I would like to calculate the catchment areas of several points in a polygon. It means, I have a city, some POIs in the city and a lot of districts (the centroids). The POIs have different weighting due to the number of persons who use it, and the districts have variable population count. Now, I would like to have the nearest districts to every point separated, which has approximately the same count of people in the sum as the count of people, who use the certain POI.
Is it possible to make calculation like that with QGIS or R, or in worst case with ArcGIS? Or maybe with another tool?