Thanks, I will look at using a Genetic Algorithm approach. Since I posted my original post I found some articles on line that describe this as a "separable assignment problem" (or SAP), a subset of a "general assignment problem," and evidently it is proven to be NP hard to solve, which I think means any maximum (best) solution is going to be computational expensive.

Here are some links to some articles in case anyone is looking to solve a similar problem (warning, heavy on math):

http://www.zib.de/Publications/Reports/SC-94-14.pdf

http://www-math.mit.edu/~goemans/ga-soda06.pdf