Fair enough, but a paperwork, or it's electronic equivalent, nightmare. Do they require each troop to 'file' separately, or do they go by units. It would be possible to do it automatically from the orders, but I wouldn't count on that being the way they do it.
Probably have to add a clerk to each platoon or maybe just a couple to the company, or equivalent, just to keep up with the accounting. Of course they’ll add the clerk by taking away a slot from the sharp end, be that an infantry type, or a maintenance troop, someone contributing to mission accomplishment rather than “paper pushing”
The orders sounds like the most logical way. They have to figure the time of troop presence in the field whether it is in granularity of days or granularity of months.