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 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.

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 interval-valued transportation problem using a new ranking function for octagonal fuzzy numbers

2022 ◽  
Author(s):  
Monika Bisht ◽  
Rajesh Dangwal
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Feasible Solution ◽  
Interval Data ◽  
Ranking Function ◽  
Basic Feasible Solution ◽  
Numerical Example ◽  
Fuzzy Transportation Problem ◽  
Ranking Technique ◽  
Interval Valued

In this paper, we introduce a new method to solve Interval-Valued Transportation Problem (IVTP) to deal with those problems of transportation wherein the information available is imprecise. First, a newly proposed fuzzification method is used to convert the IVTP to octagonal fuzzy transportation problem and then with the help of ranking function proposed in this paper, the fuzzy transportation problem is converted into crisp transportation problem. Lastly, Initial Basic Feasible Solution (IBFS) of this problem is obtained using Vogel’s Approximation Method and the solution is improved using Modified Distribution (MODI) method. A numerical example with interval data is solved using the proposed algorithm to make comparison of the solution with some other methods. Also, a numerical example with parameters in the form of octagonal fuzzy numbers is illustrated to compare the effectiveness of the proposed ranking technique. The proposed fuzzification and ranking technique can be used in the other fields of decision making dealing with the data in the same form as considered in this paper.

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 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.

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.

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 A New Approach for Solving Type-2-Fuzzy Transportation Problem

2019 ◽  
Vol 4 (3) ◽  
pp. 683-696
Author(s):  
Somnath Maity ◽  
Sankar Kumar Roy
Keyword(s):  
Transportation Problem ◽  
Original Problem ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Simplex Algorithm ◽  
New Approach ◽  
Fuzzy Variables ◽  
Linear Programming Problems ◽  
Fuzzy Transportation Problem

In this paper, a new approach is introduced to solve transportation problem with type-2-fuzzy variables. In most of the real-life situations, the available data do not happen to be crisp in nature. It gives rise to the fuzzy transportation problem (FTP). This proposed approach concentrates on the problem when the vertical slices of type-2-fuzzy sets (T2FSs) are trapezoidal fuzzy numbers (TFNs). The original problem reduces to three different linear programming problems (LPPs) which are solved using the simplex algorithm. Then the effectiveness of this paper is discussed with numerical example. In conclusion, the significance of the paper and the scope of future study are discussed.

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>

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