Multiobjective Transportation Problem Using Fuzzy Decision Variable Through Multi-Choice Programming

2017 ◽  
Vol 8 (3) ◽  
pp. 82-96 ◽  
Author(s):  
Gurupada Maity ◽  
Sankar Kumar Roy
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Real Variable ◽  
Programming Approach ◽  
Solution Technique ◽  
Decision Variable ◽  
Fuzzy Decision ◽  
Fuzzy Goal ◽  
Fuzzy Transportation Problem ◽  
New Formulation

This paper analyzes the study of Multiobjective Transportation Problem (MOTP) under the consideration of fuzzy decision variable. Usually, the decision variable in a Transportation Problem is taken as real variable. But, in this paper, the decision variable in each node is selected from a set of multi-choice fuzzy numbers. Inclusion of multiple objectives into transportation problem with fuzzy decision variable makes it a Multiobjective Fuzzy Transportation Problem (MOFTP). In this paper, a new formulation of mathematical model of MOFTP with fuzzy goal of each objective function is enlisted. Thereafter the solution technique of the formulated model is described through multi-choice goal programming approach. Finally, a numerical example is presented to show the feasibility and usefulness of this article.

Multiobjective Transportation Problem Using Fuzzy Decision Variable Through Multi-Choice Programming

2018 ◽  
pp. 866-882
Author(s):  
Gurupada Maity ◽  
Sankar Kumar Roy
Keyword(s):  
Mathematical Model ◽  
Transportation Problem ◽  
Real Variable ◽  
Programming Approach ◽  
Solution Technique ◽  
Decision Variable ◽  
Fuzzy Decision ◽  
Fuzzy Goal ◽  
Fuzzy Transportation Problem ◽  
New Formulation

This paper analyzes the study of Multiobjective Transportation Problem (MOTP) under the consideration of fuzzy decision variable. Usually, the decision variable in a Transportation Problem is taken as real variable. But, in this paper, the decision variable in each node is selected from a set of multi-choice fuzzy numbers. Inclusion of multiple objectives into transportation problem with fuzzy decision variable makes it a Multiobjective Fuzzy Transportation Problem (MOFTP). In this paper, a new formulation of mathematical model of MOFTP with fuzzy goal of each objective function is enlisted. Thereafter the solution technique of the formulated model is described through multi-choice goal programming approach. Finally, a numerical example is presented to show the feasibility and usefulness of this article.

Solving fuzzy transportation problem using multi-choice goal programming

2017 ◽  
Vol 09 (06) ◽  
pp. 1750076 ◽  
Author(s):  
Gurupada Maity ◽  
Sankar Kumar Roy
Keyword(s):  
Goal Programming ◽  
Transportation Problem ◽  
Real Life ◽  
Real Variable ◽  
Solution Procedure ◽  
Programming Approach ◽  
Decision Variable ◽  
Proposed Model ◽  
Fuzzy Goal ◽  
Fuzzy Transportation Problem

This paper explores the study of fuzzy transportation problem (FTP) using multi-choice goal-programming approach. Generally, the decision variable in transportation problem (TP) is considered as real variable, but here the decision variable in each node is chosen from a set of multi-choice fuzzy numbers. Here, we formulate a mathematical model of FTP considering fuzzy goal to the objective function. Thereafter, the solution procedure of the proposed model is developed through multi-choice goal programming approach. The proposed approach is not only improved the applicability of goal programming in real world situations but also provided useful insight about the solution of a new class of TP. A real-life numerical experiment is incorporated to analyze the feasibility and usefulness of this paper. The conclusions about our proposed work including future studies are discussed last.

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.

Goal programming approach for solving multi-objective fractional transportation problem with fuzzy parameters

2019 ◽  
Vol 53 (1) ◽  
pp. 157-178 ◽  
Author(s):  
Paraman Anukokila ◽  
Bheeman Radhakrishnan ◽  
Antony Anju
Keyword(s):  
Goal Programming ◽  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Decision Makers ◽  
Programming Approach ◽  
Multi Objective ◽  
Proposed Model ◽  
Fuzzy Goal ◽  
Fuzzy Parameters ◽  
Interval Valued

In this paper, authors studied a goal programming approach for solving multi-objective fractional transportation problem by representing the parameters (γ, δ) in terms of interval valued fuzzy numbers. Fuzzy goal programming problem with multiple objectives is difficult for the decision makers to determine the goal valued of each objective precisely. The proposed model presents a special type of non-linear (hyperbolic) membership functions to solve multi-objective fractional transportation problem with fuzzy parameters. To illustrate the proposed method numerical examples are solved.

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.

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>

scholarly journals Solving the four index fully fuzzy transportation problem

2020 ◽  
Vol 11 (2) ◽  
pp. 199-215
Author(s):  
Manal Hedid ◽  
Rachid Zitouni
Keyword(s):  
Numerical Analysis ◽  
Comparative Study ◽  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Feasible Solution ◽  
Second Phase ◽  
Approximation Methods ◽  
Initial Feasible Solution ◽  
Fuzzy Transportation Problem ◽  
Two Phases

In this paper, we will solve the four index fully fuzzy transportation problem (\textit{FFTP$_{4}$}) with some adapted classical methods. All problem's data will be presented as fuzzy numbers. In order to defuzificate these data, we will use the ranking function procedure. Our method to solve the \textit{FFTP$_{4}$} composed of two phases; in the first one, we will use an adaptation of well-known algorithms to find an initial feasible solution, which are the least cost, Russell's approximation and Vogel's approximation methods. In the second phase, we will test the optimality of the initial solution, if it is not optimal, we will improve it. A numerical analysis of the proposed methods is performed by solving different examples of different sizes; it is determined that they are stable, robust, and efficient. A proper comparative study between the adapted methods identifies the suitable method for solving \textit{FFTP$_{4}$}.

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