Draw the boundary at the machine, not the room
A common mistake is to exclude the entire workshop, which leaves the floor, walkways, amenities and office window in nobody's schedule. A better boundary runs at the equipment itself. The contractor handles circulation floor, walkway markings, general surfaces, bins and amenities; the operator handles machines, tooling, swarf trays and anything that must be isolated or locked out before it is touched. That division reads clearly to a new starter and does not depend on anyone recognising a particular machine.
Written that way, the scope covers the parts of the workshop that actually affect safety and presentation, without asking a cleaner to make judgements about plant they have not been trained on. It also gives your own team a clear list, which matters when an auditor or insurer asks who is responsible for housekeeping in the production area. It removes the argument that housekeeping was somebody else's job on the day it was not done.
