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For example, in this sentence:
Remind employees to write their name/names on the schedule/schedules on the lid/lids of the photocopiers.
How do you think it should be written?
Personally, I think the following is best:
Remind employees to write their names on the schedules on the lids of the photocopiers.
I would write
1. each employee has access to ALL copiers and needs to put his/her name on the single schedule which is on the lid of each copier
Remind each employee to write their name on the schedule on the lids of the photocopiers.
2. each employee has access ONE copier and needs to put his/her name on the single schedule which is on the lid of that copier
Remind each employee to write their name on the schedule on the lid of the photocopier.
or
Remind each employee to write their name on the schedule on the lid of the photocopier they use.
Who is your audience and what is the context?
It would depend on where this notice or message is placed or received. If you can put one such notice/manual/flyer on each copy room or copier, the singular might suffice.
Remind each employee to write their name on the schedule on the lid of the photocopier.
It would also depend on who the audience is. If it's an email/mass notice, and you're addressing multiple shift managers or other such responsible persons, then I would word it such that plurals could be formed as needed. E.g.:
Remind each employee to write his or her own name on the particular schedule on the lids of each of the appropriate photocopiers.
Again, lacking context it's difficult to determine exactly what this sentence is attempting to instruct.
I would put everything in singular: every employee has only one name, every photocopier one lid.
