The other awy to do it is to use a combination bitmap/tied hash. This way would have a number of distinct drawbacks, but would save you having to use a database (which, IMO, is the better way).
You could build a bitmap for each employee/employer, and then AND them together to see what's left -- what's left, of course, are the available times for interviews.
Then, assuming that you get a match, you could tie() to a hash and create a reference in (for instance) the appropriate employer's timeslot that points to the person being interviewed (or you could just enter their name, but I like the idea of a hashref) and use it to print out reports and so forth.
Now, suddenly, the database method looks a little bit better, no? ;)