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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).




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