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Evacuation in emergency situations can be modeled by a dynamic flow network.Two criteria have been used before: one is the evacuation completion time andthe other is the aggregate evacuation time of individual evacuees. The aim ofthis 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) isto be introduced. The evacuees are initially located at the vertices, but theirprecise numbers are unknown, and are given by upper and lower bounds. Underthis 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 thenumber of vertices.

Minmax Regret 1-Sink for Aggregate Evacuation Time on Path Networks