I am working on a facility location problem where I want to allocate a mix of vulnerable and non-vulnerable people to the facilities. I want to make sure that most or all vulnerable people will be prioritized to be allocated to the facilities and then non-vulnerable people will be allocated. Is there a way to formulate this type of problem in facility location problem?
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 fraction less than 1, then you might also want to penalize unassigned people in the objective, with higher penalties for unassigned vulnerable people.