DEA (data envelopment analysis) can be used. One good feature is that it does not assume any function - it is non-parametric. I used this to validate the quality of a ranking/funding formula for portuguese universities. Basically you compare the efficiency of how universities transform inputs into outputs taking real best-practice as the reference. You can't have too many criteria because the model looses quality.
You can use:
Inputs (costs):
-Public funding to the university. You must be very careful here and weight this cost by the operating areas of the faculty, whether labs are needed, etc (humanities is a lot cheaper than engineering) - I can get you a table on these differences if you need it.
-Quality of candidates to the university. This is probably new and it should be dificult to measure. But the more selective a university is (attracting more international students for example) maybe the higher this input would be. This idea would have to be widely discussed first however - it is polemic and I have not thought about this enough.
Outputs:
-Number of graduates (quantity)
-Something like average graduation length/average time to graduation (graduation efficency)
-% of teachers holding a phd (quality)
-Research (some impact measure - I don't know much about this because in my problem I disregarded research funding which was separate from university funding). However I do believe that this measure should not be too prescriptive - it is dificult to anticipate or measure research success above a certain minimum level of achievement.
Of course that you can also try to put this in a formula - I did it, and do things like calculate what would the weight for graduation eficiency have to be compared to number of graduates so that a university does not profit from student retention.