Pareto-optimal solution for fixed-charge solid transportation problem under intuitionistic fuzzy environment

2021 ◽  
pp. 107368
Author(s):  
Divya Chhibber ◽  
Dinesh C.S. Bisht ◽  
Pankaj Kumar Srivastava
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Pareto Optimal Solution ◽  
Fixed Charge ◽  
Pareto Optimal ◽  
Solid Transportation Problem ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment

scholarly journals Geometric Mean Method to Solve Multi-Objective Transportation Problem Under Fuzzy Environment

2020 ◽  
Vol 9 (5) ◽  
pp. 1739-1744
Keyword(s):  
Transportation Problem ◽  
Geometric Mean ◽  
Method Comparison ◽  
Optimal Solution ◽  
Pareto Optimal Solution ◽  
Pareto Optimal ◽  
Numerical Examples ◽  
Multi Objective ◽  
Fuzzy Environment ◽  
Single Objective

Transportation problem is a very common problem for a businessman. Every businessman wants to reduce cost, time and distance of transportation. There are several methods available to solve the transportation problem with single objective but transportation problems are not always with single objective. To solve transportation problem with more than one objective is a typical task. In this paper we explored a new method to solve multi criteria transportation problem named as Geometric mean method to Solve Multi-objective Transportation Problem Under Fuzzy Environment. We took a problem of transportation with three objectives cost, time and distance. We converted objectives into membership values by using a membership function and then geometric mean of membership values is taken. We also used a procedure to find a pareto optimal solution. Our method gives the better values of objectives than other methods. Two numerical examples are given to illustrate the method comparison with some existing methods is also made.

scholarly journals Multi-Objective Restricted Solid Transportation Problem in Intuitionistic Fuzzy Environment with Emission Cost

2019 ◽  
Vol 8 (2S3) ◽  
pp. 722-727 ◽  
Keyword(s):  
Transportation Problem ◽  
International Energy Agency ◽  
Optimal Solution ◽  
Transport Sector ◽  
Solid Transportation Problem ◽  
Energy Agency ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Weighted Sum Method ◽  
Fuzzy Environment

Transportation plays key role in logistic and supply chain management for decreasing cost and enhances service. The transport sector contributes 23% of the total CO2 emissions in the world according to the latest estimates of the International Energy Agency (IEA).There is a direct link between weight of the quantity transported and co2 emission for the freight transport. This paper presents multi objective restricted solid transportation problem in intuitionistic fuzzy ambiance with emission cost which is based on weight of the quantity transported and vehicle cost under some restriction on transported amount. An extra constraint on the total budget at each destination is imposed. Transportation models are formulated under crisp and fuzzy environments and fuzzy models are converted into crisp using average method. The total time and emission cost based on weight of the quantity transported for restricted and unrestricted models are compared. The optimal solution is obtained by using weighted sum method and Lingo 13.0 Software. Mathematical example is given to validate the proposed mode

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.

Solving Intuitionistic Fuzzy Solid Transportation Problem Via New Ranking Method Based on Signed Distance

2016 ◽  
Vol 24 (04) ◽  
pp. 483-501 ◽  
Author(s):  
Shashi Aggarwal ◽  
Chavi Gupta
Keyword(s):  
Transportation Problem ◽  
Ranking Method ◽  
Mathematical Programming Problem ◽  
Solid Transportation Problem ◽  
Basic Feasible Solution ◽  
Ranking System ◽  
Intuitionistic Fuzzy Numbers ◽  
Signed Distance ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment

In this paper, signed distance of Symmetrical Intuitionistic Fuzzy Numbers (SIFNs) is introduced. Based on this signed distance and the crisp ranking system on real numbers, a new ranking system for SIFNs is defined, which seems to be very realistic. To illustrate the applicability and suitability of the proposed ranking method and to deal with ambiguity and imprecision, one of the vital mathematical programming problem viz. Solid Transportation Problem (STP) is formulated in intuitionistic fuzzy environment. A new method has been proposed to compute initial basic feasible solution for the same. Also the significance of the proposed approach over existing methods is illustrated. Finally numerical examples are solved to demonstrate the efficiency of the proposed methods.

scholarly journals A Fuzzy Approach Using Generalized Dinkelbach’s Algorithm for Multiobjective Linear Fractional Transportation Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Nurdan Cetin ◽  
Fatma Tiryaki
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Pareto Optimal Solution ◽  
Pareto Optimal ◽  
Fuzzy Approach ◽  
Operator Model ◽  
Numerical Example

We consider a multiobjective linear fractional transportation problem (MLFTP) with several fractional criteria, such as, the maximization of the transport profitability like profit/cost or profit/time, and its two properties are source and destination. Our aim is to introduce MLFTP which has not been studied in literature before and to provide a fuzzy approach which obtain a compromise Pareto-optimal solution for this problem. To do this, first, we present a theorem which shows that MLFTP is always solvable. And then, reducing MLFTP to the Zimmermann’s “min” operator model which is the max-min problem, we construct Generalized Dinkelbach’s Algorithm for solving the obtained problem. Furthermore, we provide an illustrative numerical example to explain this fuzzy approach.

A fixed charge multi-objective solid transportation problem in random fuzzy environment

2015 ◽  
Vol 28 (6) ◽  
pp. 2643-2654 ◽  
Author(s):  
Sutapa Pramanik ◽  
Dipak Kumar Jana ◽  
Manoranjan Maiti
Keyword(s):  
Transportation Problem ◽  
Fixed Charge ◽  
Solid Transportation Problem ◽  
Multi Objective ◽  
Fuzzy Environment
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