I was a housekeeper before. I had a really nice supervisor. She was so helpful with our schedules. If we ever needed a day off, or we wanted to change hours, she tried to accommodate the hotel's needs and our needs.
She was also the one who assigned rooms to each housekeeper. She always did this very fairly, everyone got the same number of rooms. This is important because housekeepers receive tip when a customer is leaving the hotel. So for example, if there were 5 rooms that were being left that day, she would try to give each housekeeper one of those rooms. This way, each got some tip that day.
The housekeeping supervisor just has to be very accommodating and fair with everyone, so that the housekeepers are not upset or think that someone is being preferred over another.