scholarly journals The Intelligence of Dual Simplex Method to Solve Linear Fractional Fuzzy Transportation Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
S. Narayanamoorthy ◽  
S. Kalyani
Keyword(s):  
Objective Function ◽  
Simplex Method ◽  
Transportation Problem ◽  
Optimal Solution ◽  
Dual Simplex Method ◽  
Transportation Problems ◽  
Dual Simplex ◽  
Fuzzy Transportation Problem

An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example.

Methods for Solving Fully Fuzzy Transportation Problems Based on Classical Transportation Methods

2013 ◽  
pp. 328-347 ◽  
Author(s):  
Amit Kumar ◽  
Amarpreet Kaur
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Programming Formulation ◽  
Transportation Problems ◽  
Fuzzy Optimal Solution ◽  
Linear Programming Formulation ◽  
Fuzzy Transportation Problem

There are several methods, in literature, for finding the fuzzy optimal solution of fully fuzzy transportation problems (transportation problems in which all the parameters are represented by fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, two new methods (based on fuzzy linear programming formulation and classical transportation methods) are proposed to find the fuzzy optimal solution of unbalanced fuzzy transportation problems by representing all the parameters as trapezoidal fuzzy numbers. The advantages of the proposed methods over existing methods are also discussed. To illustrate the proposed methods a fuzzy transportation problem (FTP) is solved by using the proposed methods and the obtained results are discussed. The proposed methods are easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems occurring in real life situations.

A Novel Ranking Approach to Solving Fully LR-Intuitionistic Fuzzy Transportation Problems

2018 ◽  
Vol 15 (01) ◽  
pp. 95-112 ◽  
Author(s):  
Abhishekh ◽  
A. K. Nishad
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Ranking Functions ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Fuzzy Transportation Problem

To the extent of our knowledge, there is no method in fuzzy environment to solving the fully LR-intuitionistic fuzzy transportation problems (LR-IFTPs) in which all the parameters are represented by LR-intuitionistic fuzzy numbers (LR-IFNs). In this paper, a novel ranking function is proposed to finding an optimal solution of fully LR-intuitionistic fuzzy transportation problem by using the distance minimizer of two LR-IFNs. It is shown that the proposed ranking method for LR-intuitionistic fuzzy numbers satisfies the general axioms of ranking functions. Further, we have applied ranking approach to solve an LR-intuitionistic fuzzy transportation problem in which all the parameters (supply, cost and demand) are transformed into LR-intuitionistic fuzzy numbers. The proposed method is illustrated with a numerical example to show the solution procedure and to demonstrate the efficiency of the proposed method by comparison with some existing ranking methods available in the literature.

scholarly journals PENERAPAN PROGRAM LINIER MENGGUNAKAN METODE DUAL SIMPLEKS DAN METODE QUICK SIMPLEKS UNTUK MEMINIMUMKAN BIAYA (STUDI KASUS: KELOMPOK WANITA TANI (KWT) SENTOSA SANTUL)

2021 ◽  
Vol 4 (1) ◽  
pp. 117-132
Author(s):  
Elfira - Safitri ◽  
Sri Basriati ◽  
Elvina Andiani
Keyword(s):  
Simplex Method ◽  
Feasible Solution ◽  
Research Result ◽  
Optimal Solution ◽  
Women Farmers ◽  
Food Crops ◽  
Dual Simplex Method ◽  
Dual Simplex ◽  
Number Of Iterations ◽  
Minimum Costs

The Sentosa  Santul Women Farmers Group (KWT) is a group of women farmers in Dusun Santul, Kampar Utara District an is engaged in the field of food crops is chili. The Sentosa Santul Women Farmers group (KWT) uses 4 types of fertilizers for chili plant fertilization, namely hydro complex fertilizer, phonska, NPK Zamrud and goat manure.The KWT wants the minimum fertilizer cost but the nutrients in the plants are met. The method used in this research is the dual simplex method and the quick simplex method. The purpose of this study is to determine the minimum costs that must be incurred by the Womens Farmer Group (KWT) for fertilization using the dual simplex method and the quick simplex method to obtain an optimum and feasible solution. For the dual simplex method, the optimum and feasible solution were obtained using the Gauss Jordanelimination. While the quick simplex method, the solution is illustrated using a matrix to reduce the number of iterations needed to achieve the optimal solution. Based on the research result, it is found that the quick simplex method is more efficient than the dual simplex method. This can be seen from the number of iterations carried out. Dual simplex method iteration there are two iterations and quick simplex one iteration. The dual simplex method and the quick simplex method produce the same value.

scholarly journals A New Approach to Solve Mixed Constraint Transportation Problem Under Fuzzy Environment

2017 ◽  
Vol 16 (4) ◽  
pp. 6895-6902
Author(s):  
Nidhi Joshi ◽  
Surjeet Singh Chauhan (Gonder) ◽  
Raghu Raja
Keyword(s):  
Transportation Problem ◽  
Real Life ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
New Approach ◽  
Transportation Problems ◽  
Mixed Constraints ◽  
Fuzzy Environment ◽  
Mixed Constraint ◽  
Fuzzy Transportation Problem

The present paper attempts to obtain the optimal solution for the fuzzy transportation problem with mixed constraints. In this paper, authors have proposed a new innovative approach for obtaining the optimal solution of mixed constraint fuzzy transportation problem. The method is illustrated using a numerical example and the logical steps are highlighted using a simple flowchart. As maximum transportation problems in real life have mixed constraints and these problems cannot be truly solved using general methods, so the proposed method can be applied for solving such mixed constraint fuzzy transportation problems to obtain the best optimal solutions.

Methods for Solving Fully Fuzzy Transportation Problems Based on Classical Transportation Methods

2011 ◽  
Vol 2 (4) ◽  
pp. 52-71 ◽  
Author(s):  
Amit Kumar ◽  
Amarpreet Kaur
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Transportation Problems ◽  
New Methods ◽  
Fuzzy Optimal Solution ◽  
Linear Programming Formulation ◽  
Fuzzy Transportation Problem

There are several methods, in literature, for finding the fuzzy optimal solution of fully fuzzy transportation problems (transportation problems in which all the parameters are represented by fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, two new methods (based on fuzzy linear programming formulation and classical transportation methods) are proposed to find the fuzzy optimal solution of unbalanced fuzzy transportation problems by representing all the parameters as trapezoidal fuzzy numbers. The advantages of the proposed methods over existing methods are also discussed. To illustrate the proposed methods a fuzzy transportation problem (FTP) is solved by using the proposed methods and the obtained results are discussed. The proposed methods are easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems occurring in real life situations.

scholarly journals A Modification of Quadratic Programming Algorithm

2020 ◽  
Vol 10 (1) ◽  
pp. 167-176
Keyword(s):  
Quadratic Programming ◽  
Objective Function ◽  
Simplex Method ◽  
Optimal Solution ◽  
Linear Constraints ◽  
Programming Algorithm ◽  
Basic Solution ◽  
Dual Simplex Method ◽  
Modified Method ◽  
Feasible Solutions

In the existing methods for solving Quadratic Programming Problems having linearly factorized objective function and linear constraints, all the linear factors of the objective function are supposed to be positive for all feasible solutions. Here, a modification of the existing methods is proposed and it has been proved that the modified method can be applied to find the optimal solution of the problem even if all the linear factors of the objective function are not necessarily positive for all feasible solutions. Moreover, the proposed method can be applied to find the optimal solution of the problem even if the basic solution at any stage is not feasible. If the initial basic solution is feasible, we use simplex method to find the optimal solution. If the basic solution at any stage is not feasible, we use dual simplex method to find the optimal solution. Numerical examples are given to illustrate the method and the results are compared with the results obtained by other methods.

scholarly journals إيجاد الحل المقبول (الممكن) والأمثل لأنموذج البرمجة الخطية في ظل عدم تحقق شرطّي الإمكانية والأمثلية

2008 ◽  
Vol 14 (52) ◽  
pp. 257
Author(s):  
سرمد علوان صالح
Keyword(s):  
Linear Programming ◽  
Decision Maker ◽  
Simplex Method ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Dual Simplex Method ◽  
Effective Factor ◽  
Dual Simplex

Consider the Linear Programming (LP) active & effective factor in decision maker & taker process . So that given certain goals , the Significance of (LP) in solving & evaluation the activity during one tools (General Simplex Mehtod)that the solution is Feasible &no optimal then called (Primal Simplex Method) or vice-versa then called(Dual Simplex Method).Same of cases the solution is infeasible & no optimal then using the two methods alternatively once to find the feasible solution and other to find optimal solution              

scholarly journals Solving Fuzzy Transportation Problem Using ASM Method and Zero Suffix Method

2021 ◽  
Vol 1 (01) ◽  
pp. 28-35
Author(s):  
Aurora Nur Aini ◽  
Ali Shodiqin ◽  
Dewi Wulandari
Keyword(s):  
Linear Programming ◽  
Fuzzy Number ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Demand And Supply ◽  
Transportation Problems ◽  
Initial Feasible Solution ◽  
Fuzzy Transportation Problem ◽  
Special Case

The transportation problem is a special case for linear programming. Sometimes, the amount of demand and supply in transportation problems can change from time to time, and thus it is justified to classify the transportation problem as a fuzzy problem. This article seeks to solve the Fuzzy transportation problem by converting the fuzzy number into crisp number by ranking the fuzzy number. There are many applicable methods to solve linear transportation problems. This article discusses the method to solve transportation problems without requiring an initial feasible solution using the ASM method and the Zero Suffix method. The best solution for Fuzzy transportation problems with triangular sets using the ASM method was IDR 21,356,787.50, while the optimal solution using the Zero Suffix method was IDR 21,501,225.00. Received February 5, 2021Revised April 16, 2021Accepted April 22, 2021

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