## 3 Results and Discussion
### Optimized Site Selection  
According to Sections 3.1 and 3.2, the risk distribution and actual travel distances needed to be calculated. The number of calculations for travel distance was around 95.7 million for 19,140 protected units and 5000 candidate fire station points, which was  
Figure 5: (**a**) The scores of the fire incident density and (**b**) 4-level risk classification in Shanghai.  
Figure 6: The schematic of (**a**) the units and candidate site, (**b**) the program using Baidu Map API to calculate the travel time of the protected units and (**c**) the results of one selected protected units.  
massive. Gurobi 9.1.2 [31] academic version was used to solve the category of a typical integer linear programming problem, which was easy to obtain.  
In this study, the optimal siting for fire stations was determined for six different scenarios by employing the methods mentioned in Section 3.2. The optimization object was set as 50, 100, 150, 200, 250, and 300 stations. Figure 7 illustrates the layout and coverage area of the various objective fire stations calculated by Gurobi. The points represent the optimized locations of fire stations for the specified quantity targets. The purple solid lines indicate the connections between the fire stations and the centers of the protected areas. The coverage area expanded with the increase in the number of constructed stations. All administrative districts could not be covered by only 50 stations, due to which certain areas in Chongming and Pudong were left.  
Figure 8 further shows the response coverage rate and average response time for six different scenarios calculated by the model. Figure 8a illustrates the response coverage rate of four levels of risk units and overall and cross-response coverage rates. The response coverage rate of four risk classifications is the percentage of units that met the travel time requirements in Table 2 for all areas. The average response coverage rate is the average of four response coverage rates. The cross-response rate is the percentage of repeated cross-sections of all units. The model prioritized covering areas with A-classification risk, followed by B, C, and D-level areas when a certain number of stations was given. As the number of stations increased from 50 to 100, the response coverage rate for B- and C-level areas rapidly rose, with slight increases in A- and D-level areas. When the number of stations reached 100, the overall response coverage rate was already close to 90%. With more than 150 stations, the response coverage rate approached 100% and the marginal effect decreased significantly. The cross-response coverage rate continued to increase as the number of stations increased, showing the serious wastage of the existing fire stations. Also, increasing the number of stations from 0 to 150 led to a decrease in the average travel time, as shown in Figure 8b. However, when the number of stations exceeded 150, the rate of decline slowed down and essentially remained unchanged. Therefore, it can be  
Figure 7: The layout and coverage area of the various objective fire stations.  
concluded that the re-planning of fire station sitting in Shanghai should include around 150 stations.