There are a lot of other things that need this treatment. There is also limited ability to make doses. If you don't already have the infrastructure in place, then you will get notified when you shipment is arriving, and you get a few days to administer it. You schedule everyone who will get a dose for their shot and they are in and out quickly. If it takes more than half a day to use up their entire shipment it is because some dosages are reserved for 3rd shift and will be administered 12 hours later. Then repeat 3 weeks latter.
Of course larger institutions already have everything in place and will get shipments with less warning (but they will also get smaller shipments since they don't have to get everyone done at once)