I am currently trying to work on this problem that determines the best constraints on how to place these 'bids'- please see the second column in the screenshot:
The ask at hand is to uncover a model or set of rules on how to place these 'bids' to maximize the amount of net revenue. The way that generating profits is that a bid is placed at a FIXED price- which is either $\\\$3$, $\\\$35$, $\\\$50$, or $\\\$75$. Revenue is generated when the bid is accepted (when the value in the accepted column is $1$). Once the bid is accepted, the revenue is a product of the expected revenue and the expected conversion for each line.
Simply put, here is an example, if we place a bid of $\\\$35$ and it is accepted the profit would be the $(expected\_revenue \cdot expected\_conversion) - \\\$35$. Those entries where the bids are not excepted (value of $0$) have no revenue nor costs, so here's how the profit would be calculated per bid...
$(accepted\_bid \cdot expected\_revenue \cdot expected\_conversion) - bid\_price$.
My problem with figuring out how to tackle these lies in the below constraints/context:
- The likelihood of a bid being 'accepted' (equal to 1) increases as the bid price increases, and the value of the accepted_bid field can be EITHER $0$ or $1$
- This set of data has both leads where bids were placed as well as those that weren't- I'm not exactly sure how to work with these as if no bid is place it automatically isn't accepted (0)
- The quantity of bids purchased must be within $\pm 2\%$ of the quantity of bids in this data set
- The number of leads we expect to see over time are the same amount in the data set e. The bid NEEDS to be either $\\\$3$, $\\\$35$, $\\\$50$ or $\\\$75$
I was thinking about building a model with PuLP, but it doesn't look like it is possible with these given constraints (unless it is).
Can PuLP be used to define rules? What model should I employ?