review the basic algorithms of convex and concave QP as well as general NLP problems. We also focus on the development of the graphical representations. We use MATHEMATICA 9.0 to develop this algorithmic technique. We present a number of numerical examples to demonstrate our method.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 41-55

scholarly journals A Computer Technique for Solving Linear Fractional Programming Problems by Using Dinkelbach’s Algorithm

2016 ◽  
Vol 64 (2) ◽  
pp. 121-125
Author(s):  
Sajal Chakroborty ◽  
Md Babul Hasan
Keyword(s):  
Linear Programming ◽  
Mathematical Programming ◽  
Programming Language ◽  
Fractional Programming ◽  
Computer Code ◽  
Linear Fractional Programming ◽  
Computer Technique ◽  
Numerical Examples

In this paper, we introduce a computer oriented technique for solving linear fractional programming (LFP) problems by converting it into a single linear programming (LP) problem. We have used the idea of Dinkelbach’s algorithm. We use a mathematical programming language (AMPL) to develop computer code. A number of numerical examples are used to demonstrate the technique. Dhaka Univ. J. Sci. 64(2): 121-125, 2016 (July)

THE DS/AHP METHOD UNDER PARTIAL INFORMATION ABOUT CRITERIA AND ALTERNATIVES BY SEVERAL LEVELS OF CRITERIA

2012 ◽  
Vol 11 (02) ◽  
pp. 307-326 ◽  
Author(s):  
LEV V. UTKIN ◽  
NATALIA V. SIMANOVA
Keyword(s):  
Linear Programming ◽  
Incomplete Information ◽  
Decision Problem ◽  
Partial Information ◽  
Decision Makers ◽  
Ahp Method ◽  
Numerical Examples ◽  
Finite Set ◽  
Linear Programming Problems ◽  
Decision Alternatives

An extension of the DS/AHP method is proposed in the paper. It takes into account the fact that the multi-criteria decision problem might have several levels of criteria. Moreover, it is assumed that expert judgments concerning the criteria are imprecise and incomplete. The proposed extension also uses groups of experts or decision makers for comparing decision alternatives and criteria. However, it does not require assigning favorability values for groups of decision alternatives and criteria. The computation procedure for processing and aggregating the incomplete information about criteria and decision alternatives is reduced to solving a finite set of linear programming problems. Numerical examples explain in detail and illustrate the proposed approach.

Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 2—Analysis of Spatial Mechanisms

1971 ◽  
Vol 93 (1) ◽  
pp. 67-73 ◽  
Author(s):  
M. S. C. Yuan ◽  
F. Freudenstein ◽  
L. S. Woo
Keyword(s):  
Computer Program ◽  
Kinematic Analysis ◽  
Static Force ◽  
Single Degree Of Freedom ◽  
Numerical Examples ◽  
Spatial Mechanism ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Torque Analysis ◽  
Basic Concepts

The basic concepts of screw coordinates described in Part I are applied to the numerical kinematic analysis of spatial mechanisms. The techniques are illustrated with reference to the displacement, velocity, and static-force-and-torque analysis of a general, single-degree-of-freedom spatial mechanism: a seven-link mechanism with screw pairs (H)7. By specialization the associated computer program is capable of analyzing many other single-loop spatial mechanisms. Numerical examples illustrate the results.

scholarly journals Elasto - plastic analysis of anisotropic hardening materials by finite element method

1985 ◽  
Vol 7 (1) ◽  
pp. 8-13
Author(s):  
Tran Duong Hien
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computer Program ◽  
Yield Criterion ◽  
Element Model ◽  
Isotropic Hardening ◽  
Anisotropic Hardening ◽  
Numerical Examples ◽  
Plastic Analysis ◽  
Hill's Yield Criterion

An elasto- plastic analysis for general three dimes10nal problems using a finite element model is presented. The analysis is based on Hill's yield criterion which included anisotropic materials displaying kinematic - isotropic hardening. The validity and practical applicability of the algorithm are illustrated by a number of numerical examples, calculated by a computer program written in fortran.

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.

scholarly journals Statistical Methods for Solving Transportation Problems

2019 ◽  
Vol 25 (2) ◽  
pp. 10-13
Author(s):  
Alina Baboş
Keyword(s):  
Linear Programming ◽  
Statistical Methods ◽  
Approximation Method ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Basic Feasible Solution ◽  
Statistical Tools ◽  
Numerical Examples ◽  
North West ◽  
Shipping Cost

Abstract Transportation problem is one of the models of Linear Programming problem. It deals with the situation in which a commodity from several sources is shipped to different destinations with the main objective to minimize the total shipping cost. There are three well-known methods namely, North West Corner Method Least Cost Method, Vogel’s Approximation Method to find the initial basic feasible solution of a transportation problem. In this paper, we present some statistical methods for finding the initial basic feasible solution. We use three statistical tools: arithmetic and harmonic mean and median. We present numerical examples, and we compare these results with other classical methods.

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