Linear optimization: Parametrical objective function 4: Unterschied zwischen den Versionen
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In Tableau 3 you have an optimal solution if you define <math>q</math> <math>\le</math> <math>0</math> ,because your head row gets positive <math>\rightarrow</math> acceptable and optimal solution | In Tableau 3 you have an optimal solution if you define <math>q</math> <math>\le</math> <math>0</math> ,because your head row gets positive <math>\rightarrow</math> acceptable and optimal solution | ||
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+ | == Origin == | ||
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+ | -Skript OperationResearch_2012SS_Wendt | ||
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+ | - http://www.orklaert.de/parametrische-lineare-optimierung | ||
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+ | - https://bisor.wiwi.uni-kl.de/orwiki/Parametrische_Optimierung |
Version vom 26. Juni 2013, 17:24 Uhr
Parametrical objective function is a special part of linear optimization. The foundation of parametrical optimization is the sensitivity analysis. Compared to the sensitivity analysis the Parametrical objective function makes a statement about large changes in the input data.
Basic Knowledge
To include large changes in the input data you have to add a new variable "". For simple cases you just summate the new variable "" multiplicated with a constant vektor " " to the objective function. In this case the constant vektor is the value which change the input parameter "".
The objectiv function is now with a parameter:
Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): c(q)=c+q*
Thereby there is a new optimization problem which can be solved.
Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): \rightarrow
Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): \ge
Exemplification
From this tableau you can read out the profit function with a variable inside:
Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): G(q)= q*x_1+500x_2-36000
Transformed into the Simplex-Tableau:
In Tableau 1 and 2 you do the normal simplex iteration. "Ignoring" the variable "", setting it equal "0".
In Tableau 3 you have an optimal solution if you define Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): \le
,because your head row gets positive Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): \rightarrow
acceptable and optimal solution
Origin
-Skript OperationResearch_2012SS_Wendt
- http://www.orklaert.de/parametrische-lineare-optimierung
- https://bisor.wiwi.uni-kl.de/orwiki/Parametrische_Optimierung