Schedule on PHP

Description of the problem:

It is necessary to make the allocation of applications for the lesson on teachers

1) The database from the site gets an application for introductory occupation, name/date and time (it is already there!)

2) Teachers are included in the database and their work schedules are marked (it is already there!)

graphs can be set randomly

http://joxi.ru/bmoNKggUyjDOJr

3) for each teacher for a maximum of 4 pupils (classes in mini groups of 4 pupils)

The task is to distribute applications for teachers, to show the schedule in the admin and to make the opportunity to redistribute applications manually, and those applications that can not get to anyone in a separate list in the admin