# Finding number of offices to establish based on proximity to merchants

• Jan 6th 2006, 02:03 PM
Oldenberg
Finding number of offices to establish based on proximity to merchants
The basic problem case is that I have 150,000 customers all over the country. I would like to establish offices throughout the country to service these customers. I would like to establish the fewest number of offices as possible in order to realize the highest ROI on this project.

I have the longitude and latitude for each of my 150,000 customers. I would like to have each office be within a 50 mile radius to each of the customers that it services.

If anyone has any ideas I would appreciate any advise. If I need to provide more information I can do that as well.

Thanks,

Jeff
• Jan 6th 2006, 04:43 PM
Jameson
Hmm.. This is a very complex problem. I would come up with some kind of density function to help visualize the location of your customers and where they are the densest. I think this kind of problem is one of the hardest types of problems.
• Jan 6th 2006, 10:45 PM
CaptainBlack
Quote:

Originally Posted by Oldenberg
The basic problem case is that I have 150,000 customers all over the country. I would like to establish offices throughout the country to service these customers. I would like to establish the fewest number of offices as possible in order to realize the highest ROI on this project.

I have the longitude and latitude for each of my 150,000 customers. I would like to have each office be within a 50 mile radius to each of the customers that it services.

If anyone has any ideas I would appreciate any advise. If I need to provide more information I can do that as well.

Thanks,

Jeff

I would consider using Simulated Annealing for this problem.

RonL
• Jan 7th 2006, 10:47 PM
Oldenberg
I have been doing some more research on my question above and have come to the conclusion that a Voronoi Diagram might be what I'm looking for, however, I'm not sure that I know how to apply it to my situation. Given a list of coordinates, based on long & lat, does anyone know the best way to divide the country into Voronoi Cells?

The one twist I have on this method is the fact that I want to limit the number of points that exist in any particular cell.