You didn't have any issues with left over tasks after personnel changes
Task scheduling, production scheduling, weekly mgmt meetings around "where are we?" let us keep track of what needed doing.
Managers managed...
Steve, you have a light load today...compact the hazmat waste and label it when you have a chance today. (Today being a key word).
Bob, the calibration crew is in today...you are the runner for bringing them gages, verify the data and stickers before putting stuff back. If you have any down time, get your inventory caught up.
Angela, you aren't casting product today...shipping is overwhelmed...go ship your face off and get the backlog down to 5 orders or less.
Your "job description" is to be able to cast product...and whatever else we need you for and train you for.
Management happened all day, every day...worked so much better that way...if you saw someone killing time, there was always a wide array of what you could sic them on...and you got to know the people and could sic them on jobs they didn't mind too much (usually).
If you don't have good hands-on managers...you fall back on job descriptions...and waste a ton of talent (IMO).
or identifying tasks that had been picked up by someone but were not formally assigned to any job?
Again, managers managed.
The jobs were assigned to the managers...and delegated from there. The managers had access to competency and training records electronically, so sorting out the "who does what today" took very little time.
If there weren't trained people available, looks like you need to free someone up next week to be trained to this...at the manager's discretion.
That would be my main concern without having a job description. If not, could you provide the nitty gritty details of your boilerplate process? You have peaked my curiosity.
Certainly not a "Boilerplate process"...just a boilerplate "keep ISO satisfied" while we go get stuff done.
Give your mid level and line managers access to 'who can do what'...and let them do their jobs...
then you can see whether or not you promoted the right people to manager...