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Say I have a number of customers in a geographical area, marked "c":

enter image description here

Each customer has a Lat/Long. I would like to find x number of points, in the same space, that best serve the customers, ie. they are closest to the customers.

Its easy to do when x = 1, because that is the geographical center of gravity, and there are a few ways to find that out. However I am struggling to think of how I would approach this problem if x > 1

Say x = 2, then I would like to know, where would I place the two points so the distances to customers are minimised, how would I even approach this problem?

I would eventually try and solve this using a programming language, so I am not after a purely mathematical formula, even though that would help.

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  • Sorry, probably totally offtopic and maybe even a little out of line, but red Cs on a green background are really hard to read, even if you're not colorblind (no, I'm not colorblind). Is there a reason why you chose those colors?
    – Nzall
    Commented Nov 7, 2015 at 23:49
  • @NateKerkhofs Sorry the green seemed like a good color for land, and the red, well that was for no particular reason.
    – sprocket12
    Commented Nov 8, 2015 at 7:12

2 Answers 2

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You should have a look at the K-means clustering algorithm, which produces what you are looking for.

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Approximate solution. Cover area by regularly spaced points. Go through every combination of thrm by 2 ( itertools can be handy) computing total of distances to nearest of 2. Pick pair with min total.

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  • Go through every combination by 2? Sorry I do not understand.
    – sprocket12
    Commented Nov 8, 2015 at 7:13

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