## 1 Introduction  
The maximal covering location problem (MCLP), introduced by [PERSON] and [PERSON] [1] maximizes the demands covered by the specified number of facilities to be located. MCLP has a wide range of applications in locating public facilities--such as health care facilities, police stations, schools, and fire stations, etc.--but it can also be used in locating private sector facilities such as warehouses, distribution centers, chain supermarkets, etc. Developing a model for each of the applications with the specific real situation, resulted in various extensions developed for the covering models since their introduction. The hierarchical MCLP [2, 3], probabilistic MCLP [4, 5] MCLP in competitive environments [6], large-scale dynamic MCLP [7], continuous MCLP for natural disasters [8], and maximal hub location problem [9] are some examples among the vast literature of the MCLP. The growing attention and interest in covering location problems are due to their applications. However, the developed models are far from real-world problems and there is still much work to do [10]. [PERSON] et al. [11] suggested the areas that could be considered for further research, such as having different facilities and capacitated facilities. In the current paper by considering modular capacitated facilities, we attempt to modify a closer model to real-world problems such as disaster relief service location problems. Disaster relief services have been receiving global attention due to the scarcity of resources, accountability concerns, and the potential opportunities provided by advances in global information technologies [12]. One of the solutions to overcome the scarcity of resources is modularization. Modularization of services in the case of disaster can be interpreted as what the World Vision International is doing, i.e., relief supplies are stored in four locations globally, and can be immediately shipped anywhere in the world [13]. Furthermore, using mobile housing structures--such as temporary and portable offices, shelters, restrooms, warehouses, etc.--even modularization of the facilities is possible. These mobile structures are commonly used now and result in fast construction that is profoundly essential in a disaster situation like the Chinese government action caused by COVID-19 in building the Wuhan city 1000 bed hospital in 10 days utilizing the prefabricated constructions [14]. In modular facilities, the mobile structures can move to the other areas when their mission is finished and it can result in total cost reduction because of the reusability of modules in other situations like the unique solution Japan has decided to offer praying rooms during the 2020 Olympic games [15]. Attempting to optimize the module assignment decision, it increases flexibility [16], reduces the costs and as a result increases sustainability. The rescue missions [17], temporary housing [18], and goods distribution [19] in a disaster situation are more or less investigated in the literature, but addressing the service providing facilities in a modular and dynamic framework remains as a research gap that this gap is fulfilled in the current study. In this paper, another extension of the MCLP is presented that mainly concentrates on the structure of the facilities to be located. Almost all facilities are composed of different units and departments, which provide a special kind of services or products called modules of facilities. In real examples of hospital application, facilities are hospital location and modules are ambulances, operating rooms and staff members over time horizon. In the disaster relief centers, facility is the location of centers and the modules are tents, waters, foods, etc. In the supermarkets, facility is the location of supermarkets and the modules are hot food shelf, beverage shelf, cold product shelf, etc. In a practical setting, e-commerce companies adopt different pricing policies over different time periods under different demand forecasts.