How to design a computer-based multiple-choice quiz? I am currently the course leader of an introductory course for undergraduates.
Each semester, more than 500 students take the course.
One of the course assessment tasks
is a multiple-choice quiz which is held twice a semester.

One of the problems is that the quiz is currently paper-based,
which makes the quiz logistically challenging.
For example,
we have to reserve multiple large lecture rooms,
we have to print question papers,
we have to collect multiple-choice answer sheets and scan them.
In addition, it is not environmentally friendly
to print and destroy such a large number of pieces of papers
(our quiz consumes a few thousand sheets of paper!).

I am thinking of moving to a computer-based multiple-choice quiz,
which will be held in a computer lab in the university.
Unfortunately, the maximum capacity of a computer lab is about 80 people,
and due to the limited number of computer labs available,
we would not be able to give the quiz to all of the students at the same time.
In order to avoid the students who take the quiz earlier
leaking the questions to the students who take the quiz later,
I would have to design a test bank,
so that the computer system would randomly draw questions from the test bank
to assign them to students.

Questions:


Would such a system be "fair",
given that each student is taking a "different" test?
Do I need to design a very large test bank to protect against
students who take the test early sharing the questions
with students who take the test late?


I would especially appreciate it if teachers
who had successfully administered computer-based quizzes
could share their best practices.
What you describe is pretty much exactly what we do with final exams in our large-section math courses at my institution. For a quantitative-heavy subject like ours, the following is feasible: effectively ask everyone the same questions but with different numerical values involved. 

Our elementary algebra course uses the Maple T.A. platform, where question formats can be coded and somewhat different numerical values presented to each student. 

Our remedial arithmetic course uses the Blackboard testing system, which does not support randomizing values for fraction or radical-form answers (but could for decimal-form answers: see questions of type Calculated Formula), so the faculty have manually drafted about a half-dozen separate, parallel tests of equivalent difficulty. 

The Maple product is definitely a better system for this kind of setup, but it may cost money, whereas Blackboard is potentially already on site. In each case, the order of questions, and the order of responses, can be randomized for each student. 

The overall process works tolerably well. Downsides: To my mind, the questions are rather obviously functionally "the same" for every student -- but the students (at least at this level) don't seem to perceive them this way. Also, because the overall scope of the questions is fixed, in some sections it leads to rather degenerate teaching-to-the-test, and students in the next course in the sequence don't really have any understanding or depth with the skills in question. (For example: Some instructors only teach checking multiple-choice solutions to equations, not actually solving them, etc.) In any case, quite a bit of work is involved setting up your tests.