Dimitar, your answer is helpful, but incomplete.

As you suggest, I am using a distance measure (real numbers) to make the match. It is very unlikely that any 2 distances will be the same, but it's something I should check.

Your code gives each B to the A that wants it the most, ensuring that no B is used more than once. However, it does not ensure that each A gets a B. I could repeat the process to match up the unmatched A's with the unmatched B's, but that's not very satisfactory because I have no way of predicting how many repeats would be needed (it's data dependent).

Any more ideas?