Related Experiment Video
Updated: Apr 15, 2026
11:41
Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation
Published on: February 1, 2020
21.1K
The intelligence of dual simplex method to solve linear fractional fuzzy transportation problem
S Narayanamoorthy1, S Kalyani1
1Department of Applied Mathematics, Bharathiar University, Coimbatore, Tamil Nadu 641 046, India.
Computational Intelligence and Neuroscience
|March 27, 2015
Summary
This study introduces a new method to solve complex fuzzy transportation problems with fractional objectives. The approach decomposes the problem into simpler linear fuzzy transportation problems, efficiently finding the optimal solution.
Area of Science:
- Operations Research
- Fuzzy Mathematics
- Optimization Techniques
Background:
- Fuzzy transportation problems (FTPs) are common in logistics and supply chain management.
- Linear fractional objective functions add complexity to traditional FTPs.
- Existing methods may struggle with the intricacies of fractional fuzzy objectives.
Purpose of the Study:
- To propose a novel approach for solving linear fractional fuzzy transportation problems (LFFTPs).
- To simplify LFFTPs by decomposing them into manageable sub-problems.
- To provide a clear methodology for obtaining optimal solutions for LFFTPs.
Main Methods:
- Decomposition of the LFFTP into two linear fuzzy transportation problems.
- Application of the dual simplex method to solve the resulting linear fuzzy transportation problems.
- Integration of solutions from sub-problems to derive the optimal solution for the original LFFTP.
Main Results:
- The proposed decomposition method effectively transforms an LFFTP into solvable linear fuzzy transportation problems.
- The dual simplex method efficiently yields optimal solutions for the decomposed problems.
- A clear pathway to obtain the optimal solution for the original LFFTP is established.
Conclusions:
- The presented approach offers an effective and systematic way to solve LFFTPs.
- Decomposition combined with the dual simplex method provides a robust solution strategy.
- The method is validated and explained through a detailed example.
Related Concept Videos
01:25Systems of Linear Equations in Two Variables
402
Solving a system of linear equations is a fundamental concept in algebra. A system of equations consists of two or more linear equations involving the same set of variables. One of the most efficient algebraic methods for solving such systems is the substitution method. This technique involves expressing one variable in terms of the other from one equation and substituting it into the second equation. This method is particularly useful when one of the equations is easily rearranged.Consider the...
402
01:28Partial Fractions
344
A partial fraction is a component of a rational expression represented as the sum of simpler fractions. When a rational function is expressed as a ratio of two polynomials, it can often be decomposed into a sum of fractions whose denominators are simpler polynomials, typically linear or irreducible quadratic factors. This process is called partial fraction decomposition, and it is used to simplify complex expressions for integration, solving equations, or analysis.Partial fraction decomposition...
344
01:26Linearization and Approximation
210
Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
210
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
413
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
413
01:30Gaussian Elimination: Problem Solving
289
Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...
289
01:29Evaluating Limits by Direct Substitution
254
In the analysis of functions that represent continuous physical phenomena, it is often necessary to determine the output value as the input approaches a specific point. When a combination of algebraic terms defines the function and exhibits no discontinuities or abrupt changes near the point of interest, the limit of the function can be evaluated directly. This process, known as direct substitution, involves replacing the variable in the expression with the value it approaches.Direct...
254