## 2 Related Work
### Previous Related Metaheuristic Studies  
One of the first studies to address the problem of locating new facilities applying a metaheuristic model was [PERSON] et al. in 1994 [PERSON] et al. (1994). In this study, the total weighted distances between new and existing facilities were minimised so that total travel cost per unit time was minimal. In this case, the applied optimisation algorithm was simulated annealing.  
Some previous studies in the literature addressed the FS location problem with heuristic methods following the LSCP model, while others applied the MCLP formulation ([PERSON] et al., 2015).  
In the first case, heuristic methods minimised the number of facilities so that the whole population was served within a standard distance and with standard FS equipment ([PERSON] et al., 2016), or minimised the longest distance from a FS to any incident site given a possible maximum number of FS ([PERSON] et al., 2016). In the first case, the heuristic concentration method was applied, while a genetic algorithm was applied in the second case. [PERSON] and [PERSON] (2018) and [PERSON] et al. (2019) followed the MCLP approach by combining genetic algorithms with GIS, which allowed MCLP to be formulated as a maximal service area problem (MSAP), whereby the decision variable was the size of the area rather than the population ([PERSON] and [PERSON], 2019). Several simplifications were proposed in these heuristic approaches to ensure the responses to all incidents--each demand was assigned to one and only one crew ([PERSON] et al., 2016), and one fire engine was always available when a call was received ([PERSON] et al., 2016) following the MCLP approach ([PERSON] et al., 2016). [PERSON] et al. addressed the multiperiod location planning problem of emergency medical service stations by applying another metaheuristic method--tabu search. The objective was to maximise the total population serviced by two different stations within two different response time limits over a multiperiod planning horizon ([PERSON] et al., 2016).  
A mixed LCP-MCLP model was presented by [PERSON] et al. to address the ordered capacitated multiobjective location-allocation problem for fire stations ([PERSON] et al., 2016). In this model, the distance between the demand and the station and the arrival time from the station were minimised, while the station's coverage was maximised. The authors applied and compared genetic algorithm and simulated annealing models. The results showed that for small problems, the genetic algorithm was more efficient than simulated annealing, although the reverse was true for large problems.  
Other studies by [PERSON] et al. and [PERSON] et al. were related to the study described in this paper. [PERSON] et al. developed a general facility location approach in which the objective was to minimise the total distance travelled by the products or resources by applying a model based on simulated annealing ([PERSON] et al., 2016).  
[PERSON] et al. presented a study applying both linear programming and simulated annealing to determine the optimal allocation of resources to incidents in real time in a roadside assistance problem that minimised operating costs while maintaining the level of service above a certain threshold. These authors introduced a constraint similar to the one presented in this paper [33].  
Finally, [PERSON] et al. addressed the problem of forecasting relocation in a carsharing framework with the objective of balancing the distribution of cars at the end of the day, which was similar to the objective of balancing the workload of FS [34].  
These previous studies showed that optimal location of FS works have not been formulated yet to minimise the annual workload of the FS to avoid the collapse of the emergency fire system.