Multi-variable scheduling formula?

Are there formulas available to handle the following variables in creating a clinical education schedule?

Total number of students 34
Number of students allowed at each clinical site (one site can have up to 28, one 8, seven 2, one 3 the rest just 1)
Number of different experiences required of each student 9
Time required at each experience in weeks 3, 3, 4, 6, 2, 6, 6, 6, 6
Number of clinical sites offering a particular medical experience (varies among 27 sites)
Total number of weeks available in program 47

Quite a mess, I’ve already spent 34 hrs on this. Thanks for you opinion,

Rich