Sorting table by Student ID's incomplete

[RoboticRice]

Let's say we have 3 student ID's:
111
222
333

When you load the page, that's the order they appear. Then, student 222 scan's in, and it re-orders as:
222
111
333

Cool, b/c it sorts by scan-in vs scan-out! Now, student 222 is done for the day, so they scan out and the table re-orders as:
111
333
222

WAIT! What? This is nonsense! Now everything is out of order!

[RoboticRice]

Alternatively, take the same scenario:
111
222
333

When you load the page, that's the order they appear. Then, student 222 scan's in, and it re-orders as:
222
111
333

Now, student 333 scans in, and it re-orders as:
333
222
111

What? Shouldn't it be ordered numerically within the scan-in and scan-out sections? Like so:
222
333
111

[RoboticRice]

This can be done by removing the contents of the table and redrawing everything, but that might be a resource-intensive operation. Any ideas?