scholarly journals A Simple and Efficient Algorithm for Solving Type-1 Intuitionistic Fuzzy Solid Transportation Problems

2018 ◽  
Vol 9 (3) ◽  
pp. 90-122 ◽  
Author(s):  
P. Senthil Kumar
Keyword(s):  
Transportation Problem ◽  
Feasible Solution ◽  
Real Life ◽  
Optimal Solution ◽  
Intuitionistic Fuzzy Number ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy ◽  
Triangular Intuitionistic Fuzzy Number

This article describes how in solving real-life solid transportation problems (STPs) we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation, many authors have suggested the intuitionistic fuzzy (IF) representation for the data. In this article, the author tried to categorise the STP under uncertain environment. He formulates the intuitionistic fuzzy solid transportation problem (IFSTP) and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The STP has uncertainty and hesitation in supply, demand, capacity of different modes of transport celled conveyance and when it has crisp cost it is known as IFSTP of type-1. From this concept, the generalized mathematical model for type-1 IFSTP is explained. To find out the optimal solution to type-1 IFSTPs, a single stage method called intuitionistic fuzzy min-zero min-cost method is presented. A real-life numerical example is presented to clarify the idea of the proposed method. Moreover, results and discussions, advantages of the proposed method, and future works are presented. The main advantage of the proposed method is that the optimal solution of type-1 IFSTP is obtained without using the basic feasible solution and the method of testing optimality.

scholarly journals PSK Method for Solving Mixed and Type-4 Intuitionistic Fuzzy Solid Transportation Problems

2019 ◽  
Vol 10 (2) ◽  
pp. 20-53 ◽  
Author(s):  
P. Senthil Kumar
Keyword(s):  
Fuzzy Number ◽  
Transportation Problem ◽  
Graphical Representation ◽  
Optimal Solution ◽  
Intuitionistic Fuzzy Number ◽  
Uncertain Environments ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy ◽  
Triangular Intuitionistic Fuzzy Number ◽  
Fuzzy Optimal Solution

In this article, the author categorises the solid transportation problem (STP) under uncertain environments. He formulates the mixed and fully intuitionistic fuzzy solid transportation problems (FIFSTPs) and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The PSK (P. Senthil Kumar) method for finding an intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem (FIFTP) is extended to solve the mixed and type-4 IFSTP and the optimal objective value of mixed and type-4 IFSTP is obtained in terms of triangular intuitionistic fuzzy number (TIFN). The main advantage of this method is that the optimal solution of mixed and type-4 IFSTP is obtained without using the basic feasible solution and the method of testing optimality. Moreover, the proposed method is computationally very simple and easy to understand. Finally, the procedure for the proposed method is illustrated with the help of numerical examples which is followed by graphical representation of the finding.

scholarly journals An algorithm for solving a capacitated indefinite quadratic transportation problem with enhanced flow

2014 ◽  
Vol 24 (2) ◽  
pp. 217-236 ◽  
Author(s):  
Kavita Gupta ◽  
S.R. Arora
Keyword(s):  
Special Class ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Flow Problem ◽  
Optimal Solution ◽  
Total Flow ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
Indefinite Quadratic

The present paper discusses enhanced flow in a capacitated indefinite quadratic transportation problem. Sometimes, situations arise where either reserve stocks have to be kept at the supply points say, for emergencies, or there may be extra demand in the markets. In such situations, the total flow needs to be controlled or enhanced. In this paper, a special class of transportation problems is studied, where the total transportation flow is enhanced to a known specified level. A related indefinite quadratic transportation problem is formulated, and it is shown that to each basic feasible solution called corner feasible solution to related transportation problem, there is a corresponding feasible solution to this enhanced flow problem. The optimal solution to enhanced flow problem may be obtained from the optimal solution to the related transportation problem. An algorithm is presented to solve a capacitated indefinite quadratic transportation problem with enhanced flow. Numerical illustrations are also included in support of the theory. Computational software GAMS is also used.

scholarly journals Solving unbalanced intuitionistic fuzzy transportation problem

10.26524/cm61 ◽  
2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Soundararajan S ◽  
Suresh Kumar M
Keyword(s):  
Approximation Method ◽  
Fuzzy Number ◽  
Transportation Problem ◽  
Optimal Solution ◽  
Intuitionistic Fuzzy Number ◽  
Numerical Example ◽  
Intuitionistic Fuzzy ◽  
Triangular Intuitionistic Fuzzy Number ◽  
Fuzzy Transportation Problem ◽  
Number Of Iterations

In this paper, we find the optimal solution for an unbalanced intuitionistic fuzzy transportation problem by using monalisha’s approximation method. The main aim of this method is to avoid large number of iterations. To illustrate this method a numerical example Triangular intuitionistic fuzzy number, unbalanced intuitionistic fuzzy transportation problem, accuracy function.is given.

scholarly journals A New Technique for Solving Transportation Problems by Using Decomposition-Based Pricing and its Implementation in Real Life

2016 ◽  
Vol 64 (1) ◽  
pp. 45-50
Author(s):  
Sajal Chakroborty ◽  
M Babul Hasan
Keyword(s):  
Feasible Solution ◽  
Real Life ◽  
Optimal Solution ◽  
Computer Code ◽  
The Other ◽  
New Technique ◽  
Business Organization ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
A New Technique

In this paper, we develop a new technique for solving transportation problems (TP) and develop a computer code by using mathematical programming language AMPL. There are many existing techniques for solving TP problems in use. By these techniques one has to determine initial basic feasible solution at first then improve this solution to determine optimal solution by another method. But this process is very lengthy and time consuming. By our technique we can determine optimal solution directly without determining initial basic feasible solution and optimal solution separately and we hope that this technique will provide an easier way than that of the other methods. We use the idea of decomposition based pricing (DBP) method to develop our technique. To our knowledge, there is no other paper which used DBP to solve TP. We demonstrate our technique by solving real life models developed by collecting data from a business organization of Bangladesh.Dhaka Univ. J. Sci. 64(1): 45-50, 2016 (January)

Optimizing a fully rough interval integer solid transportation problems

2021 ◽  
pp. 1-11
Author(s):  
T. AnithaKumari ◽  
B. Venkateswarlu ◽  
A. Akilbasha
Keyword(s):  
Feasible Solution ◽  
Real Life ◽  
Optimal Solution ◽  
Logistic Models ◽  
Zero Point ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
Decision Variables ◽  
Rough Interval ◽  
The Given

An innovative method, namely modified slice-sum method using the principle of zero point method is proposed for finding an optimal solution to fully rough interval integer solid transportation problems (FRIISTP). The proposed method yields an optimal solution to the fully rough interval integer solid transportation problem directly. In this method, there is no necessity to find an initial basic feasible solution to FRIISTP and also need not to use the existing MODI and stepping stone methods for testing the optimality to improve the basic feasible solution to the FRIISTP but directly obtain an optimal solution to the given FRIISTP by using the proposed method. The optimal values of decision variables and the objective function of the fully rough interval integer solid transportation problems provided by the proposed method are rough interval integers. The advantages of the proposed method over existing method are discussed in the context of an application example. The modified slice-sum method has been applied to calculate the optimal compromise solutions of FRIISTP, and then it was solved by using TORA software. The proposed method can be served as an appropriate tool for the decision makers when they are handling logistic models of real life situations involving three items with rough interval integer parameters.

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.

scholarly journals PSK Method for Solving Intuitionistic Fuzzy Solid Transportation Problems

2018 ◽  
Vol 7 (4) ◽  
pp. 62-99 ◽  
Author(s):  
P.Senthil Kumar
Keyword(s):  
Real Life ◽  
Optimal Solution ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Optimal Solution ◽  
Fuzzy Representation ◽  
Objective Value

This article proposes a method for solving intuitionistic fuzzy solid transportation problems (IFSTPs) in which only the transportation costs are represented in terms of intuitionistic fuzzy numbers (IFNs). The remaining parameters, namely: supply, demand and conveyance capacity, are all considered into crisp numbers. This type of STP is called a type-2 IFSTP. When solving the real life solid transportation problems (STPs) those tend to face the uncertainty state as well as hesitation due to many uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this article, the author tried to categorise the STPs under the uncertain environment. He formulates the intuitionistic fuzzy STPs and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The PSK (P.Senthil Kumar) method for finding an intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem (FIFTP) is extended to solve the type-2 IFSTP and the optimal objective value of type-2 IFSTP is obtained in terms of TIFN. The main advantage of this method is that the optimal solution of type-2 IFSTP is obtained without using the basic feasible solution and the method of testing optimality. Moreover, the proposed method is computationally very simple and easy to understand. A case study is presented to illustrate the procedure of the proposed method.

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 Fundamentals of Transportation Problem

2021 ◽  
Vol 10 (5) ◽  
pp. 90-103
Author(s):  
Bhabani Mallia ◽  
Manjula Das ◽  
C. Das
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Basic Feasible Solution ◽  
Distribution Method

Transportation Problem is a linear programming problem. Like LPP, transportation problem has basic feasible solution (BFS) and then from it we obtain the optimal solution. Among these BFS the optimal solution is developed by constructing dual of the TP. By using complimentary slackness conditions the optimal solutions is obtained by the same iterative principle. The method is known as MODI (Modified Distribution) method. In this paper we have discussed all the aspect of transportation problem.

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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