  Evacuation in emergency situations can be modeled by a dynamic flow network.
Two criteria have been used before: one is the evacuation completion time and
the other is the aggregate evacuation time of individual evacuees. The aim of
this paper is to optimize the aggregate evacuation time in the simplest case,
where the network is a path and only one evacuation center (called a sink) is
to be introduced. The evacuees are initially located at the vertices, but their
precise numbers are unknown, and are given by upper and lower bounds. Under
this assumption, we compute the sink location that minimizes the maximum
"regret." We present an $O(n^2\log n)$ time algorithm to solve this problem,
improving upon the previously fastest $O(n^3)$ time algorithm, where $n$ is the
number of vertices.
