Three City Scheduling
Generalizing with $kn$ people and $k$ cities we can see "move to city $j$" as a task. Furthermore, we have $n$ copies of each task. For all copies of a task $j$, the cost for person $i$ to move to that task is $c_{i, j}$. 

But now the problem is a direct instance of the balanced assignment problem, with complexity $O((kn)^3)$.