scholarly journals Newly Proposed Matrix Reduction technique Under Mean Ranking Method for Solving Trapezoidal Fuzzy Transportation problems Under Fuzzy Environment

2021 ◽  
Author(s):  
Tekalign Regasa Ashale
Keyword(s):  
Transportation Problem ◽  
Ranking Method ◽  
Numerical Illustration ◽  
Transportation Problems ◽  
Matrix Reduction ◽  
Fuzzy Algorithms ◽  
Fuzzy Environment ◽  
Optimal Value ◽  
Fuzzy Transportation Problem ◽  
Ranking Fuzzy Number

In this paper, improved matrix Reduction Method is proposed for the solution of fuzzy transportation problem in which all inputs are taken as fuzzy numbers. Since ranking fuzzy number is important tool in decision making, Fuzzy trapezoidal number is converting in to crisp set by using Mean techniques and solved by proposed method for fuzzy transportation problem. We give suitable numerical example for unbalanced and compare the optimal value with other techniques. The Result shows that the optimum profit of transportation problem using proposed technique under robust ranking method is better than the other method. Novelty: The numerical illustration demonstrates that the new projected method for managing the transportation problems on fuzzy algorithms.

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 Absolute point algorithm for solving unbalanced fuzzy transportation problem

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
K. Rathi 1 ◽  
S. Muruganantham 2
Keyword(s):  
Real Time ◽  
Transportation Problem ◽  
Optimal Allocation ◽  
Minimum Cost ◽  
Market Demand ◽  
Absolute Point ◽  
Transportation Problems ◽  
Fuzzy Environment ◽  
Fuzzy Transportation Problem ◽  
Future Demands

 In real time situations, the total availability of goods or product may be more or less than the actual market demand and the unbalanced transportation situation arise more commonly. Such unbalanced Transportation Problems (TP) are solved by introducing dummy source or destination which do not exist in reality. The optimal allocation involves cells from such dummy source or destination and the allocated number of quantities are held back at one or more origins. The paper aims to propose an algorithm based on Absolute Points to solve unbalanced TP under fuzzy environment. The proposed algorithm is advantageous than the existing algorithms  in such a way that it provides the added information of transporting the excess availability from dummy supply point to appropriate destination to meet future demands at minimum cost. Finally, by virtue of the proposed algorithm an example is done to illustrate the practicality and the effectiveness of the proposed algorithm. 

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.

scholarly journals An Inventive Approach to Optimize Fuzzy Transportation Problem

2020 ◽  
Vol 5 (5) ◽  
pp. 985-994
Author(s):  
Nirbhay Mathur ◽  
Pankaj Kumar Srivastava
Keyword(s):  
Transportation Problem ◽  
Solution Process ◽  
Innovative Approach ◽  
Numerical Examples ◽  
Transportation Problems ◽  
North West ◽  
Fuzzy Environment ◽  
Innovative Method ◽  
Fuzzy Transportation Problem

The present paper wraps an innovative approach to optimize transportation problems through generalized trapezoidal numbers in a fuzzy environment. The main contribution here is to develop an innovative method to optimize the generalized fuzzy trapezoidal transportation problem and reduce the computational intricacy of the existing methods. Then again this method confers many improved results against classical North-West Corner and Least-Cost schemes in Fuzzy environment. An additional merit of the proposed scheme is that for several fuzzy transportation problems it furnishes the best possible way out directly. It is simple to understand and apply. The solution process is exemplified through two numerical examples and comparison with some standard existing methods.

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.

Solving Intuitionistic Fuzzy Solid Transportation Problem Via New Ranking Method Based on Signed Distance

2016 ◽  
Vol 24 (04) ◽  
pp. 483-501 ◽  
Author(s):  
Shashi Aggarwal ◽  
Chavi Gupta
Keyword(s):  
Transportation Problem ◽  
Ranking Method ◽  
Mathematical Programming Problem ◽  
Solid Transportation Problem ◽  
Basic Feasible Solution ◽  
Ranking System ◽  
Intuitionistic Fuzzy Numbers ◽  
Signed Distance ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment

In this paper, signed distance of Symmetrical Intuitionistic Fuzzy Numbers (SIFNs) is introduced. Based on this signed distance and the crisp ranking system on real numbers, a new ranking system for SIFNs is defined, which seems to be very realistic. To illustrate the applicability and suitability of the proposed ranking method and to deal with ambiguity and imprecision, one of the vital mathematical programming problem viz. Solid Transportation Problem (STP) is formulated in intuitionistic fuzzy environment. A new method has been proposed to compute initial basic feasible solution for the same. Also the significance of the proposed approach over existing methods is illustrated. Finally numerical examples are solved to demonstrate the efficiency of the proposed methods.

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 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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