how can we model the distribution of the population from a facility to other near facilities (for example a school or a hospital) when it is decided to be destroyed
Once you have the addresses of the members of the original facility (which is to be closed) use geocoding in ARCGIS or other mapping software to obtain the locations of people's residences. Then you can do Thiessen polygon or some other such allocation method to see how the people will be apportioned to other open facilities.
I recommend using thePlugins MMQGIS and GEOCODE of QGIS (qgis.org) free software.
https://www.youtube.com/watch?v=XdKV5fyz5U0
You may use spatial analyst and geostatistics.
The buffering method in Qgis spatial statistics are the best way first , i think.
To geolocation with adress you may use a geocoder motor.
In Qgis you may have Google map or Openstreet map.
The adress must respect the fields structure with the best precision.
You have to decide the best tool for the task. It should be either location-allocation model or nearest distance model. The nearest distance can be either Euclidean or road network.
Using ArcGIS, chose the best location-allocation and in this case it should maximal coverage problem, I think.
To calculate Euclidean model, use nearest neighbour tool but you have use the join tool to link the population file. In the network analysis you should have a ready road network data.
Please, let me know if that was helpful.
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