Who should be in charge of making the school timetable?
Someone with a teaching background
Passing off timetable creation to a non-teaching staff member can be a mistake. Some people - incorrectly in my view - think of timetabling as an administrative task, however the best timetables will be made where the timetabler has a strong understanding of the curriculum and pedagogy.
Whilst there are some elements of timetabling that can be performed by non-teaching staff - data entry etc. - the implications of even the smallest decision made by a timetabler can have a significant impact. Which teacher should be assigned to which class? How much of a given class should be scheduled etc. - If the timetabler is not even aware of these implications, then learning outcomes and even teacher morale can suffer as a result.
Someone who was involved with the creation of the curriculum
Given that the timetable is a large component of the delivery of the school curriculum, then ideally, someone who was involved in its creation should be the one to ensure that the goals of the curriculum are put front and centre.
Someone with authority
Anyone who has made a timetable from start to finish will know, timetablers will sometimes need to make tough decisions that might not make everybody happy. If they do not have the authority to make such decisions, then it will put them in a tough situation - not only making the job harder to complete but also impeding the delivery of the curricular priorities of the school. In my opinion, the ideal timetabler would be on the senior management team, or otherwise, be at the same level or higher in the pecking order than heads of departments.
Someone who is a good communicator
Some timetablers might have a reputation for locking themselves away in a cupboard for extended periods of time without speaking to anyone - and whilst they might get away with it sometimes, the best timetables are made where the timetabler is in constant contact with stakeholders.
Ensuring that the timetable doesn’t go sideways at the last minute requires keeping open lines of communication with heads of departments. They will usually have their ear closer to the ground regarding any rumours of staffing changes that could threaten to spanner the timetable.
If a timetabler does lock themselves away for two months without speaking to their colleagues, they will emerge from their lair, having discovered the situation on the ground has changed.
Besides that - some level of diplomacy is required when a timetabler inevitably has to make a tough decision that someone will be unhappy with.
Someone with experience making timetables
If you're lucky enough to have someone on your team who has experience making timetables then congratulations! They are likely best placed to build your timetable for the next year. If that's not the case, you may wish to think about promoting this experience within your team.
While there is no replacement for experience, bringing in external help and training can help support first-time timetablers to get through that challenging first year. Likewise - if you do have a timetabling veteran at hand, try to encourage other members of staff to shadow them so that they too can get the relevant experience. At the very least, they might gain some familiarity with the timetabling software.
Someone who enjoys puzzles/problem solving
There is often a large intersection between timetablers and those who enjoy solving mathematical problems - think more crossword than candy crush. Whilst a large part of the timetabling process involves good communication skills - certainly the scheduling portion of the process requires a logical mind.