The Simplex Method Approach to Linear Programming Solutions | Chapter 2 | Research Updates in Mathematics and Computer Science Vol. 6

 

The SIMPLEX METHOD (SM) is a fundamental technique in the optimization field [1, 2], designed specifically to solve linear programming problems manually with high efficiency and accuracy by understanding limitations, specifying decision variables,creating objective functions and defining the feasible region by using slack variables, tableaus, and pivot variables as a means of finding the optimal solution to an optimization problem.

 

Author(s)details:-

 

Ghada A. Ahmed
Department of mathematics, Faculty of Science, AL-Baha University, ALBaha,
ALBaha, Saudia Arabia.

 

Please See the book here :-   https://doi.org/10.9734/bpi/rumcs/v6/28

Study on Linear Programming in Risk Management | Chapter 13 | Novel Research Aspects in Mathematical and Computer Science Vol. 1

 The deterministic nature of the linear programming model is well-known. One method for dealing with uncertainty is to calculate the range of optimality. The effect of changing each objective function coefficient one at a time is studied after achieving the optimal solution (typically using the simplex approach). The optimality range is defined as the region in which the choice variables remain constant. This sensitivity analysis aids the analyst in gaining a better understanding of the problem. It is, however, impractical since the coefficients of objective functions do not tend to stay constant. They are frequently profit contributions from sold items, and their selling prices fluctuate at random. A realistic linear programme is built for simultaneously randomising the coefficients from any probability distribution. A novel method for creating a copula of random objective function coefficients based on a given rank correlation is also presented. The value distribution of the applicable objective function is generated. This distribution is analysed directly for central tendency, spread, skewness, and extreme values for the purposes of risk analysis. Risk analysis and business analytics are important areas in education and training for the information economy.

Author(S) Details

Dennis Ridley
School of Business and Industry, Florida A&M University, USA and Department of Scientific Computing, Florida State University, USA.

Felipe Llaugel
Universidad Autonoma de Santo Domingo, USA.

Inger Daniels
School of Business and Industry, Florida A&M University, USA.

Abdullah Khan
School of Business, Claflin University, USA.

View Book:- https://stm.bookpi.org/NRAMCS-V1/article/view/6559

Computing and Applications: The Maximum Flow and Minimum Cost – Maximum Flow Problems | Chapter 6 | Theory and Practice of Mathematics and Computer Science Vol. 10

 Both the maximum flow and minimum cost-maximum flow challenges are concerned with determining flows between a source and a destination across a network. The term "maximum flow" refers to any problem in which the goal is to transport as many products, objects, or people as possible between two sites via intermediate places. Maximum flow-lowest cost refers to flow problems including both capacities and expenses. Computing enables one to come at a solution to a problem when provided knowledge about a network (network flow diagram, capacities, and expenses). When the solution is ready, it must be tested on a real-world problem. The usage of R (many packages and functions), specially designed Pascal programmes, and Excel SOLVER in the solution of these problems will be discussed. The following problems' minimum cost-maximum flow solutions will also be discussed: Transportation problem, assignment problem, shortest path problem, caterer problem, maximum flow, minimum cost-maximum flow.

Author(s) Details

W. H. Moolman
Department of Mathematical Sciences and Computing, Walter Sisulu University, Mthatha, South Africa.

View Book :- https://stm.bookpi.org/TPMCS-V10/article/view/1076