## 2 Literature Review
[PERSON] and [PERSON] [33] developed a multi-period maximal hub location model that allows the number of located hubs to be expanded in upcoming time periods when the demands are increasing. As the authors have considered the customers' preferences in choosing the cheapest price for multiple carriers, their developed model is a bi-level model in a Stackelberg game framework, who used dual based and Karush-Kuhn-Tucker based reformulations to achieve single-level problem and solved the single level problem with a Benders decomposition-based method. There are also many applications of MCLP in modeling real-life situations. Locating bicycle sharing stations in this way that users take the bikes, use them, and then return the bikes at the same or any other located stations were addressed by [PERSON] et al. [34]. They considered a lower bound for the workload of each station that could also lead to improved results quality. By the appearance of rechargeable electric vehicles and addressing the need to build charging stations for these kinds of vehicles, [PERSON] et al. [35] formulated and solve the problem of locating vehicles charging stations using MCLP and took into account the spatial information statistic of charging demand as a stochastic process. Similar to the application studied by [PERSON] et al. [26], [PERSON] et al. [36] studied the problem of assigningthe drones used for carrying the delivery packages in commercial services. [PERSON] et al. [36] used MCLP to formulate their problem considering package weight, battery, and coverage constraints and developed a heuristic method to solve the problem with sensitivity analysis of the problem parameters. Furthermore, to locate ambulances in response to urban emergency requests, [PERSON] and [PERSON] [37] used MCLP in combination with an improved biogeographical-based optimization method. To refine the number of candidate locations for ambulance stations, they used geographic information system and the analytical hierarchy process method and compared the results of their developed solving procedure with similar methods. [PERSON] et al. [38] studied the location of ambulance bases by utilizing MCLP and the real-time information obtained from social media like Twitter. They studied the reallocation of ambulances in response to demand fluctuation in a dynamic framework and validated the model by applying it to the emergency medical services in Bangkok. The problem studied in this paper has applications in locating facilities in disaster relief situations that will be specified in the following sections. One of the assumptions of the basic MCLP is the binary coverage, which supposes a demand point to be covered completely if it is located within a critical distance or travel time of the facility, and if the demand point is outside of the critical distance or travel time, it cannot be covered by the facilities. Most of the researchers have found this assumption to be too restrictive, especially for the applications in emergency systems like the current study. [PERSON] et al. [39], [PERSON] et al. [40], and [PERSON] and [PERSON] [41] are among those who studied the MCLP by modeling coverage as a gradual or partial coverage which means the coverage provided to a demand point decreases gradually with the increasing distance or travel time from a facility. [PERSON] et al. [42] extended the gradual coverage to the case that the coverage can be provided from multiple facilities with applications in cell phone tower service providers. They tested several methods to solve the developed model, such as the greedy heuristic method, tabu search, ascent heuristic, and tangent line approximation method. Locating undesirable facilities like nuclear plants in the presence of gradual coverage was addressed by [PERSON] and [PERSON] [43]. As the objective of undesirable facilities is contrary to the common commercial facilities, the model is called a minimal covering location problem that seeks to locate the facilities in places that covers a minimum number of residents.