  We consider the problem of locating a set of $k$ sinks on a path network with
general edge capacities that minimizes the sum of the evacuation times of all
evacuees. We first present an $O(kn\log^4n)$ time algorithm when the edge
capacities are non-uniform, where $n$ is the number of vertices. We then
present an $O(kn\log^3 n)$ time algorithm when the edge capacities are uniform.
We also present an $O(n\log n)$ time algorithm for the special case where $k=1$
and the edge capacities are non-uniform.
