## 1 Introduction  
The rapid urban development and bustling social activities accompanying economic growth have brought along a plethora of risks, leading to various types of disasters, such as traffic accidents, industrial accidents, and fire incidents [1]. The fire service is one of the foremost important emergency response services relying on fire stations [2]. The location of fire stations directly determines arrival times, which are crucial to the efficiency of emergency responses for fire suppression and personnel rescue operations. Locating fire stations in geographical space is a multi-dimensional problem that typically involves a number of factors regarding improving access and service coverage [3, 4]. For the former purpose, referring to the ease of travel distance/time from fire stations to risk sites, a P-Center model [5, 6, 7] was proposed to maximize access to places requesting services. For the latter purpose, referring to the maximum distance or service area of a fire station with a minimum number of facility points, other models including Location Set Covering Problem (LSCP) [8] and Maximum Covering Location Problem (MCLP) are used widely. For example, the MCLP model [9], focusing on the rational layout of P facility points under the conditions where the number of service facilities and the coverage radius are predetermined, has been used in the planning of fire stations in Istanbul [10, 11, 12], California [13, 14], and Belgium [15]. However, considering the expansion and development of cities, the applicability of these models is basically unitary. In China, most fire stations are sited in urban built-upareas, accounting for only a small portion of the country's land area. For example, Shanghai is the city with the highest urbanization rate in China, reaching 89.3% in 2022 [16]. Although the built-up area of Shanghai has increased to 1242 km\({}^{2}\) in the past 30 years, it still only accounted for less than 20% of the total in 2022. Figure 1 illustrates the distribution of fire stations and the extent of the built-up area in Shanghai in 2022. The thick lines represent the four major ring roads of Shanghai while the black lines are the administrative divisions for streets and towns. The red areas signify the built-up regions. The number of fire stations in Shanghai is up to 152 in general. However, more than 70% of fire stations are located in built-up areas. In suburban areas, the placement of fire stations aligns with administrative divisions, with one fire station constructed for each town or street. Figure 2 further presents the number of incidents at all fire stations in Shanghai in 2022. Figure 2a shows the distribution of jurisdictional areas and annual incidents for all fire stations in 2022. The red points represent the fire stations in the built-up areas while the black points represent those in suburban areas. The fire station with the most annual incidents, such as Qingning, reached 1600 incidents. Other stations that exceeded 1000 incidents are all located in built-up areas. In contrast, suburban fire stations have significantly larger jurisdictional areas, exceeding 50 km\({}^{2}\) compared to those in built-up areas. The largest jurisdiction is Dishuihu station, covering over 350 km\({}^{2}\). Figure 2b specifically presents the counts of fire stations for different incident ranges. The annual incidents for most fire stations in built-up areas consistently exceeded 500 cases. One-third of the incidents counted in the 48 suburban fire stations also surpassed 300 cases. Moreover, the jurisdictions of these fire stations tend to be extensive, exceeding 50 km\({}^{2}\). Additionally, the incident counts for some fire stations within the core urban area were lower than 200, which were notably dispersed due to the densely concentrated placement, resulting in a significant waste of firefighting resources. This may be because fire stations in the core urban area must meet the standard requirement of a 5 min response time.