Is it possible to use SMCA (Spatial Multi Criteria Analysis) for determining simultaneously where to locate various facilities?
Suppose, for example, I'm planing to build a new city and everything has already been determined, with the exception of the hospital locations. If I needed to build a single hospital, it would be easy to use Spatial Multi Criteria Analysis to determine where it should be placed. Nevertheless, how can the problem of determining the locations of possibly many hospitals be approached?
I googled every possible keyword to find similar problems, but no success so far. My current guess is that I should break the problem in two, first creating a model with SMCA to assign a cost to each choice of hospital location and then creating a single utility function combining the costs of any combination of choice locations. Then I could use gradient descent (or other non-linear optimization procedure) to find the combination of locations which maximizes my utility function.
I hope this makes sense! I'm new to Operations Research and I just got the opportunity to receive "free consulting" for my company, but for that I need to submit a project until Friday and my boss believes this is a problem we could tackle.