Research On Vehicle Routing Problem Of Emergency Materials Considering Alternative Utility

The utility of emergency supplies to meet demand points after a catastrophic disaster has important theoretical significance and practical value.In this paper,we consider that there are two kinds of emergency materials in distribution centers:primary and secondary materials,and the primary and secondary materials have different unit utilities for demand points.The total amount of primary materials cannot meet the total demand of all demand points,and the secondary materials can replace the unmet primary materials and have certain substitution utility.The main work and innovative results are as follows.Optimization of the distribution path of emergency materials considering the substitution utility and the maximum total utility of all materials to generate demand.Considering the situation that the emergency main supplies cannot meet the total demand,and the auxiliary supplies can replace the unmet main supplies and have certain substitution utility,the emergency supplies distribution vehicle route optimization model is build on with the maximum target of the total utility of demand generated by all supplies to the demand point,and the model is analyzed according to the two different situations of sufficient number of vehicles and insufficient number of vehicles.When the distribution vehicles are sufficient,the exact algorithm A₁ is designed to solve the distribution quantity of main and auxiliary materials and the driving path of distribution vehicles at each demand point,and the time complexity of the proof is O（ln²）;and l and n denotes the number of vehicles and the number of demand points,respectively.When the total amount of main material is insufficient and the number of vehicles is not sufficient,the exact algorithm A₂ is designed and the time complexity of the proof is O（ln²）.Finally,the actual distribution of emergency supplies in the earthquake-stricken areas of Lu shan County,Ya’an City,is used as an instance to certify the validity and feasibility of the model and algorithm.Optimization of emergency materials distribution route considering the substitution utility and the maximum utility of main materials to a single demand point.Considering the situation that the main emergency materials cannot meet the total demand and the auxiliary materials can replace the main materials and have the substitution effect,the optimization model of the distribution route of emergency materials is established with the goal that the main materials have the maximum effect on a single demand point.According to the sufficient number of vehicles in the distribution center,the model is analyzed in two different situations and the algorithm is designed to solve it.When the total amount of main materials is scarce and the number of vehicles in the distribution center is sufficient,the accurate algorithm EA*is designed and the time complexity of proof is:When the total amount of main materials is scarce and the number of vehicles in the distribution center is insufficient,the approximate algorithm is designed,and the time complexity of the algorithm is proved to be and the approximate ratio is analyzed.Finally,the actual distribution of emergency supplies in earthquake-stricken areas in Lu shan County,Ya’an City,Sichuan Province is used as an instance to certify the validity and feasibility of the model and algorithm...