Research On Regional Maximal Covering Facility Location Problem Based On Continuous Demand

Regional facility location problem is to study and determine the optimal locations of one or more service facilities within a candidate area and to serve the customers in a satisfactory way.As the important part before the construction of the facilities,the location decisions of the facilities have obvious aftereffects of decision-making.The results of locations will directly affect the service performance of the facilities.Therefore,this thesis studies the errors caused by discretization in the continuous covering facility location problem and proposes a discretization method based on hierarchical grid method.An improved model based on the maximal coverage model and an optimization method based on facility movement are also proposed to maximize the elimination of error.The specific contents of this thesis are as follows:Firstly,the discretization method for continuous covering location problem is studied.According to the analysis of the demand areas discretized as points,lines and areas,the conditions for the facilities to cover different types of discrete demands are given.The discretization methods commonly used in the continuous covering facility location problem are analyzed,and the factors affecting the discretization are also discussed.Aiming at the problems of the existing discretization methods,an area-based hierarchical grid discretization method is proposed.Secondly,the problems existing in the maximal covering facility location model are analyzed.Based on the classical maximal coverage model,an improved model considering partial coverage is proposed to reduce the error caused by the discretization of continuous problems.At the same time,according to the research problem,the genetic algorithm is selected to solve the problem.The genetic algorithm based on hierarchical grid method is also constructed which can improve the solution speed while ensuring the quality of the solution.Then,according to the solutions of the genetic algorithm,an optimization method based on facility movement is proposed to further optimize the solution errors and overlapping service areas.This method achieve the movement by identifying the uncovered coverage areas and calculating the direction of movement in accordance with the step size to further improve the effect of coverage.Finally,the locations of Tianjin bank branches of Tianjin Heping District are taken as an example for analysis.The effectiveness of the methods are verified by the case application.According to the distribution of the existing banks,the optimization solutions are given.