PHP/MySQL Automatic lesson scheduler for classrooms/teachers

I would like a php/mysql script (it should NOT be developed in a framework, just pure php) to schedule lessons, classes and teachers in an automatic way. Script should find the BEST possible class/lesson schedule according to teacher's availability without gaps and pauses in the daily timetable. - Each teacher will be generally available for lessons in specified days and hours - Each class contains lessons and each lesson is connected to specific teachers - Each lesson of each class should have a specified amount of weekly hours - Each class should have daily limits regarding the total amount of hours of all lessons - Admin should be able to specify that a specific lesson of a class should not have more than X hours per day. - Admin should be able to specify daily limits regarding the hour of lessons. For example all lessons should take place between 10am and 10pm without weekends. - Each class should have continuous daily lesson hours without gaps - Each teacher should have continuous daily lesson hours without gaps - Script should check the availability of each teacher between classes (each teacher could work for many classes so we have to take into account his availability). - A nice visual calendar is needed to see the result of the lessons and weekly timetable of each class (each class will have his own schedule/daily timetable). - A nice visual calendar is needed to see the result of the teacher's timetable (each teacher will have his own schedule/daily timetable) Example: History classroom has 3 lessons: Roman History (4 hours per week), Greek History (5 hours per week) and Arabic History (3 hours per week). John is a Greek History Teacher and Ahmed is an Arabic History teacher. Admin specifies that History classroom should have a maximum amount of 4 hours per day. All lessons should take place between 10am and 10pm without weekends. Paul is available every Tuesday and Friday from 11am to 6pm and John every day from 10am to 5pm but John also has another lesson in another classroom each Tuesday from 11:30am to 2:30pm. Each lesson (Greek History, Arabic History and Roman history) should not have more than 2 hours per day. Script should find the best schedule possible for this classroom so that History students and History teachers will not have gaps in their timetable. There should also be an option to produce schedules including the possibility of teachers' gaps/blank hours between lessons (in case a continuous daily lesson schedule is not possible for them).