scholarly journals PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems

2016 ◽  
Vol 5 (4) ◽  
pp. 121-146 ◽  
Author(s):  
P. Senthil Kumar
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Triangular Fuzzy Numbers ◽  
Multiplication Operation ◽  
Fuzzy Transportation Problem ◽  
Objective Value ◽  
Type 3

In conventional transportation problem (TP), supplies, demands and costs are always certain. In this paper, the author tried to categories the TP under the mixture of certain and uncertain environment and formulates the problem and utilizes the crisp numbers, triangular fuzzy numbers (TFNs) and trapezoidal fuzzy numbers (TrFNs) to solve the TP. The existing ranking procedure of Liou and Wang is used to transform the type-1 and type-3 fuzzy transportation problem (FTP) into a crisp one so that the conventional method may be applied to solve the TP. The solution procedure differs from TP to type-1 and type-3 FTP in allocation step only. Therefore, the new method called PSK method and new multiplication operation on TrFN is proposed to find the mixed optimal solution in terms of crisp numbers, TFNs and TrFNs. The main advantage of this method is computationally very simple, easy to understand and also the optimum objective value obtained by our method is physically meaningful. The effectiveness of the proposed method is illustrated by means of a numerical example.

scholarly journals PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems

Fuzzy Systems ◽  
2017 ◽  
pp. 367-392 ◽  
Author(s):  
P. Senthil Kumar
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Solution Procedure ◽  
New Method ◽  
Ranking Procedure ◽  
Multiplication Operation ◽  
Fuzzy Transportation Problem ◽  
Type 3

In conventional transportation problem (TP), supplies, demands and costs are always certain. In this paper, the author tried to categories the TP under the mixture of certain and uncertain environment and formulates the problem and utilizes the crisp numbers, triangular fuzzy numbers (TFNs) and trapezoidal fuzzy numbers (TrFNs) to solve the TP. The existing ranking procedure of Liou and Wang is used to transform the type-1 and type-3 fuzzy transportation problem (FTP) into a crisp one so that the conventional method may be applied to solve the TP. The solution procedure differs from TP to type-1 and type-3 FTP in allocation step only. Therefore, the new method called PSK method and new multiplication operation on TrFN is proposed to find the mixed optimal solution in terms of crisp numbers, TFNs and TrFNs. The main advantage of this method is computationally very simple, easy to understand and also the optimum objective value obtained by our method is physically meaningful. The effectiveness of the proposed method is illustrated by means of a numerical example.

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 DA systematic approach for solving mixed constraint fuzzy balanced and unbalanced transportation problem

2020 ◽  
Vol 19 (1) ◽  
pp. 85 ◽  
Author(s):  
Ahmed Hamoud ◽  
Kirtiwant Ghadle ◽  
Priyanka Pathade
Keyword(s):  
Transportation Problem ◽  
Mixed Type ◽  
Systematic Approach ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Mixed Constraint ◽  
Real Life Situation ◽  
Fuzzy Transportation Problem

<p>In the present article, a mixed type transportation problem is considered. Most of the transportation problems in real life situation have mixed type transportation problem this type of transportation problem cannot be solved by usual methods. Here we attempt a new concept of Best Candidate Method (BCM) to obtain the optimal solution. To determine the compromise solution of balanced mixed fuzzy transportation problem and unbalanced mixed fuzzy transportation problem of trapezoidal and trivial fuzzy numbers with new BCM solution procedure has been applied. The method is illustrated by the numerical examples.</p>

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.

scholarly journals A new Approach for Obtaining Optimal Solution of Unbalanced Fuzzy Transportation Problem

2016 ◽  
Vol 15 (6) ◽  
pp. 6824-6832
Author(s):  
Nidhi Joshi ◽  
Surjeet Singh Chauhan
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
New Approach ◽  
Trapezoidal Fuzzy Numbers ◽  
Numerical Example ◽  
Fuzzy Optimal Solution ◽  
Fuzzy Transportation Problem ◽  
Ranking Technique

The present paper attempts to study the unbalanced fuzzy transportation problem so as to minimize the transportationcost of products when supply, demand and cost of the products are represented by fuzzy numbers. In this paper, authorsuse Roubast ranking technique to transform trapezoidal fuzzy numbers to crisp numbers and propose a new algorithm tofind the fuzzy optimal solution of unbalanced fuzzy transportation problem. The proposed algorithm is more efficient thanother existing algorithms like simple VAM and is illustrated via numerical example. Also, a comparison between the resultsof the new algorithm and the result of algorithm using simple VAM is provided.

scholarly journals Search for an Optimal Solution to Vague Traffic Problems Using the PSK Method

2018 ◽  
pp. 219-257 ◽  
Author(s):  
P. Senthil Kumar
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
History Of Mathematics ◽  
Optimal Solution ◽  
Numerical Examples ◽  
Fuzzy Optimal Solution ◽  
Practical Usefulness ◽  
History Of ◽  
Single Method ◽  
Fuzzy Transportation Problem

There are several algorithms, in literature, for obtaining the fuzzy optimal solution of fuzzy transportation problems (FTPs). To the best of the author's knowledge, in the history of mathematics, no one has been able to solve transportation problem (TP) under four different uncertain environment using single method in the past years. So, in this chapter, the author tried to categories the TP under four different environments and formulates the problem and utilizes the crisp numbers, triangular fuzzy numbers (TFNs), and trapezoidal fuzzy numbers (TrFNs) to solve the TP. A new method, namely, PSK (P. Senthil Kumar) method for finding a fuzzy optimal solution to fuzzy transportation problem (FTP) is proposed. Practical usefulness of the PSK method over other existing methods is demonstrated with four different numerical examples. To illustrate the PSK method different types of FTP is solved by using the PSK method and the obtained results are discussed.

scholarly journals Fuzzy Hungarian Approach for Transportation Model

2013 ◽  
pp. 189-192
Author(s):  
Arun Patil ◽  
S. B. Chandgude
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Transportation Model ◽  
Trapezoidal Fuzzy Numbers ◽  
Fuzzy Optimal Solution ◽  
Transportation Models ◽  
Fuzzy Transportation Problem ◽  
The Cost

In this paper, a method is proposed to find the fuzzy optimal solution of fuzzy transportation model by representing all the parameters as trapezoidal fuzzy numbers. To illustrate the proposed method a fuzzy transportation problem is solved by using the proposed method and the results are obtained. The proposed method is easy to understand, and to apply for finding the fuzzy optimal solution of fuzzy transportation models in real life situations. However, we propose the method of fuzzy modified distribution for finding out the optimal solution for minimizing the cost of total fuzzy transportation. The advantages of the proposed method are also discussed.

scholarly journals Goal programming approach for solving heptagonal fuzzy transportation problem under budgetry constraint

2020 ◽  
Vol 30 (1) ◽  
Author(s):  
Hamiden Abd El-Wahed Khalifa
Keyword(s):  
Goal Programming ◽  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Programming Approach ◽  
Solution Approach ◽  
Fuzzy Transportation Problem ◽  
The Stability ◽  
The Cost

Transportation problem (TP) is a special type of linear programming problem (LPP) where the objective is to minimize the cost of distributing a product from several sources (or origins) to some destinations. This paper addresses a transportation problem in which the costs, supplies, and demands are represented as heptagonal fuzzy numbers. After converting the problem into the corresponding crisp TP using the ranking method, a goal programming (GP) approach is applied for obtaining the optimal solution. The advantage of GP for the decision-maker is easy to explain and implement in real life transportation. The stability set of the first kind corresponding to the optimal solution is determined. A numerical example is given to highlight the solution approach.

scholarly journals Algorithmic Approach for Solving Intuitionistic Fuzzy Transportation Problem

2017 ◽  
Author(s):  
R. Jahir Hussain ◽  
P. Senthil Kumar
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Zero Point ◽  
Point Method ◽  
Algorithmic Approach ◽  
Intuitionistic Fuzzy Numbers ◽  
Numerical Example ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Transportation Problem

In this paper, we investigate transportation problem in which supplies and demands are intuitionistic fuzzy numbers. Intuitionistic fuzzy zero point method is proposed to find the optimal solution in terms of triangular intuitionistic fuzzy numbers. A new relevant numerical example is also included.

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