Given the coordinates of N people on a regular 2-dimensional plane and N target points-of-interest (POI) on the same plane, determine the set of pairs of people and POIs that minimize the sum of straight-line distances between the locations in each pair. No two people can go to the same POI, and all POIs must be covered.
In other words, if I have 5 trucks that need to go to 5 locations and trucks are interchangeable, where do I send the trucks so that the least amount of fuel is used (assuming fuel use is proportional to distance traveled)?
Brute force would take N factorial. Is there a better way? This would seem to be a pretty common operations research problem, but my google-fu is insufficient.