Here are the sequence diagrams describing the use cases defined in step #1:
  Sequence diagram for ETTO
 

For each teaching chosen in the NPP by the Courses manager, he has to initialize the corresponding constraints for Teachers and Students groups. He may update these constraints. When all the constraints are defined, he may start the solving and then display the result at any time.
 
 

For each Room, the Rooms manager looks for constraints on this Room and then he defines those constraints in the system. He may update those constraints if they evolve.
 
 

A Teacher is able to define availability constraints and to update them. After the Courses manager has launched the solving, a teacher is also able to display the result provided by the system.
 
 

A Students group is only able to display the result provided by the system after the Courses manager launched the resolution.