The timetable is built once, and the clashes surface while you are building it rather than in the first week of term when a teacher is standing in two rooms at the same time.
Periods before lessons
The day is defined first — period numbers, start and end times, and which slots are breaks. Lessons are then placed into that frame, so the grid matches the bell the school actually rings.
Class, subject, teacher, room
Each entry ties a class and subject to a teacher, a day and a period, with a room against it. Because the teacher is on the entry, every teacher can be shown their own day rather than made to read the whole school's grid.
When somebody is on leave
A teacher on leave leaves a hole. The timetable shows where the holes are and who is free to cover them, and the affected teachers see their own updated day rather than a circular in the staff room.