7

Formulating as one big problem requires more memory, some way to recognize that the problem decomposes into disjoint subproblems, and some way to then solve the subproblems independently. At least one commercial solver (SAS) looks for such structure after presolve and suggests using the decomposition algorithm in that case. The decomposition algorithm ...


4

Cost matrixes are discussed in the book: "Assignment Problems" by Rainer Burkard, Mauro Dell'Amico, Silvano Martello (on pages 73, and 200, etc.). Yes, some parts would be unconnected (most likely) in such a large problem. Seperation and calculation of the cost matrixes is only the start of the problem. Solving using traditional methods, for so ...


3

You can add a constraint that says the number of vulnerable people assigned to a facility is at least a specified fraction of the total number of vulnerable people (where the fraction is set to 1 if you want to ensure all vulnerable people are assigned, or something less than 1 indicating your tolerance for leaving vulnerable people unassigned). If you use a ...


1

One way to try is to have lower assignment cost (assuming a minimization objective) to vulnerable people compared to non-vulnerable for a given facility.


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