Fair transit trip planning in emergency evacuations: A combinatorial approach

Abstract

This paper introduces the concept of proportional fair trip planning in the context of short-notice transit-based emergency evacuation. Proportional fairness attempts to meet social fairness among evacuees without sacrificing the efficiency of the evacuation process. The proportional fair trip planning concept is compared to the commonly used maximum safety concept that attempts to maximize the summation of safety functions of evacuees. We use a combinatorial approach to model the transit mass emergency evacuation in moving people from dangerous areas to safe shelters. High-density population and medium-density population variations of the problem are studied. For each variation of the problem, we study the computational complexity of the problem. We develop polynomial or pseudo-polynomial algorithms for each problem. Our numerical analysis shows that pure consideration of efficiency may result in highly unfair plans that only consider the portion of the population with the most payoffs (e.g., the population with the highest danger level) while ignoring the rest (potentially the vast majority of the population). While still considering efficiency, proportional fairness is shown to address this issue by also allocating resources to the population that has non-optimal payoffs.