Study On Optimal Allocation And Equity Of Emergency Materials In Large Scale Earthquake Disasters Based On Bi-level Programming

Large-scale earthquake disasters happen almost every year,which will often cause serious consequences.In order to reduce the influence,emergency rescue should be carried out quickly after the disasters happen.Emergency materials are prerequisite of effective emergency rescue.Thus,studying on the optimal allocation is of great value.The existing researches mainly use optimization-modeling methods to build mathematical model,and most optimization objectives focus on minimizing the number of rescue points,delivery time and delivery cost.Research that from the perspective of the utility of emergency materials to study the problem is few.Meanwhile,as supply fails to meet the demand at the initial stage of the disasters,according to social welfare theory,there must be a fair allocation.Based on this,the paper specifically studies the optimal allocation and equity of emergency materials from the angle of utility,and main contents includes:(1)Analyze emergency logistics and emergency materials' supply and demand characteristics in large-scale earthquake disasters.The paper focus on the analysis of emergency logistics' operation characteristics,emergency materials' supply and demand characteristics and allocation principles,so as to make the objective functions and constraint conditions of the emergency materials optimization allocation model that will be established in the next chapter more reasonable.(2)Study on the emergency materials optimization allocation model in large-scale earthquake disasters based on multi-objective planning.In this paper,the emergency materials' quantity utility is measured by the demand satisfactory rate of affected areas,and the time utility is measured through the number of emergency materials that accepted by affected areas per unit time.Then the quantity utility function and time utility function are constructed with introducing the logarithmic utility function.On this basis,the emergency materials optimization allocation model in large-scale earthquake disasters based on multi-objective planning is established,with two optimal objectives,one is to maximize the quantity utility value and the other is to maximize the time utility.Finally,the algorithm is designed through NSGA-II.(3)Study on the emergency materials optimization allocation model in large-scale earthquake disasters based on bi-level programming.This paper constructs the equity function expression based on Theil index.And the objectives of equity and optimal allocation of emergency materials are hierarchical,thus a model based on bi-level programming is established.The upper level objective is to minimize the value of Theil index,and the lower level objective is to maximize the value of quantity utility and time utility.Similarly,the algorithm is designed through NSGA-II.(4)The analysis of simulation results.Firstly,solve the multi-objective programming model,and analyze the changes of schemes in different pareto optimal solutions.It can be seen that when decision makers pay more attention to the quantity utility of schemes,the affected area with less demand can obtain more emergency materials;when decision makers pay more attention to the time utility of schemes,the less the distribution time between certain affected area and certain supply,the more emergency materials it can gain.Secondly,solve the bi-level programming model,and similarly analyze the changes of schemes in different pareto optimal solutions.It can be seen that when decision makers pay more attention to equity,the quantity utility of schemes will be reduced.Besides,the demand satisfactory rate of the affected area with more urgent demand will increase gradually.Finally,compare with two models,it can be seen that when the equity is considered the demand satisfactory rates of serious affected areas are larger.