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.

本文介绍了在基于短通知的紧急疏散情况下按比例安排公平旅行计划的概念。比例公平试图在不牺牲撤离过程的效率的情况下满足撤离人员之间的社会公平。将比例公平旅行计划概念与试图最大化撤离者安全功能总和的常用最大安全概念进行比较。我们使用组合方法对将人们从危险区域转移到安全庇护所的过境大规模紧急疏散进行建模。研究了高密度人口和中密度人口的变化问题。对于问题的每个变体，我们研究问题的计算复杂性。我们针对每个问题开发多项式或伪多项式算法。我们的数值分析表明，单纯考虑效率可能会导致高度不公平的计划，该计划仅考虑收益最大的部分（例如，危险级别最高的部分），而忽略其余部分（可能占绝大多数） ）。在仍在考虑效率的同时，通过按比例分配公平性也可以解决这一问题，方法是也将资源分配给收益不理想的人群。