Quote:
Originally Posted by Titchou
They look at all of it. It's not an either/or thing. So, it could go either way at any given time. The goal is to place the most women in the highest placement possible. So they try to determine what that is.
|
Okay, my question was mainly around whether they looked at WHERE women placed.
I'm always interested in the pieces done by hand, rather than automated, and why/how they are done by hand. In this case, automation would be an Integer Program (IP) something like:
Maximize "Total PNM happiness"
by changing the variable "quota"
subject to "all chapters make quota"
Basically, you'd come up with some sort of measure of PNM happiness, like 3 points for a woman placed in her first choice, 2 for a woman placed in her second choice, and one for a woman placed in her third choice. Then each time bid matching was run for a different value of quota, a value for Total PNM happiness could be calculated, and there'd be a "best" value of quota.
I'm not sure that "all chapters make quota" would be a hard constraint, though, as we know that won't happen at all on some campuses. Rather, I'd adjust the objective function to call it something like "CPH Strength" and define it as "Total PNM happiness - missed quota penalty," i.e. for each chapter not making quota, we'd subtract some quantity from the total PNM happiness.
Of course, you can't *really* just hand it over to the computer...who decides if a PNM in her first choice is three times happier than in her third choice, or four times? Maybe the points should be 4-2-1 or 6-3-1 instead of 3-2-1.
Even if someone were to write the program and hand it over to the computer during bid matching, the fact remains that the design would require a huge amount of up-front subjective judgment calls. In any case, I think it's fun to think about, and a good example of why real-world modeling is very difficult.
I think I'd make missed quota a huge penalty, because that way, if a chapter was NEVER going to make quota, it would apply to every scenario, and wouldn't make a difference, but if a chapter makes quota under some scenarios and not others, it would automatically avoid the latter. But then again, does it matter if a chapter misses quota by one instead of making quota? Then why penalize by number of chapters missing quota rather than the number of women they are below quota?