A ton of reporting and manual inspection. I imagine it would increase the ROI significantly too. Currently if it's green, it's good. I think there are spots which would be better for us if more budget is allocated there.
What if you started by "zooming out" so that the variables (and constraints) are limited and manageable in a semi-manual way (i.e. you can put together a high-level model with http://scpsolver.org/) and try to understand if there is anything that stands out and then try to decompose that?
(Note: this is not how LP is supposed to work - you do not "optimize" the whole by iteratively optimize subsets, but it could give you a better understanding of the process, and maybe also get some low-hanging fruit to motivate you and your colleagues to go forward).
DSLs are WAY over my head though.