I have a table of 3 columns and a huge number of rows.
The cells (columns) in each row state the following:
- The name of an item that you can sell
- The value that you will get for selling it
- The real value of that item on the market
The selling platform is provided by a mediator who takes commission on every sale.
So the value that you get for selling an item is always less than its real market value.
Let's call the value that you get $X$ and the value on the market $Y$.
There are two ways for you to assess the worthiness of a deal:
- The absolute commission that you pay: $Y-X$
- The relative commission that you pay: $1-X/Y$
Very important: both ways are equally preferable.
What I'm looking for, is a way to find the worst case.
And here is the problem - if I just search for the highest of each, then I get something like:
- The highest absolute commission is huge, but in relative terms it is close to $0\%$
- The highest relative commission is close to $100\%$, but in absolute terms it is tiny
So I guess I need to define some sort of heuristic function that will take a tuple "abs,rel" as input and return a "grade" value as output.
But I'm not really sure how to approach this.
Thank you for your help.
If you do a search on "multiobjective optimization", you will find a fair number of approaches. One is to define a "utopia" point $u$: the pairing of the best attainable absolution commission and the best attainable relative commission. This very likely does not represent an actual row; if you had the best of both measures in one row, you probably wouldn't bother scoring the others. So $u$ represents your unattainable ideal.
Now pick a norm $\parallel \cdot \parallel$ and score each point $x=(abs, rel)$ by its distance $\parallel x - u \parallel$ from utopia. Smaller distances are better. Common choices are the $L_p$ norms for $p\in \{0,1,2\}$, but ultimately the choice of norm is fairly arbitrary.
Since absolute and relative commissions are presumably on different scales, you'll want to use a weighted norm.