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

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.

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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

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I would consider using Simulated Annealing for this problem.

RonL

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.

Looking forward to your input.

Thanks,

Jeff