I started learning linear programming to solve a personal challenge but I cannot formulate the model. This is not for a class but for something I am personally working on. I can do the simple optimization examples but this is above me currently.
I have data on j (actually 3) categories of people P. Each category has a score ranging from 0 to 100. I have the individual people, which category, and their scores.
There are i (actually 4) score cutoffs C ranges. There are i (4) values V which are dependent on the score range.
- $V_1$ is applied to number of people in any category with score <= $C_1$
- $V_2$ is applied to number of people in any category with score > $C_1$ && <= $C_2$
- $V_3$ is applied to number of people in any category with score > $C_2$ && <= $C_3$
- $V_4$ is applied to number of people in any category with score > $C_3$
- 0 <= $C_i$ <= 100 (alignment to the scores)
- 500 <= $V_1$ <= $V_2$ <= $V_3$ <= $V_4$ <= 100000
I need to determine V and C to maximize the equation
$$\max \sum (V_i * P_{1i}) - (2 * V_i * P_{2i}) - (V_i * P_{3i})$$ where $V_i$ is the value in the i cutoff range and $P_{ji}$ is the number of people in the j category with a score in the i cutoff range.
I have a few sticking points - how to sync $V_i$ and $C_i$ and how to select the correct $P_{ji}$ for the C_i cutoff range. I believe I need to restructure the data, perhaps some boolean multiplication, but my experience does not cover that part yet. Soon hopefully
I eventually will place this into cvxopt. Currently I am want to write the model in standard form so I understand it. If I do not understand it, I cannot program it.
Any help or pointers of where to look for is appreciated.
Thank you