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  1. I want to use OSM to extract a set of facilities e.g. school, park, hospital inside a given region.

  2. from that, transform the area in grid and for each cell in a grid compute its score mixing the distances of the closest point for each type of facilities (distance from the closest school+ distance from the closest park + distance from the closest hospital)

score area 1= distance from the closest school (= 1.2 miles) + distance from the closest hospital = (2.2 miles)+ distance from the closest park= (0.2 miles) (each distance for each type of facility will be normalized actually)

and 3. represents it on a map (via a HeatMap)

I am sure this is a common practice to determinate for instance the best location to build a facility according to other existing facilities?

Can someone indicate the common process, lib and algorithms for doing such thing?

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I'm assuming that you are interested in distances through the road network?

(If you are happy with straight-line distances then I think that it is just a case of learning a GIS package. Grids, within queries, distances, thematic mapping - all standard. I believe that MapInfo is the easiest to pick up)

Using Arc's Network Analyst you can certainly do this. For example, see:

http://help.arcgis.com/en/arcgisdesktop/10.0/pdf/network-analyst-tutorial.pdf

If you learn towards an open source solution, there are several options. I took my initial inspiration from this accessible blog:

http://underdark.wordpress.com/tag/pgrouting/

With both of these, allow time for a steep learning curve.

PS for the UK some accessibility indices have already been calculated by the government. http://www.dft.gov.uk/statistics/releases/accessibility-statistics-2011/

Also locations of schools, hosptials, GPs etc can be found on the "Neighbourhood Statistics" website.

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