Centroid

The centroid of a country (or area) can de defined in multiple ways. On the earth surface it is more useful to speak of the geographical center. It is possible to find lists of these centers for area's on earth.

One quickly realises that these centers are not (always) good enough. Either they are in a location far away from population centers, or they fall in between a set of islands, etc. So we need to come up with a better estimate.

Any better estimate must reflect what we intend to achieve in the first place. We are talking about transportation and its impact. So we talk about distances, mode of transportation, the amount transported and the impact of it all. Any centroid should take this into account.

If we know only the country a product is bought in, we can either assumes the worst or the best. The worst is the maximum impact and the best the minimum impact. The minimum impact will imply transportation from the most centered location in a country.

What is now the most centered location? The distances to all other locations should be small as possible. And the usage of these distances should be as small as possible. This will take into account the population sizes of all the locations.

This seems to be a Weber problem. This problem is not solvable exactly, but must be solved iteratively. The locations are then the towns and cities in a country. And the weights are defined by the population sizes of each towns. And the distances are defined by the distances by road.

In practice it will be quite difficult to solve this for all towns in an area. But can we do it for the largest towns? And how many towns should we incorporate?