## 7 Conclusions  
To address the facility location problem in a disaster relief situation, a novel model combining the advantages of two major covering location problems was developed in this paper. The coverage concept of two major covering location problems: set covering location problem and maximal covering location problem was utilized to develop the model of the hybrid covering location problem. In the developed HCLP, the location of the facilities was determined by using SCLP, and the limited number of modules providing different services can be assigned to the facilities to provide services in tactical periods. To investigate the capability of the developed hybrid covering location problem, an application for it was introduced as locating aid centers in humanitarian relief services. A case study using real data for demand points in Japan was used, together with some more randomly generated test problems. The results of the studied problems showed that the developed mathematical model can obtain accurate solutions compatible with the real situations and the assumptions of the model.  
Furthermore, the other possible combinations of covering location problems were developed as the variants of the main hybrid covering location problem. To evaluate the four developed models, some test problems were generated and solved for all variants. The computational results approve that the main developed hybrid model of this paper can outperform the other three variants in terms of coverage percentage, solution quality, and feasibility of the solutions.  
One important fact about the developed hybrid covering location problem in this paper is that it can be solved with commercial solver (GAMS) for problems of an acceptable size of real-life situations, which is an important specification for problems arising in disaster situations that need quick responses. However, in most of the problems studied with other researches, the difficulty in solving the problems to obtain the solutions is a barrier to be applicable in disaster situations. The main purpose of this paper was to introduce the basic and original framework of the hybrid covering location problem, while the problem developed in this paper can be used to be coupled with other decisions of the supply chain, such as inventory management and vehicle routing. In addition, it can be studied as a two-stage or multi-stage stochastic programming model that can be a future direction for research.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Problem** & **Number of Constraints** & **Example** \\ \hline HCLP & \(\Delta+||||T|+||L||T||T||\) & \(\Delta+50\times 3+2\times 3\times 2=\Delta+162\) \\ MCLP-MCLP & \(\Delta+|T|+|L||T||T|\) & \(\Delta+3+2\times 3\times 2=\Delta+15\) \\ MCLP-SCLP & \(\Delta+|T|+||L||T||T||\) & \(\Delta+3+50\times 2\times 3\times 2=\Delta+603\) \\ SCLP-SCLP & \(\Delta+||||T|+||L||T||T||\) & \(\Delta+50\times 3+50\times 2\times 3\times 2=\Delta+750\) \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparing total number of constraints in HCLP, MCLP-MCLP, MCLP-SCLP, and SCLP-SCLP.  
**Funding:** This research was conducted by the aid of funding provided by JSPS KAKENHI(A) 18H03826.  
**Conflicts of Interest:** The authors declare no conflict of interest.