scholarly journals Sorting Out Fuzzy Transportation Problems via ECCT and Standard Deviation

2021 ◽  
Vol 12 (2) ◽  
pp. 1-14
Author(s):  
Krishna Prabha Sikkannan ◽  
Vimala Shanmugavel
Keyword(s):  
Standard Deviation ◽  
Approximation Method ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
New Method ◽  
Transportation Problems ◽  
North West ◽  
Numerical Example ◽  
Optimum Solution ◽  
Better Than

A well-organized arithmetical procedure entitled standard deviation is employed to find the optimum solution in this paper. This technique has been divided into two parts. The first methodology deals with constructing the entire contingency cost table, and the second deals with optimum allocation. In this work, the method of magnitude is used for converting fuzzy numbers into crisp numbers as this method is better than the existing methods. This technique gives a better optimal solution than other methods. A numerical example for the new method is explained, and the authors compared their method with existing methods such as north west corner method, least cost method, and Vogel's approximation method.

scholarly journals An Approach for Solving the Fixed Charge Transportation Problems

2021 ◽  
Vol 23 (07) ◽  
pp. 583-590
Author(s):  
Hanan Hussein Farag ◽  
Keyword(s):  
Approximate Solution ◽  
Lower Limit ◽  
Approximation Method ◽  
Transportation Problem ◽  
Optimal Solution ◽  
Fixed Charge ◽  
Transportation Problems ◽  
Numerical Example ◽  
Fixed Charge Transportation Problem ◽  
Better Than

This paper presents modified Vogel’s method that solves the fixed charge transportation problems, the relaxed transportation problem proposed by Balinski in 1961 to find an approximate solution for the fixed charge transportation problem (FCTP). This approximate solution is considered as a lower limit for the optimal solution of FCTP. This paper developed the modified Vogel’s method to find an approximate solution used as a lower limit for the FCTP. This is better than Balinski’s method in 1961. My approach relies on applying Vogel’s approximation method to the relaxed transportation problem. In addition, an illustrative numerical example is used to prove my hypothesis.

Trapezoidal fuzzy model to optimize transportation problem

2016 ◽  
Vol 07 (03) ◽  
pp. 1650028 ◽  
Author(s):  
Nirbhay Mathur ◽  
Pankaj Kumar Srivastava ◽  
Ajit Paul
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Fuzzy Model ◽  
Optimal Solution ◽  
Transportation Cost ◽  
New Method ◽  
Trapezoidal Fuzzy Numbers ◽  
North West ◽  
Fuzzy Environment ◽  
Practical Usefulness

The main aim of this paper is to develop an approach based on trapezoidal fuzzy numbers to optimize transportation problem in fuzzy environment. The present algorithm has representation of availability, demand and transportation cost as trapezoidal fuzzy numbers. This algorithm is found quicker in terms of runtime as comparison to fuzzy VAM discussed in [Kaur A., Kumar A., A new method for solving fuzzy transportation problem using ranking function, Appl. Math. Model. 35:5652–5661, 2011; Ismail Mohideen S., Senthil Kumar P., A comparative study on transportation problem in fuzzy environment, Int. J. Math. Res. 2:151–158, 2010]. On the other hand this technique gives much better results than some classical methods like north-west corner and least cost method. Another benefit of this algorithm is that for certain transportation problems it directly gives optimal solution. It is one of the simplest methods to apply and perceive. Practical usefulness of the new method over other existing methods is demonstrated with two numerical examples.

scholarly journals METHODOLOGY RECOMMENDATION FOR ONE‐CRITERION TRANSPORTATION PROBLEMS: CAKMAK METHOD

Transport ◽  
2007 ◽  
Vol 22 (3) ◽  
pp. 221-224 ◽  
Author(s):  
Tanyel Çakmak ◽  
Filiz Ersöz
Keyword(s):  
Approximation Method ◽  
Operations Research ◽  
Feasible Solution ◽  
New Method ◽  
Basic Solution ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
Solution Methods ◽  
Optimum Solution

Transportation problems (TP) are one of the most prominent fields of application of the mathematical disciplines to optimization and operations research. In general, there are three starting basic feasible solution methods: Northwest Corner, Least Cost Method, VAM – Vogel's Approximation Method. The three methods differ in the quality of the starting basic solution. In this study, we actually show a new method for starting basic feasible solution to one‐criterion‐transportation problems: Çakmak Method. This method can be used for balanced or unbalanced one-criterion transportation problems, and gives the basic feasible optimum solution accordingly.

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.

EXPERIMENTAL ANALYSIS OF SOME VARIANTS OF VOGEL'S APPROXIMATION METHOD

2004 ◽  
Vol 21 (04) ◽  
pp. 447-462 ◽  
Author(s):  
M. MATHIRAJAN ◽  
B. MEENAKSHI
Keyword(s):  
Approximation Method ◽  
Opportunity Cost ◽  
Optimal Solution ◽  
Efficient Solutions ◽  
Transportation Problems ◽  
Cpu Time ◽  
Problem Instances ◽  
Time Required ◽  
The Military

This paper presents a variant of Vogel's approximation method (VAM) for transportation problems. The importance of determining efficient solutions for large sized transportation problems is borne out by many practical problems in industries, the military, etc. With this motivation, a few variants of VAM incorporating the total opportunity cost (TOC) concept were investigated to obtain fast and efficient solutions. Computational experiments were carried out to evaluate these variants of VAM. The quality of solutions indicates that the basic version of the VAM coupled with total opportunity cost (called the VAM–TOC) yields a very efficient initial solution. In these experiments, on an average, about 20% of the time the VAM–TOC approach yielded the optimal solution and about 80% of the time it yielded a solution very close to optimal (0.5% loss of optimality). The CPU time required for the problem instances tested was very small (on an average, less than 10 s on a 200 MHz Pentium machine with 64 MB RAM).

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 PENERAPAN MODIFIED VOGEL'S APPROXIMATION METHOD (MVAM) UNTUK MEMINIMUMKAN BIAYA TRANSPORTASI (STUDI KASUS: PABRIK TAHU TAUFIK)

2019 ◽  
Vol 16 (2) ◽  
pp. 143
Author(s):  
Marie Afiani ◽  
Susi Setiawani ◽  
Toto Bara Setiawan
Keyword(s):  
Approximation Method ◽  
Applied Research ◽  
Equilibrium Problems ◽  
Optimal Solution ◽  
Product Distribution ◽  
Transportation Costs ◽  
Real Cost ◽  
Minimum Solution ◽  
Cost Calculations ◽  
Better Than

This research aims to determine the tofu product distribution transportation model at Taufik Tofu Factory. This type of research is applied research with a quantitative approach. The method used to solve transportation problems in this study is the Modified Vogel’s Approximation Method (MVAM) and optimized using the Modified Distribution (MODI) method. The results of this study indicate that the application of MVAM at the Taufik Tofu Factory provides a more minimum solution for calculating transportation costs, both in equilibrium and non-equilibrium problems. MVAM provides the same transportation costs as the optimal solution for the simplex method, which is equal to Rp1.164.911,00 for equilibrium problems and Rp2.176.838,00 for unequal problems. These results have been tested for optimism using MODI and better than the real cost calculations issued by the factory.

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