We are trying to create a fixed number of facilities across a region to service a bunch of demand points.
After we ran the problem we summed the total amount of length in the problem.
We then ran the problem again but with the facilities and demand points broken up into smaller regions.
The problem is: when the total length in all of the smaller problems is summed together the result is lower than in the single larger problem.
Our premise that makes us think this is a problem is: the larger problem contains the solutions of the smaller problems, so the algorithm should be at be able to at least match the solution.
Is our premise wrong, or is there some limitation of the algorithm that we are not aware of?