关键词: 应急物资分配, 公平, 成本效益, 模糊机会约束规划, 分式规划

Abstract: Fairness, as a principle in disaster management and humanitarian relief, aims to ensure equal access to treatment for all individuals. However, achieving absolute fairness is challenging, particularly in resources-constrained scenarios like the early stages of disaster.
In contrast to absolute fairness objective, the relative fairness perspective aims to control the distribution disparities within a reasonable range and do not deliberately pursue complete equality. One common approach is to minimize the distribution disparity, for example, the variance or maximum gap among recipients. Another typical approach is based on Rawls’ theory of justice, which attempts to improve the worst-treated individuals’ outcome through max-min or min-max type optimization. In fact, fairness perception matters more than the distribution outcomes. However, both approaches aim to reduce objective inequality, either in a direct or indirect manner, without considering the beneficiaries’ subjectively acceptable range towards inequity. It could be possible that the distribution outcomes may exceed the beneficiaries’ acceptance range or tolerance zone, thus leading to a lack of fairness and even triggering social conflicts. To address these issues, this paper puts forward an alternative method to describe beneficiaries’ fairness requirements and ensure fair distribution in disaster relief. The proposed beneficiaries-oriented model framework could integrate the relative fairness standards of disaster beneficiaries, and achieve a balance between fairness and efficiency. This research will contribute to deepening the understanding of fairness perception for humanitarian organizations or governments, and broadening the research on the fairness in beneficiary’s preservative.
The requirement for fairness varies from person to person, so it is not easy to define a clear boundary or accurate threshold to describe this vague concept. To tackle with the subjective uncertainty in describing this variable, fuzzy numbers are introduced to represent the beneficiaries’ acceptance range towards inequality distribution. A fuzzy chance constrained model with a cost-effectiveness objective is then formed to limit the probability of fairness violation, and meanwhile achieve maximum relief efficiency. By setting different confidence levels, the model can adjust the probability of constraint violation, reflect the risk preference of decision-makers and make it adapt to different relief scenarios. For ease of computation, the model is further converted into its equivalent deterministic form, so that it could be calculated by Newton iterative method. Finally, a real case study based on Ludian earthquake is presented to test the feasibility and flexibility of the proposed method and analyze the range of the fuzzy parameter and confidence level on the optimization strategy.
Two important insights can be drawn from this article. Firstly, this study provides an integrated model for balancing fairness and efficiency. As is shown in the case study, when the acceptance range for unfairness gets wider, the allocation plan gradually favors the nodes with greater demand, leading to higher efficiency. Conversely, it tends to be more equity driven. In addition, as the confidence level decreases, the allocation results will get closer to equal division. The case also shows that the nodes with higher confidence levels are more likely to be prioritized for delivery, while the nodes without higher confidence may be slightly delayed and subject to greater inequality. Based on the above results, we demonstrate the adaptability and flexibility of the proposed model. By adjusting the relative fairness threshold and confidence level, the model can be applied to different allocation principles, including demand, equality, and priority or efficiency. Secondly, in contrast to Gini Index measuring objective inequality, fairness acceptance range is derived from beneficiaries’ preference and therefore is more suitable for describing their demands for fairness. It is much easier to understand and can be quickly measured through surveys before or after disasters occur, hence making it more flexible and reliable in complex scenarios such as disaster relief.
To assess the impacts of key parameter changes on the allocation results, we haven’t pointed out a specified inequality acceptance range. Nevertheless, the rise of fuzzy measurement methods such as semantic difference analysis has indicated the possibility of successfully measuring this vague and fuzzy variable. As a reflection of subjective preferences, the acceptance range may vary depending on a series of factors such as relief supplies and emergency management stages. In connection with different relief scenarios, future research could focus on developing methods to characterize inequality acceptance range and measure the membership function of fuzzy number, thus making it more in line with the feelings and psychological demands of the affected groups.

Key words: relief distribution, fairness, cost-effectiveness, fuzzy chance-constrained programming, fractional programming