Linear optimization: Sensibility analysis 3
Inhaltsverzeichnis
Theory
The sensitivity analysis is concerned with the effects and changes in the output data to the optimal solution. You can also ask this question a little differently: to what extent can size change without affecting the essential properties of the solution?
Finding the optimal solution to a linear programming model is important, but one can derive the Sensitivity Analysis important additional information from the linear model (but there are much more information that can be read from an analysis). There is a tremendous amount of sensitivity information, or information about what happens when data values are changed.
Other analysises you could only use under the condition that a constancy of the output data is given. However, such a stability of the output data does not exist in reality. That is a problem because you usually cannot modify any data simultaneously, only one size while keeping all other constant ("ceteris paribus") is changed and asked: In what area can the size in question vary, without this, the solution loses its validity?
By "valid" here are the qualitative characteristics of a solution and not understood quantitatively. A solution is qualitatively different (structural) only by another if at least one pivot operation is needed to establish admissibility and / or optimality again if it was lost in the change.
Non basis variables
The absolutely smallest negative and the smallest positive ratio from right side and the according column element of the optimal solution offer the margin of fluctutation by the primal value in the initial solution.
Basis variables
The absolutely smallest negative and the smallest positive ratio of objective function coefficient and according element of the row of the optimal solution offer the margin of fluctuation by the dual value in the initial solution.
Example
For the whole example we will stick with the following problem.
The initial tableau:
To get from the initial solution to the optimal one, should be already clear and is not part of this wiki-entry.
The optimal tableau:
Presentation of the problem
Detailed solution process with explanation
Sources
1. Script Operation Research SS 2013 Prof. Dr. Oliver Wendt
