Linear optimization: Parametrical objective function 2
Theory
Parametrical objective functions is an extension of linear optimization. It handles problems where the coefficient of the objective function and / or the right sides of constraints can not be assumed to be constant, but rather may vary depending on different parameters.
Generally the parametrical objective function is searching for an optimal solution of a linear problem independent from the parameters actual value. Commonly optimization problems like parametrical problems origin from instability in decisions especially concerning given data. One way to solve such a problem is through a modified Simplex-Method which will be presented below.
Example
The origin 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.
We are assuming that a company wants to maximize their profit. Therefor the companies controller put up a profit equation which needs to be maximized.
Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): G = qx_1 + 300x_2 - 20000
Our restrictions are:
Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): 2x_1 + 1x_2 \le 95
Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): 1x_1 + 4x_2 \le 100
Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): 1x_1 + 0x_2 \le 30
....update on july 1st
Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): kml lkmlk lkm
