## 6 Discussion  
The proposed model was built to address two issues facing decision-makers in emergency planning: maintaining overlaps below the threshold values recommended by fire department technicians and minimising and balancing feasible workloads between fire stations by adding new FS. The model incorporates GIS algorithms that reduce the visualisation time of the results and make the model more practical compared to other studies, such as the one proposed by [PERSON] et al. [29], where heuristics were run outside a GIS and the outputs were sent back to the GIS for visualisation and area calculation. The CI map based on past incidents is a useful tool that enables decision-makers to easily identify the areas with the highest CI and the greatest likelihood of causing problems in the future. These risky areas are in the belt around Madrid (see Figure 3), which contains most of the population and economic activity in the region. Here, the decrease in the CI in the optimisation process was more evident. This approach is in line with the current trend in emergency plans, which focus on resilience prior to a disaster rather than on the response once it has occurred [45; 46]. [PERSON] et al. also introduced a system reliability index, although in this case the threshold can be violated, leading to an additional cost in the objective function, which is minimised. They avoided fixing a specific value for each territory depending on its characteristics. Assigning a threshold to the CI was quite challenging, since this value depends on the number of FS and vehicles, number of incidents per year, and the population of the regions, so it was established by analysing the frequency of the CI calculated for each incident and by consulting experts from the firefighting service [33]. The results of the optimisation process showed that the optimal locations of one to five FS increased the efficiency of the system. The maximum collapse index in one pixel of the territory decreased 28% when one FS was added, and by 35%, 42%, 56%, and 76% when 2, 34, and 5 FS were added, respectively. The average overlap in terms of the CI was also lower by 13% when one FS is added, and by 21.4%, 32.4%, 41%, and 50.1% when 2, 3 4, and 5 FS were added, respectively. Adding new FS means that the risk of collapse is reduced due to the increased availability of resources to deal with other incidents, thereby enhancing the efficiency of the system. Previous studies have also addressed the problem of overlapping, although their approaches focused on only one disaster, in general a natural hazard, involving a number of agencies instead of considering incidents in parallel, or they offered a solution to the overlap problem at a specific time and not as a global strategy to increase the resilience of the system [3; 29; 47; 48; 49]. In terms of balancing the fire stations' feasible workloads, the cost function value for the optimum method decreased by 32% compared to the initial conditions when one FS was added, and by 53.4%, 63.2%, 66%, and 68% when 2, 3, 4, and 5 FS were located, respectively. It is worth noting that the value of the cost function for the best solution stabilised with the addition of three FS, so it would not be necessary to build more than two new FS, since the new maximum value of the collapse index, 6800 min, and then average of 2074 min, were significantly below the established threshold. This would also avoid the possibility that too many additions to the existing services may produce overall system inefficiencies [21; 25]. One of the main contributions of this study is that the optimisation model considers the interactions between the resources of the new and old FS in the location process. This implies that by simply adding one FS, the workload of the set of FS decreases by 32%.