I am working on location allocation problem for a network consists of 2000 nodes and 2500 lines. I have found the locations of facilities to cover the whole 2000-demand using minimum facilities solver. I have a case when a node (orange color in the figure) either itself or one of the adjacent nodes can be removed from demand. Which one to be removed is my question; I can remove those orange nodes from my demand and solve for minimum facilities but it is not going to give me a global solution for the problem, instead, some adjacent nodes can be removed (only one adjacent node).
Ex: Demand-21 can be removed from the total demand OR demand-20 (adjacent to 21) can be removed OR demand -22 (adjacent to 21). The same is true for the other orange-color demand or their adjacents.
Is there any way (using the model builder or a python script) to do so so that the solver finds the minimum number of facilities for the reduced demand? I am asking because I've tried many cases with known results but did not get the global solution for most of them.
Thanks for any idea