Fuzzy Transportation Problem Research Articles

Row Column Reduction Method for Solving Trapezoidal Fuzzy Transportation Problem

The primary goal of the transportation issue is to reduce the cost of moving goods from several warehouses to various showrooms. Fuzzy approaches are frequently employed to eliminate uncertainty. When the cost of transportation is uncertain, we sometimes use a fuzzy approach to resolve the issue. In this paper the values used in constraint equation are trapezoidal number and applied our proposed method, row column reduction method to get an optimal transportation cost.

Retraction Note: An algorithmic approach to solve unbalanced triangular fuzzy transportation problems

Retraction Note: An algorithmic approach to solve unbalanced triangular fuzzy transportation problems

Facebook Addiction: Advanced Vogel's Approximation Method of Unbalanced Fuzzy Transportation Problems.

In this article, we discuss the Advanced Vogel's Approximation Method (AVAM), a revolutionary solution for an imbalanced fuzzy transportation problem that avoids making it balanced. Notably, Facebook is the social network that is most popular and well-known globally. Some have characterized it as an invaluable resource for leisure and cross-cultural communication. Conversely, excessive use and a lack of self-control lead to Facebook addiction, which negatively affects the daily lives of many users, mostly young people. Facebook use appears to be connected to the drive to fit in, affiliate with people, and present oneself. Excessive Facebook use and addiction may also be linked to reward and pleasure systems.

An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems

An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems

A New Solution Technique for Fuzzy Transportation Problem Using Novel Ranking Functions on Heptagonal Fuzzy Numbers: A Case Study of Regional Shipment

This study focuses on the fuzzy transportation problem that manifests as a problem of optimization in an uncertain environment. The idea of fuzziness in the objective of transportation cost is based on real-world decision-making difficulties, and the efficiency is demonstrated using the proposed heptagonal fuzzy number. We propose a new ranking technique to de-fuzzify the Linear heptagonal fuzzy number and the proposed $\alpha$-cut based ranking technique has been compared with the existing ranking technique. In addition, we presented an approach for performing multiplication and division for any two heptagonal fuzzy numbers incorporating an example. Furthermore, we have presented a generalized ranking heptagonal fuzzy method (GRHFM) algorithm to solve the heptagonal fuzzy transportation. This article determines the best transportation cost for vegetable shipment from the markets utilizing heptagonal fuzzy numbers, which further compares the feasible solutions obtained using various strategies for fuzzy transportation problems and provides the result from the algorithm. We have demonstrated the effectiveness of our proposed method through a numerical example of an adopted case study. The conclusions section discusses the suggested GRHFM efficiency, outcomes, decision management and future directions based on the existing transportation study.

An extended Vogel’s approximation algorithm for efficiently solving Fermatean fuzzy solid transportation problems

An extended Vogel’s approximation algorithm for efficiently solving Fermatean fuzzy solid transportation problems

Solution of fuzzy transportation problem based upon pentagonal and hexagonal fuzzy numbers

Solution of fuzzy transportation problem based upon pentagonal and hexagonal fuzzy numbers

Heuristic algorithm for an optimal solution of fully fuzzy transportation problem

Heuristic algorithm for an optimal solution of fully fuzzy transportation problem

A NOVEL METHOD FOR SOLVING FULLY FUZZY SOLID TRANSPORTATIONS PROBLEMS

In this paper, we proposes a new method for solving solid transportation problem under uncertainty environments. The fully fuzzy solid transportation problem has been formulated. To reduce the model into crisp equivalent, we have used existing method for approximation of fuzzy numbers by interval numbers and its arithmatics. A simplex method and existing method for solving Interval Linear Programming problems are used for solving solid transportation problem with fuzzy parameters and decision variables. Furthermore, for illustration, some numerical examples are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy and reasonable.

A Comparison of Proposed Ranking Method for Fuzzy Transportation Problem with the Existing Method

A Comparison of Proposed Ranking Method for Fuzzy Transportation Problem with the Existing Method

Solving the Fuzzy Transportation Problem by a Novel Particle Swarm Optimization Approach

Solving the Fuzzy Transportation Problem by a Novel Particle Swarm Optimization Approach

Analyze the Stochastic Solid Fuzzy Transportation Problem with Mixed Constraints through Weibull Distribution

This paper proposed a general formulation of the stochastic solid transportation problem (SSTP) with mixed constraints such as supply, demand and conveyance capacity taken as uncertain under stochastic environment, following the Weibull distribution (WD). The aim of this study is to minimize the transportation cost includes probabilistic constraints have inequalities of stochastic solid transportation problem (SSTP). SSTP with probabilistic constraints is represented as a chance constrained programming problem. Obtain alpha cut representation from cost coefficient of the fuzzy objective function. We have developed four models for stochastic solid transportation problem. The suggested models are demonstrated by taken as numerical example. A sensitivity analysis is performed to understand parameter’s sensitivity in the proposed model. Introduction: In system of transportation, goods are moved from various sources to destinations using different vehicles and organizational systems, involving both technology and human efforts. Efficient resource allocation in transportation system is crucial for industries and imprecision from factors like fluctuating demand, unreliable supply chains and unpredictable traffic. To address these complexities, advanced mathematical models are needed to manage stochasticity, fuzziness and mixed constraints. The study explores the stochastic solid fuzzy transportation problem with mixed constraint by utilizing the Weibull distribution to model uncertainties inherent in transportation systems. This research addresses the complexity introduced by stochastic variables and fuzzy parameters, particularly in situations where demand, supply and cost of transportation are not deterministic. Objectives: The aim of this study is to minimize the cost of transportation includes probabilistic constraints have inequalities of stochastic solid transportation problem (SSTP). Methods: Obtain alpha cut representation form the cost coefficient of the fuzzy objective function and four models are developed for stochastic solid transportation problem. These models are demonstrating by using a numerical example and a sensitivity analysis is conducted to understand the sensitivity of the parameters in the propose model. Results: Obtained optimal solutions for developed four models of SFSTPMC and sensitivity analysis shows that cost of transportation and flow of unit are sensitive to change in probabilities of demand. Improve transportation system by understanding sensitivity patterns that help decision maker choose appropriate supply availability probabilities. Conclusions: This study presented an approach for solving the SFSTPMC using the Weibull distribution for probabilistic constraints and fuzzy objective functions for transportation cost. Developed and optimized four models, focusing on stochastic parameters. Sensitivity analysis demonstrated the impact of these parameters on transportation cost and unit flow. The results validate the model’s effectiveness in practical resource allocation and decision making under uncertainty.

Applying a Fuzzy Ordering Approach in Transportation Problems with Decagonal Intuitionistic Fuzzy Numbers

In this study, the paper delves into precision challenges within traditional transportation problem solutions, which rigidly define cost, supply, and demand. Acknowledging the inherent vagueness in real world contexts, the research explores the efficacy of intuitive fuzzy sets as a potent tool. Organized into four distinct sections, this work utilizes decagonal intuitionistic fuzzy numbers for managing supply and demand, while upholding conventional approaches for cost considerations. Employing a fuzzy ordering method, optimal solutions are derived by adjusting the configuration of decagonal intuitive fuzzy numbers across each segment. Through a comparative analysis, the Study identifies the most effective solution, with initial sections addressing balanced geometric intuitionistic fuzzy transportation problems and the final part focusing on unbalanced scenarios, specifically emphasizing supply and demand complexities.

Decision support system using Dhouib-Matrix-TP1 heuristic for pentagonal fuzzy transportation problem

In this paper, a decision support system (DSS) is provided to assist the decision-maker in obtaining the best solution for the transportation problem under uncertainty. Fuzzy parameters of the transportation problem are presented by pentagonal fuzzy numbers. The centroid ranking function transforms these pentagonal fuzzy numbers into crisp ones. Then, a novel, improved greedy method named Dhouib-Matrix-TP1 (DM-TP1) is used in order to help the decision-maker promptly find a suitable solution. Specifically, this DSS is composed of three components: the data base component considers a pentagonal fuzzy number; the Model Base component thinks through the original heuristic DM-TP1; and the User Interface component deliberates the convivial graphical output of the generated transportation plan solution using the Python programming language. Experiments in the literature on fuzzy transportation problems show that the novel proposed heuristic, DM-TP1, is easy to understand and allows the decision-maker to handle transportation problems under pentagonal fuzzy numbers. Also, the DM-TP1 is robust and can be applied to find a feasible initial solution in less time.

Cost Analysis of Fuzzy Transportation Models with Ranking Function in Two Stages

According to the research conducted so far, a crisp value is obtained by defuzzifying the fuzzy value using any defuzzification approach and this value is then used to analyze the entire problem. It is possible, however, that the crisp value generated using existing approaches may not exactly be matched with the fuzzy values. It is probable that any figure slightly early or slightly later than the obtained crisp value will produce the better outcome. So, the purpose of this research work is to provide a technique that can defuzzify fuzzy parameter values so that there are more than one possible values following a small adjustment to the technique. In this paper, the cost, demand and availability of transportation problems are taken in the form of trapezoidal fuzzy number. The advantage of the methodology developed is that the any value close to the crisp value obtained from the existing methods of trapezoidal fuzzy number or a value in the range of the trapezoidal fuzzy number as desired by the decision maker can be obtained. This method has the benefit of allowing the decision makers to receive as much crisp cost as desired in the fuzzy transportation problem. Which facilitated more accurate analysis of fuzzy transportation models. The numerical issue provides an explanation of the recommended strategy.. KEYWORDS :Fuzzy transportation problem (FTP), Trapezoidal fuzzy number (TrFN), Optimization, Ranking function.

Improved fuzzy multi-objective transportation problem with Triangular fuzzy numbers

The present study investigates a Multi-Objective Transportation Problem within a fuzzy environment. The cost of transportation, supply, and demand data are assumed to be inaccurate due to market variations. As a result, the parameters are imprecise or fuzzy data. We offer a multi-objective, balanced transportation problem during this work, where all the parameters are fuzzy numbers. Following a mathematical formulation, fuzzy arithmetic will be used to divide the Fuzzy MOTP into three levels MOTP (lower, medium, upper). After reducing the problem to a crisp MOTP and applying a harmonic mean to each objective function, a suggested solution procedure is presented. Determining the optimal solutions for the FMOTP under unknown situations is, thus, the most important objective of this research.

Dual hesitant fuzzy set in multi-objective transportation problems in time sequence frame work

Decision makers may have different information in different situations when making decisions about the same attributes, depending on the circumstances. A time-sequential framework is necessary for navigating these kinds of circumstances. We established the notion of a Time-sequential dual hesitant fuzzy set (TS-DHFS) to illustrate the significance of time sequence in decision-making with the aid of a dual hesitant fuzzy set (DHFS), one of the important tools to handle the uncertainty embedded in the real world. The proposed set describes the hesitant situations more accurately by inducing a time sequence framework. We defined the fundamental operations, two score function for ranking and a series distance measures for the proposed set. For the pragmatic application of our proposed set, we devised the mathematical model in three different types of Time-sequential dual hesitant fuzzy multi-objective transportation problems (TS-DHF-MOTPs). The proposed three models are classified based on the nature of the parameters such as transportation cost (TC), transportation time (TT), availability, and demand. The goal of the proposed transportation systems is TC and TT simultaneously in a single framework. We established an approach utilizing one of the ranking functions that have been proposed, followed by the fuzzy programming (FP) and weighted sum technique (WST), to optimize the constructed models. Additionally, numerical computations are also carried out to emphasize the efficiency and benefits of MOTP under the TS-DHF environment.

A Systematic Formulation into Neutrosophic Z Methodologies for Symmetrical and Asymmetrical Transportation Problem Challenges

This study formulates a multi-objective, multi-item solid transportation issue with parameters that are neutrosophic Z-number fuzzy variables such as transportation costs, supplies, and demands. This work covers two scenarios where uncertainty in the problem can arise: the fuzzy solid transportation problem and the interval solid transportation problem. The first scenario arises when we represent data problems as intervals instead of exact values, while the second scenario arises when the information is not entirely clear. We address both models when the uncertainty alone impacts the constraint set. In order to find a solution for the interval case, we generate an additional problem. Since this auxiliary problem is typical of solid transportation, we can resolve it using the effective techniques currently in use. In the fuzzy scenario, a parametric method is used to discover a fuzzy solution to the earlier issue. Parametric analysis identifies that the best parameterized approaches to complementary problems are characterized by the application of parametric analysis. We present a suggested algorithm for determining the stability set. Finally, we provide a numerical example and sensitivity analysis for the transportation problem, which is both symmetrical and asymmetrical.

An efficient computational approach for basic feasible solution of fuzzy transportation problems

An efficient computational approach for basic feasible solution of fuzzy transportation problems

To Solve Pythagorean Fuzzy Decagonal Transportation Problem Using Bipartite Graph with Optimal Solution

Objectives: This study aims to solve the Pythagorean fuzzy transportation problem by means of providing a novel approach. Methods: To determine the optimum decision-making, we applied the MODI approach. To illustrate the proposed approach, we applied several types of numerical issues. An algorithm for solving the suggested technique is described. Findings: This study presents a bipartite graph-based strategy to the Pythagorean fuzzy transportation problem. Applying TORA statistical software, the data analysis discovered that the crisp model becomes linear when the membership function is applied. Novelty: This study has paved a way for better optimal results to obtain when the Pythagorean fuzzy set is converted using the score function instead of the standard techniques for Defuzzification. Keywords: Score Function, Pythagorean Fuzzy, Defuzzification, Pythagorean Fuzzy Transportation Problem, Decagonal Fuzzy Number, Ranking Method, Initial Basic Feasible Solution, and Optimal Solution