Mathematical modeling - location of police stations

Problem description

The police station is the grass-roots organization of the public security system , Its main task is ： Manage account ; Publicize the legal system to the masses , Organize and mobilize the masses to fight against illegal and criminal acts ; prevent 、 Control the occurrence of various accidents , Managing public order , Maintain public order ; Find and master the suspect , Educate and reform people who have committed illegal and criminal acts ; The prevention of 、 Stop illegal and criminal activities ; Manage special industries , Maintain public order , Prevent public security disasters and accidents .

A municipal public security bureau now plans to set up a police station in a district of the city （ See the annex for the sketch map of the jurisdiction 1）. Due to the influence of geographical factors and traffic status , The traffic flow of each road section in the area is different at different time points . Through investigation and statistics, it is found that , If the time of day is divided into peak periods （7:00 ~ 9:00,17:00 ~ 20:00）, Peak period and midnight （22:00 ~ 6:00） Three different time periods , Then the maximum safe traffic speed of each road section in the area is different in these three time periods , The statistical data are shown in the annex 2.

problem 1： Please build a mathematical model , Determine the best location of the police station , So that the police station can be as timely as possible , Effectively respond to various emergencies within the jurisdiction .

problem 2： The attachment 3 It is the number of illegal crimes near each node in the jurisdiction in the past ten years , And the average amount of property lost after each crime . In order to avoid crime as much as possible , Reduce property losses caused by crimes , Please build a mathematical model , Choose the best place as the location of the police station .

problem 3： In question （2） On the basis of , The city decided to set up a new police station in this area , And by the new police station and the original police station （ The location of the original police station remains unchanged ） Jointly maintain the public security management of the jurisdiction , Mathematical model establishment , Determine the location of the new police station , And plan the management area of the two police stations .

Model solving