At a given day a number of $N$ salesmen (from the same company) are randomly scattered in a landscape with $M$ cities. At the next day as many cities as possible should have a salesman visiting, no two salesmen going to the same city. To what city $c_j$ should each salesman $s_i$ go to, in order to minimize the total distance travelled for all salesmen.
Note that if $M$ is less than $N$ some salesmen should stay on place and not go anywhere. We also assume that each salesmen can reach each city in the given time.
I would also be thankful for any pointer to algorithms solving the problem!