ON THE SOLVING METHOD FOR SOME TRANSPORTATION PROBLEMS WITH HETEROGENEITIES

2016 ◽  
Vol 9 (2) ◽  
pp. 74-77
Author(s):  
Соловей ◽  
Denis Solovey ◽  
Хухрянская ◽  
E. Khukhryanskaya
Keyword(s):  
Transportation Problem ◽  
Transportation Problems ◽  
Heterogeneous Goods

The article discusses the transportation problem for heterogeneous goods and heterogeneous vehicles. The proposed method allows to reduce the transportation problem with a heterogeneities to the classical transportation problem.

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 Dichotomized Incenter Fuzzy Triangular Ranking Approach to Optimize Interval Data Based Transportation Problem

2018 ◽  
Vol 18 (4) ◽  
pp. 111-119 ◽  
Author(s):  
Pankaj Kumar Srivastava ◽  
Dinesh C. S. Bisht
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Interval Data ◽  
Transportation Problems ◽  
Research Article

Abstract This research article discusses the problems having flexible demand, supply and cost in range referred as interval data based transportation problems and these cannot be solved directly using available methods. The uncertainty associated with these types of problems motivates authors to tackle it by converting interval to fuzzy numbers. This confront of conversion has been achieved by proposing a dichotomic fuzzification approach followed by a unique triangular incenter ranking approach to optimize interval data based transportation problems. A comparison with existing methods is made with the help of numerical illustrations. The algorithm proposed is found prompt in terms of the number of iteration involved and problem formation. This method is practical to handle the transportation problems not having a single valued data, but data in form of a range.

scholarly journals A review on fuzzy and stochastic extensions of the multi index transportation problem

2017 ◽  
Vol 27 (1) ◽  
pp. 3-29 ◽  
Author(s):  
Sungeeta Singh ◽  
Renu Tuli ◽  
Deepali Sarode
Keyword(s):  
Transportation Problem ◽  
Real Life ◽  
Review Article ◽  
Fixed Charge ◽  
Fixed Cost ◽  
Multi Index ◽  
Transportation Problems ◽  
Single Criterion ◽  
Fixed Charge Transportation Problem

The classical transportation problem (having source and destination as indices) deals with the objective of minimizing a single criterion, i.e. cost of transporting a commodity. Additional indices such as commodities and modes of transport led to the Multi Index transportation problem. An additional fixed cost, independent of the units transported, led to the Multi Index Fixed Charge transportation problem. Criteria other than cost (such as time, profit etc.) led to the Multi Index Bi-criteria transportation problem. The application of fuzzy and stochastic concept in the above transportation problems would enable researchers to not only introduce real life uncertainties but also obtain solutions of these transportation problems. The review article presents an organized study of the Multi Index transportation problem and its fuzzy and stochastic extensions till today, and aims to help researchers working with complex transportation problems.

An Innovative Method to Unravel Neutroshopic Transportation Problem Using Harmonic Mean

2021 ◽  
Vol 10 (3) ◽  
pp. 55-66
Author(s):  
S. Krishna Prabha
Keyword(s):  
Fuzzy Sets ◽  
Transportation Problem ◽  
Intuitionistic Fuzzy Sets ◽  
Harmonic Mean ◽  
Neutrosophic Sets ◽  
Transportation Problems ◽  
Numerical Example ◽  
Intuitionistic Fuzzy ◽  
Innovative Method ◽  
Optimal Resolution

As a simplification of fuzzy sets and intuitionistic fuzzy sets to symbolize hesitant, conflicting, and curtailed information about factual world tribulations, neutrosophic sets have been established. There are many existing techniques accessible to solve transportation problems in neutrosophic environment. Among those existing routines, the harmonic mean scheme is applied to obtain the optimal resolution to neutrosophic transportation problem. A numerical example is publicized that the proposed technique gives an improved estimate when compared with the existing techniques.

An Evolutionary Algorithm for Interval Solid Transportation Problems

1999 ◽  
Vol 7 (1) ◽  
pp. 103-107 ◽  
Author(s):  
Fernando Jiménez ◽  
José L. Verdegay
Keyword(s):  
Objective Function ◽  
Evolutionary Algorithm ◽  
Transportation Problem ◽  
Solid Transportation Problem ◽  
Transportation Problems ◽  
Constraint Set ◽  
Item Properties ◽  
Mode Of Transport ◽  
Nonlinear Objective Function

The Solid Transportation Problem arises when bounds are given on three item properties. Usually, these properties are source, destination and mode of transport (conveyance), and may be given in an interval way. This paper deals with solid transportation problems in which the data in the constraint set are expressed in an interval form, i.e. when sources, destinations and conveyances have interval values instead of point values. An arbitrary linear or nonlinear objective function is also considered. To solve the problem, an Evolutionary Algorithm which extends and generalizes other approaches considering only point values, is proposed.

scholarly journals Modified Approach for Optimization of Real Life Transportation Problem in Neutrosophic Environment

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Akanksha Singh ◽  
Amit Kumar ◽  
S. S. Appadoo
Keyword(s):  
Transportation Problem ◽  
Cost Minimization ◽  
Real Life ◽  
Exact Results ◽  
Transportation Problems ◽  
Incorrect Assumption ◽  
Time Minimization

To the best of our knowledge, there is only one approach for solving neutrosophic cost minimization transportation problems. Since neutrosophic transportation problems are a new area of research, other researchers may be attracted to extend this approach for solving other types of neutrosophic transportation problems like neutrosophic solid transportation problems, neutrosophic time minimization transportation problems, neutrosophic transshipment problems, and so on. However, after a deep study of the existing approach, it is noticed that a mathematical incorrect assumption has been used in these existing approaches; therefore there is a need to modify these existing approaches. Keeping the same in mind, in this paper, the existing approach is modified. Furthermore, the exact results of some existing transportation problems are obtained by the modified approach.

scholarly journals An Innovative Route to Acquire Least Cost in Transportation Problems

2019 ◽  
Vol 9 (1) ◽  
pp. 5368-5369 ◽  
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Transportation Problem ◽  
Transportation Model ◽  
Optimal Cost ◽  
Transportation Problems ◽  
Great Support ◽  
The Cost

In Linear Programming Problem, Transportation Problem (TP) is a particular approach to reach the cost. Purpose of TP is to reduce the cost. Transportation model provides a great support to find out the best way to distribute supplies to client. An inventive hypothesis is discussed for getting optimal cost in transportation problem in this paper. The proposed work compared with also Vogel’s Approximation and MODI methods. This approach is confirmed with various numerical illustrations

scholarly journals Absolute point algorithm for solving unbalanced fuzzy transportation problem

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
K. Rathi 1 ◽  
S. Muruganantham 2
Keyword(s):  
Real Time ◽  
Transportation Problem ◽  
Optimal Allocation ◽  
Minimum Cost ◽  
Market Demand ◽  
Absolute Point ◽  
Transportation Problems ◽  
Fuzzy Environment ◽  
Fuzzy Transportation Problem ◽  
Future Demands

 In real time situations, the total availability of goods or product may be more or less than the actual market demand and the unbalanced transportation situation arise more commonly. Such unbalanced Transportation Problems (TP) are solved by introducing dummy source or destination which do not exist in reality. The optimal allocation involves cells from such dummy source or destination and the allocated number of quantities are held back at one or more origins. The paper aims to propose an algorithm based on Absolute Points to solve unbalanced TP under fuzzy environment. The proposed algorithm is advantageous than the existing algorithms  in such a way that it provides the added information of transporting the excess availability from dummy supply point to appropriate destination to meet future demands at minimum cost. Finally, by virtue of the proposed algorithm an example is done to illustrate the practicality and the effectiveness of the proposed algorithm. 

scholarly journals A New Approach to Solve Mixed Constraint Transportation Problem Under Fuzzy Environment

2017 ◽  
Vol 16 (4) ◽  
pp. 6895-6902
Author(s):  
Nidhi Joshi ◽  
Surjeet Singh Chauhan (Gonder) ◽  
Raghu Raja
Keyword(s):  
Transportation Problem ◽  
Real Life ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
New Approach ◽  
Transportation Problems ◽  
Mixed Constraints ◽  
Fuzzy Environment ◽  
Mixed Constraint ◽  
Fuzzy Transportation Problem

The present paper attempts to obtain the optimal solution for the fuzzy transportation problem with mixed constraints. In this paper, authors have proposed a new innovative approach for obtaining the optimal solution of mixed constraint fuzzy transportation problem. The method is illustrated using a numerical example and the logical steps are highlighted using a simple flowchart. As maximum transportation problems in real life have mixed constraints and these problems cannot be truly solved using general methods, so the proposed method can be applied for solving such mixed constraint fuzzy transportation problems to obtain the best optimal solutions.

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