scholarly journals Implementation of Modified Best Candidate Method in Fuzzy Assignment Problem

YMER Digital ◽  
2021 ◽  
Vol 20 (11) ◽  
pp. 196-207
Author(s):  
M Maragatham ◽  
◽  
Suzane Raj L ◽  
Keyword(s):  
Assignment Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
The Other ◽  
Limited Time ◽  
Assignment Problems ◽  
Trapezoidal Fuzzy Numbers ◽  
Ranking Of Fuzzy Numbers ◽  
Ranking Technique

To meet the demands of every customer by supplying the products at the limited time by maximizing the profit is a dream for many companies. By choosing the best candidate among the other candidates and effectively reaching the optimal solution with a new modified approach using Best Candidate Method in Fuzzy assignment problems. In this paper the author solve Fuzzy assignment problem in which Triangular and Trapezoidal fuzzy numbers are used. Robust Ranking Technique is used for the ranking of fuzzy numbers.

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 Solving Fuzzy Assignment Problems with Hexagonal Fuzzy Numbers by using Diagonal Optimal Algorithm

2019 ◽  
Vol 9 (1) ◽  
pp. 54-57
Keyword(s):  
Assignment Problem ◽  
Fuzzy Numbers ◽  
Optimal Algorithm ◽  
Subject Classification ◽  
Assignment Problems ◽  
Optimal Method ◽  
Numerical Examples ◽  
Ranking Technique

In this article, an approach involving diagonal optimal method has been proposed to solve Hexagonal fuzzy assignment problem(HxFAP). To order the hexagonal fuzzy numbers Yager’s Ranking technique is applied. To understand the algorithm two numerical examples are illustrated.Mathematics Subject Classification: 90C08, 90C70, 90B06, 90C29, 90C90.

Computationally Simple and Efficient Method for Solving Real-Life Mixed Intuitionistic Fuzzy 3D Assignment Problems

2022 ◽  
Vol 14 (1) ◽  
pp. 0-0
Keyword(s):  
Assignment Problem ◽  
Graphical Representation ◽  
Real Life ◽  
Optimal Solution ◽  
Future Research ◽  
Assignment Problems ◽  
3 Dimensional ◽  
Intuitionistic Fuzzy ◽  
Comparison Results ◽  
Future Research Directions

This article addresses the 3-dimensional mixed intuitionistic fuzzy assignment problems (3D-MIFAPs). In this article, firstly, the author formulates an assignment problem (AP) and assumes the parameters are in uncertainty with hesitation. Secondly, based on the nature of the parameter the author defines various types of solid assignment problem (SAP) in uncertain environment. Thirdly, to solve 3D-MIFAP the PSK method for finding an optimal solution of fully intuitionistic fuzzy assignment problem (FIFAP) is extended by the author. Fourthly, the author presents the proofs of the proposed theorems and corollary. Fifthly, the proposed approach is illustrated with three numerical examples and the optimal objective value of 3D-MIFAP is obtained in the form of intuitionistic fuzzy number and the solution is checked with MATLAB and their coding are also given by the author. Sixthly, the author presents the comparison results and their graphical representation, merits and demerits of the proposed and existing methods and finally the author presents conclusion and future research directions.

A Lexicographic Approach to Fuzzy Linear Assignment Problems with Different Types of Fuzzy Numbers

2020 ◽  
Vol 28 (03) ◽  
pp. 421-441 ◽  
Author(s):  
Boris Pérez-Cañedo ◽  
Eduardo R. Concepción-Morales
Keyword(s):  
Assignment Problem ◽  
Fuzzy Numbers ◽  
Multiple Criteria Decision Analysis ◽  
Assignment Problems ◽  
Solution Approach ◽  
Linear Assignment Problem ◽  
Different Types ◽  
Standard Solution ◽  
The Cost ◽  
Linear Assignment

The fuzzy linear assignment problem (FLAP) is an extension of the classical linear assignment problem (LAP) to situations in which uncertainty in the cost coefficients is represented by fuzzy numbers. FLAP applications range from the assignment of workers to tasks to multiple-criteria decision analysis in fuzzy environments and many other engineering applications. Most FLAP formulations assume that all cost coefficients are fuzzy numbers of the same type (e.g. triangular, trapezoidal). The standard solution approach is the defuzzification of the cost coefficients, thus transforming the FLAP into a crisp LAP that can be solved by classical assignment algorithms such as the Hungarian method. It is known that defuzzification methods suffer from lack of discrimination when comparing fuzzy numbers which may lead to suboptimal assignments. The solution approach proposed in this paper is based on the theory of algebraic assignment problems and total orderings in the set of all fuzzy numbers, and it allows to solve FLAPs with different types of fuzzy numbers. More specifically, the FLAP is transformed into a lexicographic linear assignment problem (LLAP) which is solved in its place. We show, both theoretically and numerically, how this transformation overcomes the limitations present in existing approaches.

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.

SENSITIVITY ANALYSIS OF OBJECTIVE FUNCTION COEFFICIENTS OF THE ASSIGNMENT PROBLEM

2007 ◽  
Vol 24 (02) ◽  
pp. 203-221 ◽  
Author(s):  
CHI-JEN LIN ◽  
UE-PYNG WEN
Keyword(s):  
Sensitivity Analysis ◽  
Assignment Problem ◽  
Optimal Solution ◽  
The Other ◽  
Sensitivity Analyses ◽  
Basic Solution ◽  
Optimal Assignment ◽  
Cost Matrix ◽  
Sensitivity Range ◽  
Optimal Basic Solution

Information of sensitivity analysis, in a linear programming problem, is usually more important than the optimal solution itself. However, traditional sensitivity analysis, which perturbs exactly one coefficient and then determines the range preserving the optimality of the current optimal base, is impractical for the assignment problem. An optimal basic solution of the assignment problem is inherently degenerate, so it may be that the optimal base has changed but the optimal assignment remains unchanged. Furthermore, elements of a column (or row) in a cost matrix of assignment problem are usually closely related and change simultaneously, not uniquely. This paper focuses on two kinds of sensitivity analyses for the assignment problem. One is to determine the sensitivity range, over which the current optimal assignment or all the optimal assignments remain optimal, while perturbing the elements of one column (or row) in a cost matrix of the assignment problem simultaneously but dependently. The other is to perturb elements of one column (or row) in a cost matrix of the assignment problem simultaneously but independently. Numerical illustrations are presented to demonstrate that the approaches are useful in practice.

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