A week isn't that long. When I worked for dealers you could just about count on any repair other than the simplest, being a week or more. I usually tried to at least make a diagnosis in the first couple of days so I could get parts coming. A shop with no backlog, is a shop you don't want working on your equipment, there's probably a reason they don't have a lot of customers.
It wasn't unusual for me to have 5 tractors apart at a time, in various stages of repair. In a perfect world tractors would be diagnosed and repaired in the order received, all the parts would be on the shelf waiting, and no repair would take longer than expected or have problems going back together. It is a constant juggling match in any shop.
I could go on and on about the logistics of a dealer shop and trying to balance assembling new tractors for delivery, keeping the sales department happy, keeping different volume customers with different levels of loyalty happy, getting warranty work done in a timely fashion while also making sure you'll get paid something close to what you would if it were a cash job, and dealing with mechanics with varying rates of skill and desire.
Brian