Min. weighted average distance from multiple points

Dear list members

I am a complete beginner in mapping-related topics. Still, I´ve been wondering if anyone know this problem. It might be well known, I just don´t know its name.

Initial situation:
nx : x geographical locations
Wx: weight per location
Dx: distance between the location nx and the optimal location O

Where is the geographical position O, where the Σ (Dx*Wx) is at a minimum?

Numerical example:

n1: Rheinfelden; Wx: 20%
n2: Zurich; Wx: 40%
n3: Berne; Wx: 30%
n4: Lucerne; Wx: 10%
Result: somewhere around Aarau in Switzerland

Does anyone know the common name for this spatial problem?

I have found a tool that can do this on a straight line (“as the bird flies”, http://www.geomidpoint.com/)) but I would like to be able to calculate this on a street routing level. Is anyone aware of such a tool?

Thanks a lot for your kind feedback.


Maybe a better place to ask such a general GIS question is http://gis.stackexchange.com

HI Stephan

thanks a lot. I will post my question there…