Multi-coverage Optimal Location Model for Emergency Medical 1 Services ( EMS ) facilities under various disaster scenarios : A case study 2 of urban fluvial floods in the Minhang District of Shanghai , China

Emergency medical services (EMS) response is extremely critical for pre-hospital lifesaving when disaster events occur. 14 However, disasters increase the difficulty of rescue and may significantly increase the total travel time between dispatch and arrival, 15 thereby increasing the pressure on emergency facilities. Hence, facility location decisions play a crucial role in improving the efficiency 16 of rescue and service capacity. In order to avoid the failure of EMS facilities during disasters and meet the multiple requirements of 17 demand points, we propose a multi-coverage optimal location model for EMS facilities based on the results of disaster impact simulation 18 and prediction. To verify this model, we explicitly simulated the impacts of fluvial flooding events using the 1D/2D coupled flood 19 inundation model FloodMap. The simulation results suggested that even low-magnitude fluvial flood events resulted in a decrease in the 20 EMS response area. The integration of the model results with a Geographical Information System (GIS) analysis indicated that the 21 optimization of the EMS locations reduced the delay in emergency responses caused by disasters and significantly increased the number 22 of rescued people and the coverage of demand points. 23


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Urban disasters represent a serious and growing challenge. Against the backdrop of urbanization, demographic 28 growth, and climate change, the causes of disasters are changing and their impacts are increasing. Both natural 29 hazards such as flash flooding and human-caused accidents such as fires threaten and induce panic in people and 30 cause casualties and property loss (Kates et al., 2001;Makowski and Nakayama, 2001). In order to deal with 31 emergencies effectively, a large number of emergency service facilities may be called upon simultaneously. The 32 demands being placed upon emergency services often exceed the resources made available by governments (Liu et 33 al., 2017). Furthermore, disasters always require a longer response time than regular incidents due to high traffic 34 flows. A crash on the rescue route may block one or several lanes, resulting in congestion, significant delays of the 35 emergency vehicles, and potential additional casualties (Dulebenets et al., 2019). Therefore, the maintenance of 36 efficiency and quality of emergency services during disasters is the key to emergency management. A scientific and 37 the Maximum Covering Location Problem (MCLP) model (Church and Revelle, 1974). The focus of the LSCM is to 48 minimize the number of facilities needed to cover all demand points but it has been shown to lead to an unequal 49 allocation of facilities or a large increase in costs. Due to these limitations, the MCLP model was developed to ensure 50 that existing emergency facilities were used to obtain the maximum coverage of the demand points. Drawing upon 51 the LSCM and MCLP model, a number of researchers have optimized the associated algorithms in terms of facility 52 workload limits (Pirkul and Schilling, 1991), cost (Su et al., 2015), and the level of coverage (Gendreau and Laporte, 53 1997) to solve various practical problems or achieve rescue objectives. Other types of models are suitable for location 54 decision problems that do not include time or distance restrictions, such as the P-center model and the P-median 55 model, where P refers to the number of facilities that need to be built. The P-center model mainly considers equitable 56 service; it selects P facilities by minimizing the maximum distance between the demand points and the facilities. The 57 P-median model not only takes into account the efficiency of the emergency facilities but it also minimizes the sum 58 of the weighted distance between the demand points and the P facilities (Chen and You, 2006). 59 60 All of the above models are static in the sense that they do not consider uncertainties in the emergency service process. 61 For example, large-scale emergencies are likely to require high levels of healthcare to the extent that emergency 62 service facilities would need to provide transportation to other facilities that are beyond the immediate area. 63 Furthermore, the limited ambulance resources at any one emergency station would restrict the capacity of the 64 emergency medical service (EMS) when multiple demand points make simultaneous requests. Any further demands 65 placed upon the emergency services would cause them to fail, resulting in potential loss of life. To minimize these 66 fluctuations in an EMS system, approaches have been proposed that involve multi-coverage models (Moeini and 67 Jemai, 2015). In 1981, Daskin and Stern(1981) put forward their hierarchical objective set covering model (HOSC), 68 in which they introduced the concept of 'multiple coverage of zones'; the objective was to minimize the number of 69 necessary facilities such that the demand was still met and to maximize the coverage of the demand points. However, 70 HOSC had one major shortcoming; it potentially led to the congestion of emergency vehicles. To solve these problems, 71 Hogan and ReVelle (1986) proposed an alternative approach to coverage in their maximal backup coverage models 72 BACOP1 & BACOP2. These models cover each demand point at least once but the multiple coverage of different 73 demand points with the same coverage level resulted in a waste of vehicles resources (Ge and Wang et al., 2011). 74 Considering that there is usually a limited financial budget for the provision of emergency services, it is not feasible 75 to cover all demand points multiple times.

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The aforementioned traditional location models ignored the impacts of specific disasters but we suggest that these 78 impacts must be part of any decision regarding the location of emergency services. Apart from causing casualties, a 79 disaster may also damage emergency facilities; furthermore, damage to buildings and roads will lead to traffic 80 congestion and render emergency rescue more difficult than usual. To avoid these problems, research has been 81 conducted on choosing the location of emergency service facilities in response to large-scale emergencies. Jia et al. 82 (2007) defined the main characteristics of ideal locations of emergency service facilities as "timeliness", "fairness", 83 and "resistance to failure". Chen and You (2006) established a multi-objective decision model for the location of 84 emergency rescue facilities by integrating the MCLP model, the P-median model, and the P-center model. In this 85 integrated model (which focused on large-scale disasters), emergency facilities were allocated using different 86 strategies. Jia et al. (2007) investigated models for EMS facility location in response to disasters and compared three 87 heuristic algorithms (genetic algorithm, location-allocation algorithm, and Lagrange relaxation algorithm) applicable 88 to emergency scenarios and location models.

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After taking account the results of previous studies, here we describe a novel approach for the optimization of EMS 91 efficiency under various disaster scenarios. We propose a multi-coverage optimal location model, whose output 92 depends on the impact of a disaster and the levels of demand made on the EMSs. We use a scenario-based method 93 and Geographical Information System (GIS)-based network analysis to quantify the impacts of a disaster on the urban 94 EMS response. The coverage level of the demand points is determined by the population, the EMS calls for help, and 95 other factors that reflect the demand level of the demand points; these factors determine how often the demand point 96 needs to be covered by emergency facilities within a predefined time. The higher the demand coverage level, the 97 more often a demand point needs to be covered by the service area of the emergency facilities in a given time period. 98 The main purpose of our location model is to reduce the probability of delays in the emergency response caused by Limited EMS resources face increasing demands as the risk of wide-scale and complex urban disasters increases. 109 Previous models have not considered the probability of failure of EMS facilities, in particular those housing 110 ambulances, nor have they taken into account possible limited access by EMS to vulnerable demand points. Hence, 111 two problems need to be addressed: (1) the need for quick response times suggests that EMSs should be located close 112 to potential disaster points so that a high-risk area can be served simultaneously by many EMSs; (2) the closer to the 113 potential disaster points, the higher the possibility of EMSs are affected by the disaster and the lower the service 114 capacity, the greater the distance should be (Fig.1). Based on these problems, in this study, we propose and formulate 115 a disaster scenario-based planning and optimal location model that considers multi-coverage of zones. The coverage 116 is dependent on the demand level of the demand points (high demand with high coverage requires more ambulances 117 at the same time). In our work, we specifically consider flooding; the location plan should result in improvements in 118 the efficiency of the response and reduce the risk to EMS of flash-flood disasters.

Assumptions 135 136
To solve the above problems and simplify the model, we use the following assumptions: 137 A1:All potential points have the same probability of accepting EMS calls and their ability to serve all the demand 138 points throughout the study area is not time-limited; 139 A2: During a disaster, each emergency facility has the same service capacity and the same number of ambulances; 140 A3: During a disaster, the closer the EMS is to the source of the disaster, the higher the probability is that the 141 facility will be unable to respond; 142 A4: During a disaster, the closer the EMS is to the source of the disaster, the greater the requirements placed 143 upon it from any demand point. 144 145

Mathematical model 146 147
In accordance with the aforementioned description and assumptions, a multi-coverage optimal location model is 148 developed. In the disaster scenario used for the model, it is assumed that each emergency facility has the same number 149 of ambulances and quality of service and we must maximize the number of people it can serve within the specified 150 time. In order to simplify the model and optimize the algorithm, we use the 0-1 integer programming method. 151 The model index sets are as follows.
To keep construction costs under control, the number of emergency facilities should be limited. Emergency facilities 172 cannot be built in areas at risk of inundation and the coverage rate should be ensured within a specified time. 173 Therefore, the following constraints are added to the multi-objective function: 174 Constraint (2) indicates that F emergency facilities should be selected from the potential facilities for emergency 176 Constraint (5) guarantees that demand points will be covered within at least T minutes; 184 ≤ (∀i ∈ I; ∀j ∈ J) For the disaster risk level of the potential facility j, the closer the facility is to the disaster source, the more serious 226 the impact on the facility is, making its location unsuitable for an emergency facility. We express this indicator of the 227 alternative point as the disaster resistance capacity level ; therefore, the disaster resistance of the potential facilities 228 increases with their distance from the disaster source.  Our 280 assessment includes a network-based spatial analysis method using the road network data to derive areas that can be 281 reached from an EMS station within a certain timeframe. This method is widely used in route planning (e.g., via 282 Google Maps navigation) and considers speed limits, road hierarchy, one-way traffic, and other restrictions in the 283 road networks; this method is used by network analysis function in the ArcGIS10.2 software (New Service Area). 284 Given that the response time is the usual standard by which the efficiency of emergency rescue is assessed, we divided 285 the service area by using the ambulance travel time. In terms of the response time limit for ambulances, 8 min is 286 usually regarded as the standard for a medical emergency (Pons and Markovchick, 2002). However, the EMS calls 287 and rescue data from the Minhang District in Shanghai in 2017 indicated that the average medical emergency 288 response time was about 15 min, although the goal is to reduce this to 12 min by 2020. We have therefore used to simulate the emergency facility service areas for the different scenarios (Fig. 4). 299  Figure 4 shows that during a 100-y flooding occurs, one emergency station (Wujing Station) will lose capacity due 303 to inundation, whereas a 1000-y flooding will affect two stations(Wujing Station and Jiangchuan Station), both of 304 which are located near the middle and lower drainage basin of the Huangpu River and serve a large population. If 305 these two stations are incapacitated, it will greatly affect the efficiency of medical emergency rescue in the 306 surrounding areas. Figure 5 shows the impact on the area serviced by each station for the different flood scenarios. 307 The y-axis is the ratio of the service area before and after the disaster, the lower the ratio, the greater the decrease is 308 in the service area due to fluvial flooding. About half of the stations are affected by the disaster and their service 309 areas have decreased by more than 10%. The starting point for our simulations is the distribution of the existing 310 Minhang District emergency stations. We find that the existing EMS distribution is inadequate for any of the flood 311 scenarios used in our model. We, therefore, seek to optimize the location of the emergency stations in conjunction 312 with the flood scenarios to ensure that the emergency service facilities can handle the disasters.

Model parameter calculation 318 319
We calculated the two major model parameters (coverage level and disaster risk level) as proposed in Sect 2 based 320 on the flooding scenario results described in Sect 3.2 and used actual data for population, EMS calls for help, etc. We 321 first determined the demand points and number of potential emergency stations by dividing the study area into units 322 of representative blocks or grids. We used data on the location of the communities in the Minhang District to 323 determine the smallest block unit suitable for modeling demand (each community represents a demand unit). We 324 used the ArcGIS 10.2 software Geometry Calculation function to calculate the geometric center of each community 325 demand unit as a model demand point. To determine the location of potential EMS stations, we covered the entire 326 study area. We divided the area into grids of a certain length and assumed that every grid center point was a potential 327 emergency station. Considering the actual conditions in the research area, we divided the area into a grid with a cell 328 size of 2 km * 2 km using the ArcGIS 10.2 fishnet analysis tool (create fishnet). In addition, we added the original 329 12 emergency stations in the Minhang District to these potential stations for comparison. There were 514 demand 330 points and 106 potential stations in the study area (Fig. 6). 331 332

Coverage level calculation 333 334
The coverage level of the demand points (Question Q1) depends on the properties of each point. For example, 335 the larger the population, the more EMS stations are required and these should be located nearby. By considering the 336 existing data and the general conditions in the study area, we regarded the population density and the historical EMS 337 calls for help at each demand point as the influencing factors 1 and 2 , respectively of the demand coverage level 338 (using Eq. (9)) and used equal weights for the two factors as for a special case ( = = 0.5 * 10). The resulting 339 is the coverage level, i.e., the number of times that each demand point i should be covered by the emergency stations 340 in the service area within a specified time. The optimization objectives are to prevent delays in the emergency 341 response caused by busy emergency stations during a disaster and we constrained these objectives using . The 342 results of the demand level calculation are shown in Table 1. 343

Disaster risk level 346 347
The results of the disaster scenario analysis indicate that some existing emergency stations are themselves 348 highly vulnerable to fluvial flooding, which would delay or even prevent their EMS response. At this stage, we must 349 assess the disaster risk at all points before optimizing the locations of the emergency stations. We have considered 350 both the disaster risk level of the demand points and potential stations (Question Q2); a high risk level not only means 351 that this location is unsuitable for the location of EMS but it also indicates a high need for EMS.

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We used the disaster risk analysis method proposed in Sect 2.5. For the demand point risk level , the disaster risk 354 level assessment of the potential stations and the demand points are classified by inundation depth. Point i in the 355 inundation area (depth of more than 30 cm) is regarded as completely inundated at the highest flooding risk level; 356 therefore, we use the area with the inundation depth greater than 30 cm as the center and create three 1 km wide 357 buffer zones ( ∈ {1,2,3}). The closer a point is to the inundation center, the higher the risk level of the demand 358 points (Fig. 7). In contrast, the risk level of the potential stations can be regarded as the resistance capacity to a 359 disaster; it increases with the distance to the inundated area. Therefore, we use the center of the inundation area with 360 a depth of greater than 30 cm and divide the disaster resistance level into four 1-km wide buffer zones ( ∈ 361 {0,1,2,3}). Hence = 0 means that the potential station j is completely inundated and cannot be used as an 362 emergency station.

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Here we present the results of the proposed multi-coverage optimal location model for the assignment of the Minhang 369 District emergency stations during fluvial flooding and discuss the performance of the optimization of the EMS 370 services and coverage level. In order to test our model, we run this model based on the worst-case scenario (1000-y 371 flooding in the 2050s). We have assumed that vehicles cannot travel through areas with inundation depths greater 372 than 30 cm. We utilized origin/destination (OD) matrix in the Network Analysis function of ArcGIS to calculate the 373 ambulance driving time from each potential station to each demand point during the disaster scenario. The 374 model also included the parameters for the construction of 12 stations (F = 12) to ensure that their service area 375 could cover at least 95% of the demand points within 8 min (X ≥ 514 * 0.95, ≤ 8). In simple terms, the objective 376 of this model was to determine the locations of emergency stations to rescue the largest number of people in 8 minutes. 377 We used the demand coverage level parameters and disaster risk level parameters obtained from the above-mentioned 378 analysis as inputs for the model and used Lingo10.0 software to solve the model. The computational results are given 379 in Fig. 8. The central urban area of the Minhang District is less affected by flooding than other areas; therefore, the 380 location of the EMS stations did not change significantly. However, in the region near the Huangpu River, the 381 optimized emergency stations are located farther away from the inundation area than the current stations, indicating 382 that the station at the optimized location will be less liable to flooding and more likely to remain operational than the 383 current stations. 384 385 Figure 8 Computational results of the optimal location model 386 387

Service capacity comparison 388 389
In terms of emergency management, a service area is an intuitive measure for determining the service quality of 390 emergency service facilities and usually reflects accessibility, i.e., the larger the service area, the larger the number 391 of people who can be served by this station. In general, service areas and population are directly related to the 392 transport infrastructure conditions around the emergency facilities, including road speed restrictions and road network 393 density. During flooding, the transport infrastructure near the flooded area will be affected, which will change the 394 travel time of the emergency vehicles, thus reducing the area of emergency service and accessibility of rescue. 395 Therefore, in this context, we used the service area and population as parameters to evaluate the optimization 396 performance of the model (Question Q4). Using the ArcGIS 10.2 Service Area Analysis tool, we divided the 397 simulated emergency station service area into three response zones (8-, 12-, and 15-min journeys) under different 398 scenarios; we then used the Spatial Join function to calculate the number of people in the service area. The total 399 service area of the emergency stations for the different response times was calculated and the comparisons of the 400 service capacity for the current stations and optimal stations are shown in Fig. 9 and Fig. 10 using the worst-case 401 flooding scenario (1000-y fluvial flooding of the Huangpu River in the 2050s) and the no-flooding scenario. 402 The percent coverage is expressed as a percentage of the total area and the total population; the results suggest that 407 the optimized locations of the emergency stations obtained by the model provided improvements in the service 408 capacity over that of the original stations in both the no-flooding and extreme flooding scenario based on the 8-min 409 emergency response time. In the no-flooding scenario, the coverage of the service area increased by about 5.5% and 410 for the worst-case flooding scenario, the increase was 8.4%. (Fig.10); the number of people with access to emergency 411 services increased by almost 250,000 (10% increase). These results indicate that the optimization model increased 412 the service capacity for almost all response times and the performance is best for the 8-min response time. 413 414

Coverage level performance 415 416
A combination of limited vehicle resources, vulnerable transport infrastructure, and high requirements of the demand 417 points during a disaster inevitably places emergency services under great pressure. If one demand point is covered 418 by only one emergency station, the limited number of ambulances would soon affect the provision of services for a 419 large number of demand points, thereby causing delays in rescue. Therefore, a region with high demand should be 420 covered by multiple emergency service areas that can operate simultaneously, especially for high-need demand points. 421 The proposed model focuses on multiple coverage levels of demand points and we used the real average coverage 422 value for each demand point in a specific time as an important indicator to validate our model results (Question Q4). 423 We combined the service areas of all emergency stations and used the Spatial Join tool in ArcGIS 10.2 to calculate 424 how many times every demand point would be covered in 8, 12, and 15 minutes during the no-flooding and the worst-425 case flooding scenarios; We then compared the average values (Fig.11). 426 427 Figure 11 Comparisons of the average coverage value 428 429 Figure 11 shows that the average coverage value improved after optimization in both scenarios. Specifically, the 430 average coverage value for the no-flooding scenario is slightly higher (about 10%). The improvement in the average 431 coverage value for the no-flooding scenario was greatest for the 12-minute response time, i.e., an increase of 6.8%. 432 For the worst-case flooding scenario (1000-y fluvial flooding of the Huangpu River in the 2050s), the improvements 433 were more significant: the coverage of the 15-minute response time increased by more than one (18.4%), indicating 434 that, on the average, each demand point can be served by one additional EMS stations within 15 min. These 435 results indicate that using model optimization for locating emergency stations greatly improved the response time of 436 emergency services at the demand points, even in an extreme flood disaster scenario, thereby providing strong 437 disaster resistance. We also compared the percentage of coverage in 8, 12, and 15 minutes during the no-flooding and 438 the worst-case flooding scenarios (Fig.12). The percent coverage is expressed as a percentage of the demand points 439