Caveat:IANAIE and this answer might ignore aspects of IE in Europe.
This is an interesting question, but industrial engineering gets bunched up with mechanical engineering more often than not, and IMO that is more appropriate.
The reasons are as follows:
(1) The one part of IE that seems like a better fit to Math is Operations Research / Optimization, but in reality that fit is not a very good one.
OR researchers mostly publish in applied math journals (SIAM ***) which is not (ok, this is controversial) what gets actual mathematicians excited.
I'd say it bears the same relation to mainstream math as statistics: Closely related but a discipline which, having been motivated by applications, has taken a very different path. Also, OR folk typically do not call themselves mathematicians.
(2) Ok, even if you somehow shoehorn the OR guys into Math or CS, the rest of IE just does not fit into CS or math or even any other science department.
Manufacturing, for instance, is a heavily applied field and often considered an area of mechanical engineering. Many Mechanical Engineering departments have their own manufacturing groups. ME and IE are linked like conjoined twins, with people moving from one to the other at all stages (as faculty, as postdocs, as grad students). How would justify moving manufacturing to Math?
(3) Other areas of IE, like production engineering and human factors / ergonomics are even more distant from Math and CS, if that is possible.
(4) Moreover, you'll notice that students need a sound mechanical engineering background to succeed in most areas of IE: A pure math or CS background is not likely to be as helpful. (They're better off knowing machine design, solid mechanics and heat transfer than measure theory or complexity theory, at least in the beginning LOL).
In many IE programs, students are taught courses in Optimization Techniques, Linear and Dynamic Programming and so on. In grad school they might even prefer the more rigorous versions of these courses.
So in conclusion I'd say IE belongs in engineering, as a separate department if possible, but with Mechanical engineering if not.