Linear optimization: Sensibility analysis 1: Unterschied zwischen den Versionen
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== Theory == | == Theory == | ||
| − | The german term "sensibilitätsanalyse" was derived from the original english term sensitivity analysis by Müller-Merbach [Operations Research] in 1992. Sensibility analysis is the retranslation of that. These two terms are being used equally. | + | The german term "sensibilitätsanalyse" was derived from the original english term sensitivity analysis by Müller-Merbach [Operations Research] in 1992. Sensibility analysis is the retranslation of that. These two terms are being here used equally. |
| − | After having found an optimal solution for a linear optimization problem by the means of the Simplex algorithm, one can use the sensibility analysis to see, how much the initial | + | After having found an optimal solution for a linear optimization problem by the means of the Simplex algorithm, one can use the sensibility analysis to see, how much the initial data may be changed, without changing the structure of the optimal solution. |
In other words you can see, the robustness of your optimal programm regarding the change of the objective function or constraints. | In other words you can see, the robustness of your optimal programm regarding the change of the objective function or constraints. | ||
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=== Non basic variable change === | === Non basic variable change === | ||
| − | + | ''In the following section, all relations concerning dimensions of numbers are [http://en.wikipedia.org/wiki/Absolute_value absolute values]'' | |
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| + | The smallest negative and the smallest positive quotient of the optimal solution's '''right hand side''' and the corresponding '''column element''' define, when added or subtracted, the '''upper''' and '''lower endpoint''' of the interval in which the constraints may vary | ||
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| + | So, you can see the robustness of the optimal solution, concerning the change of the restrictions. | ||
=== basic variable change === | === basic variable change === | ||
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| + | The smallest negative and the smallest positive quotient of the optimal solution's '''Objective function coefficient''' and the corresponding '''row element''' define, when subtracted or added, the '''lower''' and'''upper endpoint''' of the interval in which the coefficients of the objective function may vary | ||
By the interval of basic variables, you can see the robustness of the optimal solution, concerning the change of the objective function. | By the interval of basic variables, you can see the robustness of the optimal solution, concerning the change of the objective function. | ||
Version vom 27. Juni 2013, 17:55 Uhr
Besetzt H&S
Inhaltsverzeichnis
Theory
The german term "sensibilitätsanalyse" was derived from the original english term sensitivity analysis by Müller-Merbach [Operations Research] in 1992. Sensibility analysis is the retranslation of that. These two terms are being here used equally.
After having found an optimal solution for a linear optimization problem by the means of the Simplex algorithm, one can use the sensibility analysis to see, how much the initial data may be changed, without changing the structure of the optimal solution. In other words you can see, the robustness of your optimal programm regarding the change of the objective function or constraints.
Non basic variable change
In the following section, all relations concerning dimensions of numbers are absolute values
The smallest negative and the smallest positive quotient of the optimal solution's right hand side and the corresponding column element define, when added or subtracted, the upper and lower endpoint of the interval in which the constraints may vary
So, you can see the robustness of the optimal solution, concerning the change of the restrictions.
basic variable change
The smallest negative and the smallest positive quotient of the optimal solution's Objective function coefficient and the corresponding row element define, when subtracted or added, the lower andupper endpoint of the interval in which the coefficients of the objective function may vary
By the interval of basic variables, you can see the robustness of the optimal solution, concerning the change of the objective function.
