The Study On New Hospital Location Under Minmax Regret Criterion

With the acceleration of China’s urbanization process,more and more people are or have been flooding into urban areas.This trend has caused great pressure on the service facilities in cities and caused many social contradictions,"the difficulty of getting medical service"is one of the typical problems.As a special type of public facilities,the location of medical facilities is related to the fair distribution of medical resources.If the layout and planning of the original medical facilities can no longer meet the social needs,and the existing facilities cannot be modified by relocation or expansion due to geographical and environmental factors,it is an effective way to ease or eliminate the contradictions by adding new medical facilities.In addition,considering the uncertainty of the environment,the weight(number of patients)of each demand point(community)can only obtain the interval estimate value.Robust optimization method can be used to model the problem in the process of facility location,and designing the new hospital location strategy that minmax regret value of the objective function.This paper focuses on the following two aspects:(1)Optimize the maximum load level of medical facilities.By adding a new hospital facility,the maximum load of all the facilities is minimized to achieve the effect of balancing the facility load.When the vertex weights are determined,the network graph can be discretized into finite facility candidate points,and a polynomial algorithm with a time complexity ofO(7)m n~2(8)is designed.When the vertex weights are given as interval values,a particular assignment of a weight to each vertex is called a scenario.By analyzing the structure of the worst scenarios corresponding to the maximum regret value,an algorithm with a time complexity of O(7)2~nm ~2 n~3(8)and an improved algorithmO(7)m ~2 n ~3(8)are proposed to solve the problem.(2)Multi-objective location problem of simultaneously optimize medical(weighted)distance and hospital load.The distance from the demand point to the medical facility is also an important factor to consider in the location process.In this part,the maximum(weighted)distance function is combined with the maximum load function,we consider the new hospital facility location problem of multi-objective under uncertain environment,the purpose is to optimize distance from the demand point to the facility point the and the hospital facilities load at the same time.For the multi-objective location problem of maximum distance and maximum load:according to the nature of the problem,the continuous points on the network are firstly discretized into a finite number of facility candidate points,and then the corresponding location strategy is designed by analyzing the worst-case scenario structure on the fixed location.For the multi-objective location problem of maximum weighted distance and maximum load:the complexity of the problem makes the location limited to network vertex only.In the analysis of the worst-case scenario,the weight structure of the worst-case scenario cannot be obtained by direct analysis because the worst-case scenario of two sub-objective function is in conflict with each other.In this part,the cycle calculation steps of"identification","test"and"adjustment"are designed.By this method,the worst-case scenario of fixed location can finally be determined,and then the optimal location of multi-objective under uncertain environment can be found by traversing all vertexes on the network.In this paper,the problem of facility location under the new objective function is studied,which enriches the relevant theories in the field of facility location,and the methods have certain guidance and reference significance to the actual medical facility location.