scholarly journals On Linear and Quadratic Two-Stage Transportation Problem

2020 ◽  
pp. 5-14
Author(s):  
P. Stetsyuk ◽  
O. Lykhovyd ◽  
A. Suprun
Keyword(s):  
Linear Programming ◽  
Mathematical Programming ◽  
Quadratic Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Transportation Problem ◽  
Quadratic Programming Problem ◽  
Modeling Language ◽  
Two Stage ◽  
Linear Programming Problems

Introduction. When formulating the classical two-stage transportation problem, it is assumed that the product is transported from suppliers to consumers through intermediate points. Intermediary firms and various kinds of storage facilities (warehouses) can act as intermediate points. The article discusses two mathematical models for two-stage transportation problem (linear programming problem and quadratic programming problem) and a fairly universal way to solve them using modern software. It uses the description of the problem in the modeling language AMPL (A Mathematical Programming Language) and depends on which of the known programs is chosen to solve the problem of linear or quadratic programming. The purpose of the article is to propose the use of AMPL code for solving a linear programming two-stage transportation problem using modern software for linear programming problems, to formulate a mathematical model of a quadratic programming two-stage transportation problem and to investigate its properties. Results. The properties of two variants of a two-stage transportation problem are described: a linear programming problem and a quadratic programming problem. An AMPL code for solving a linear programming two-stage transportation problem using modern software for linear programming problems is given. The results of the calculation using Gurobi program for a linear programming two-stage transportation problem, which has many solutions, are presented and analyzed. A quadratic programming two-stage transportation problem was formulated and conditions were found under which it has unique solution. Conclusions. The developed AMPL-code for a linear programming two-stage transportation problem and its modification for a quadratic programming two-stage transportation problem can be used to solve various logistics transportation problems using modern software for solving mathematical programming problems. The developed AMPL code can be easily adapted to take into account the lower and upper bounds for the quantity of products transported from suppliers to intermediate points and from intermediate points to consumers. Keywords: transportation problem, linear programming problem, AMPL modeling language, Gurobi program, quadratic programming problem.

scholarly journals Ranking Function Application for Optimal Solution of Fractional programming problem

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Rasha Jalal
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fractional Programming ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Ranking Function ◽  
Linear Fractional Programming ◽  
Fractional Programming Problem ◽  
Linear Programming Problems

The aim of this paper is to suggest a solution procedure to fractional programming problem based on new ranking function (RF) with triangular fuzzy number (TFN) based on alpha cuts sets of fuzzy numbers. In the present procedure the linear fractional programming (LFP) problems is converted into linear programming problems. We concentrate on linear programming problem problems in which the coefficients of objective function are fuzzy numbers, the right- hand side are fuzzy numbers too, then solving these linear programming problems by using a new ranking function. The obtained linear programming problem can be solved using win QSB program (simplex method) which yields an optimal solution of the linear fractional programming problem. Illustrated examples and comparisons with previous approaches are included to evince the feasibility of the proposed approach.

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 Modeling of Gauss Elimination Technique and AHA Simplex Algorithm for Multi-objective Linear Programming Problems

2020 ◽  
pp. 1-14
Author(s):  
Sanjay Jain ◽  
Adarsh Mangal
Keyword(s):  
Linear Programming ◽  
Numerical Solution ◽  
Objective Function ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Simplex Algorithm ◽  
Multi Objective ◽  
Linear Objective Function ◽  
Gauss Elimination ◽  
Linear Programming Problems

In this research paper, an effort has been made to solve each linear objective function involved in the Multi-objective Linear Programming Problem (MOLPP) under consideration by AHA simplex algorithm and then the MOLPP is converted into a single LPP by using various techniques and then the solution of LPP thus formed is recovered by Gauss elimination technique. MOLPP is concerned with the linear programming problems of maximizing or minimizing, the linear objective function having more than one objective along with subject to a set of constraints having linear inequalities in nature. Modeling of Gauss elimination technique of inequalities is derived for numerical solution of linear programming problem by using concept of bounds. The method is quite useful because the calculations involved are simple as compared to other existing methods and takes least time. The same has been illustrated by a numerical example for each technique discussed here.

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 An Innovative Route to Acquire Least Cost in Transportation Problems

2019 ◽  
Vol 9 (1) ◽  
pp. 5368-5369 ◽  
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Transportation Problem ◽  
Transportation Model ◽  
Optimal Cost ◽  
Transportation Problems ◽  
Great Support ◽  
The Cost

In Linear Programming Problem, Transportation Problem (TP) is a particular approach to reach the cost. Purpose of TP is to reduce the cost. Transportation model provides a great support to find out the best way to distribute supplies to client. An inventive hypothesis is discussed for getting optimal cost in transportation problem in this paper. The proposed work compared with also Vogel’s Approximation and MODI methods. This approach is confirmed with various numerical illustrations

scholarly journals Fundamentals of Transportation Problem

2021 ◽  
Vol 10 (5) ◽  
pp. 90-103
Author(s):  
Bhabani Mallia ◽  
Manjula Das ◽  
C. Das
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Basic Feasible Solution ◽  
Distribution Method

Transportation Problem is a linear programming problem. Like LPP, transportation problem has basic feasible solution (BFS) and then from it we obtain the optimal solution. Among these BFS the optimal solution is developed by constructing dual of the TP. By using complimentary slackness conditions the optimal solutions is obtained by the same iterative principle. The method is known as MODI (Modified Distribution) method. In this paper we have discussed all the aspect of transportation problem.

scholarly journals Fuzzy Multi Objective Linear Programming Problem with Imprecise Aspiration Level and Parameters

2015 ◽  
Vol 5 (2) ◽  
pp. 81-86 ◽  
Author(s):  
Zahra Shahraki ◽  
Mehdi Allahdadi ◽  
Hassan Mishmast Nehi
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Aspiration Level ◽  
Membership Functions ◽  
Objective Functions ◽  
Multi Objective ◽  
Fuzzy Goals ◽  
Linear Programming Problems

This paper considers the multi-objective linear programming problems with fuzzygoal for each of the objective functions and constraints. Most existing works deal withlinear membership functions for fuzzy goals. In this paper, exponential membershipfunction is used.

scholarly journals Two simple ways to find an efficient solution for a multiple objective linear programming problem

2018 ◽  
Vol 23 (1) ◽  
pp. 11-18
Author(s):  
Vasile Căruțașu
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Efficient Solution ◽  
Multiple Objective ◽  
Multiple Objective Linear Programming ◽  
Optimal Solutions ◽  
Nadir Point ◽  
Linear Programming Problems

Abstract A number of methods and techniques for determining “effective” solutions for multiple objective linear programming problems (MPP) have been developed. In this study, we will present two simple methods for determining an efficient solution for a MPP that reducing the given problem to a one-objective linear programming problem. One of these methods falls under the category of methods of weighted metrics, and the other is an approach similar to the ε- constraint method. The solutions determined by the two methods are not only effective and are found on the Pareto frontier, but are also “the best” in terms of distance to the optimal solutions for all objective function from the MPP. Obviously, besides the optimal solutions of linear programming problems in which we take each objective function, we can also consider the ideal point and Nadir point, in order to take into account all the notions that have been introduced to provide a solution to this problem

scholarly journals Solving Linear Programming Problems with Grey Data

2018 ◽  
Vol 3 (1) ◽  
pp. 17-23 ◽  
Author(s):  
Michael Gr. Voskoglou
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Programming Problem ◽  
Standard Method ◽  
Linear Programming Problem ◽  
Real Life ◽  
Optimal Solution ◽  
Real Numbers ◽  
Decision Variables ◽  
Linear Programming Problems

A Grey Linear Programming problem differs from an ordinary one to the fact that the coefficients of its objective function and / or the technological coefficients and constants of its constraints are grey instead of real numbers. In this work a new method is developed for solving such kind of problems by the whitenization of the grey numbers involved and the solution of the obtained in this way ordinary Linear Programming problem with a standard method. The values of the decision variables in the optimal solution may then be converted to grey numbers to facilitate a vague expression of it, but this must be strictly checked to avoid non creditable such expressions. Examples are also presented to illustrate the applicability of our method in real life applications.

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