Yes, criteria for evaluation and selection of suppliers (clause 8.4.1) is a mandatory document. If you consider graduated students as your school products, we can see your system as
We can ask what products or services the school use as inputs to perform its services. Once I helped a school at implementing its quality management system and I remember that they considered as suppliers:
* Transportation services;
* Canteen services;
* Cleaning services;
* Accommodation services;
* Maintenance services;
Perhaps you can find these examples as an inspiration to your case.