Abstract:

In the past emergency rescue of large-scale emergencies， the organizers mostly paid attention to the transportation cost and time cost in the distribution process and the goal was to reasonably transport as many materials as possible to the disaster-stricken area in the fastest time. In the new economic period， rescue activities no longer only focus on the material level， but also spiritual level. After a disaster， the victims will experience unstable psychological factors and may have risk perception due to the lack of materials， resulting in panic psychology. Such psychological factors are likely to have adverse social effects or even cause serious social problems. Moreover， in the early stage of rescue， the material reserves are limited， and it is difficult to meet the needs of all disaster-affected points for various types of materials through one delivery. Therefore， some important topics that how to consider the psychological factors of the victims in an uncertain environment and how to reasonably carry out multi-period dynamic allocation of limited resources need to be studied urgently. The prospect theory is integrated into the scheduling problem and a risk perception function is established to describe the psychological risk perception of the victims for obtaining relief materials. Considering the difference in the urgency of material demand in different disaster-stricken points， to make the disaster-stricken points with high demand urgency to be dispatched preferentially， a psychological risk perception function of the victims is established that considers the urgency of demand. In terms of timeliness， a linear time satisfaction function is used to establish a time satisfaction function that considers the urgency of demand. Because of the uncertain factors existing in the early stage of emergencies， the estimated values of the parameters are obtained utilizing expert estimation when the data is difficult to obtain. Taking into account subjective uncertainty， uncertain variables are introduced to describe them. Based on this， a multi-objective mixed-integer uncertainty programming model is established， aiming at the minimum psychological risk perception， maximum time satisfaction， and minimum transportation cost. Based on obtaining the expert's estimation information， the least squares principle is used to solve the expected value and variance of each uncertain parameter. Finally， the uncertainty theory is used to transform the uncertain programming into its deterministic equivalent form.An example based on COVID-19 is designed. The demand for daily necessities is positively correlated with the number of people affected by the disaster. According to the spread of infectious diseases， the number of infected people always shows a trend of increasing first and then decreasing gradually. The demand for materials also shows a trend of rising first and then falling； the transportation delay coefficient and damage coefficient are also set according to this trend. The material distribution and scheduling problems under emergency conditions are subject to severe time pressure， and to be able to quickly solve the parameter changes there are higher requirements for model solving efficiency and the requirements for the accuracy of the solution results are relatively loose. Since this model involves multiple cycles， multiple materials， multiple disaster-affected points， and multiple distribution centers， the algorithm for solving the model should follow the principles of fast convergence， low resource occupation， and strong robustness. In this paper， an improved artificial bee colony algorithm is designed to solve the model. Finally， through the analysis of the parameters and distribution plan， the following conclusions are drawn： ①The model can effectively control the transportation cost while considering timeliness， fairness， and the psychology of the victims； ②The psychological risk perception characteristics of the victims in different disaster scenarios are quite different when the disaster situation is more serious， the panic of the disaster victims is more serious， and the risk perception brought by the same proportion of unmet materials will gradually increase with the increase of the loss sensitivity coefficient and loss avoidance coefficient； ③The setting of the proportional fairness coefficient can effectively prevent the disaster-stricken points that are less affected by the disaster and the number of affected people can only be allocated a very small amount of materials， and reasonably control the fairness of the system. ④Decision makers can choose their attitudes toward the cost and psychological loss of victims through different combinations of decision preference coefficients， to form a multi-cycle emergency material distribution plan.The innovation of this paper is that， the prospect theory is used to establish the psychological risk perception function of the victims that considers the urgency of demand and the cognitive biases that the victims may have； In the case of incomplete information and no reference historical data， the estimated values of parameters are obtained by expert estimation， and uncertain variables are used to represent such parameters with subjective uncertainty； Considering the dynamic changes in supply and demand of multi-period materials， the proportional fairness coefficient is used to flexibly adjust the overall fairness of emergency material allocation； Finally， aiming at improving the timeliness of the arrival of materials， reducing the psychological risk perception of the victims and controlling the transportation cost， a multi-objective optimization model of emergency material distribution considering the psychology of the victims is proposed for multi-period， multi-stricken regions， multi-distribution centers， and multi-type materials.

Key words: emergency material allocation, uncertainty theory, risk perception function, artificial bee colony algorithm