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

TL;DR

This paper introduces an efficient algorithm for optimally placing a single evacuation sink on a path network to minimize maximum regret in aggregate evacuation time, considering uncertain evacuee numbers.

Contribution

It presents a faster $O(n^2 \, \log n)$ algorithm for the minmax regret 1-sink problem on path networks, improving over the previous $O(n^3)$ method.

Findings

The new algorithm reduces computational complexity significantly.

It effectively handles uncertainty in evacuee numbers with bounds.

The approach optimizes evacuation planning under worst-case scenarios.

Abstract

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.