Solving Scheduling Conflicts Using Machine Logic?

[Nuos 2]

Hey All

i have client that has a deep complex scheduling problem. They have two locations. Each location has multiple zones. Each zone has multiple activities that can be done in them. For a location to run a particular activity in a particular zone it must have a teacher. There are multiple teachers each with their own specializations. Each teacher had their own schedule of availability. 
 

With me so far?

now there are students. Each student must complete x core activities (do not require a teacher) and up to 5 specializations each week (requires teacher) 
 

they are wanting to use FM to manage the computer logic and present schedules for students that meet all the above parameters (and more). 
 

From a design/logic perspective I’ve been wondering if I off load the processing to the server and let it crunch through various permutations until it finds a solution. But my gut says there might be a more elegant response than simply brute forcing the solution. Would machine learning help? Are there other approaches I should consider? 
 

Cheers

Nuos