Optimize resource allocation based on total revenue

I've historical data about different types of interventions my nurses work on. Think about it this way: if a customer has diabetes and the nurse decides to intervene, then the nurse achieves a return $x on her effort with probability px. Aggregate data (at intervention type level) looks like: interve_type average_success average_return_on_success_cases tot_volume A 0.23$2000                           3000
B             0.07            $10000 500 C 0.65$700                            2500


If I set the total number of intervention (volume) I can do in a given time frame how do I find the optimal order of interventions? Is this as easy as deriving the expected return per intervention type and sorting on that?

Assuming each intervention takes the same time (resources), then simply sorting on highest expected return and working your way down will do the trick.

1. $E[A] = 0.23*2000 = 460$
2. $E[B] = .07 * 10000 = 700$
3. $E[C] = .65*700 = 455$
So, given that you have a large volume of cases, the financial prioritization would be $B>A>C$.
However, using a purely financial approach can lead to perverse behavior. I'm sure there are other considerations, like keeping the most people alive/good prognosis. Intervention $B$ has a very low success rate, so I presume it means most people leave uncured. If you only have, say, 500 units of nursing time, then you're only going to treat people who come in needing $B$ and turn away all others (since they have negative opportunity cost). The end result will be that $0.07 * 500 = 35$ people will be helped and the rest of the people coming into the facility will either be untreated or not helped, giving your facility a very dismal satisfaction and outcomes rating!