关键词: 应急物资分配, 用户均衡, Frank-Wolfe算法

Abstract: For the past years, large-scale natural disasters and emergencies have occurred frequently. When a large-scale disaster (e.g., earthquake or tsunami) occurs, it usually results in a large number of casualties and destroys infrastructure such as power, transportation and communications. For example, the 2008 Sichuan earthquake devastated 273 areas, killing 235,000 people and affecting 214 million people. After the occurrence of large-scale disaster events, the demand for emergency relief materials in the affected areas has surged, especially for food, medicine, rescue equipment, and other materials, leading to an oversupply of resources in a short period of time. In view of such phenomena, this paper studies the question of how rescue organizations can optimize the allocation of emergency materials under the condition of limited resources and time, so as to improve the efficiency of emergency rescue, meet the needs of disaster victims to the greatest extent, and maintain stability in disaster areas.In this paper, we change the perspective of the emergency supplies distribution problem, and transforms the “top-down” emergency material distribution problem into “bottom-up” disaster victims’ demand for emergency materials from the perspective of the difference in the needs of disaster victims, and in the case of given emergency material distribution center, the disaster victims consider their road travel costs and expectations to meet the demand costs, and construct an emergency material distribution model based on user balance, reflecting China’s “people-oriented” rescue purpose, thereby alleviating the psychological panic of disaster victims. The model has certain theoretical and practical significance for humanitarian-based emergency relief.
The sudden disaster usually generates a large amount of material demand instantaneously, and how to allocate the limited emergency materials scientifically and reasonably is the key to meeting the survival needs and recovery and development of disaster victims in disaster areas. In order to solve this problem, this paper constructs an emergency material distribution model based on user equilibrium from the perspective of the differences in the needs of disaster victims. The model optimizes the “bottom-up” distribution network of emergency supplies, in which the victims make decisions that maximize their own interests, and finally all the victims form an equilibrium state. According to the characteristics of the model, based on the Frank-Wolfe algorithm, each disaster victim is the most satisfied with the emergency material distribution strategy in the equilibrium state.In the end, taking the 2013 Sichuan Ya’an Lushan earthquake as the research background, the geographical network of the severely affected Lushan County and its surrounding disaster areas is selected as the transportation network for the arithmetic analysis, the townships with serious disasters and large populations are selected as the disaster areas(PC)for the study analysis, Ya’an City, Hanchuan County and Tianquan County are selected as the emergency material distribution centers(DC)of the study case, and the validity of the model and algorithm is verified by numerical arithmetic examples.
The results of the study show that when the cost per unit of unmet need is small, if the emphasis on meeting the needs of the victims is reduced, the decision making of the victims will be more volatile, which is contrary to the principle of “people-oriented” relief in China. As the cost per unit of unmet need gradually increases, the study finds that the number of unassisted victims gradually decreases and the unmet need of the victims gradually decreases.In a nutshell, if the level of attention to the unmet needs of victims for supplies is increased during the relief process, the effectiveness of the distribution of emergency supplies can be improved, thus the number of unassisted victims can be reduced and the role of relief centers can be fully utilized.
This paper studies the problems related to the distribution of emergency supplies from the perspective of disaster victims, but there are still many tasks that need further improvement, including: (1)The assumptions in the model need further deepening research. For example, this paper assumes that the disaster victims have equal demand for emergency supplies, and the subsequent research can be considered for situations such as unequal demand, uncertain demand, and diversity of demand types, so that the model is closer to the real relief situation. (2)The research on the distribution of emergency supplies mainly focuses on the solution of the distribution results, but does not consider the vehicle path problem in the distribution process. Further research can combine the user equilibrium theory and the vehicle path problem, so as to enrich the model at the level of emergency relief operation.

Key words: emergency material allocation, user equilibrium, Frank-Wolfe