Linear optimization: Parametrical objective function 4
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: