This answer is in support of user82630's answer that, "I scan my student's assignments. There is a big printer with scanning function in our department where you can just put in the papers and it scans all of them at once." I have also done this for several years.
Previously there was some skepticism as to whether this was physically feasible or not, so I wanted to add some research data. Today I scanned the last cycle of tests in my courses this semester, and timed how long it took. I had 4 sections of math courses with a total of 69 tests; with answer sheets, this was 74 sheets (double-sided), for a total of 148 impressions. The scanning and processing on the bulk copier took 4 minutes and 21 seconds. This was done on a Canon ImageRunner Advance 6265, produced circa 2012, which has been the standard copier in all the offices at my community college for several years.
I highly recommend this method for documenting tests. In addition to clarifying any questions afterward, there have been numerous times when I wanted to extract statistics from old tests that I couldn't have done otherwise.