## 4 Conclusions and Discussions  
This study proposed a method that determined firing scheduling to minimize the total threat from enemies inflicted on friendly forces. Here, the firing sequence was determined by considering parameters such as enemy's threat level, threat time, and time required to destroy the target. However, the enemy's threat level and threat time are enemy-related parameters, for which it is difficult to obtain the quantitative true value. Thus, those parameters should be considered as uncertain parameters. This is because enemies strive to deceive opponents and minimize exposing their actions as much as possible. Accordingly, this study considered enemy threat level and threat time as uncertain parameters and proposed a methodology to find the best worst-case solution. This study assumed the random realization of enemy threat level and threat time parameters as arbitrary war scenarios to identify the most robust solution and developed a method to find this solution using the robust optimization concept.  
It is advantageous to determine firing scheduling in war as quickly as possible. This is because more operation preparation time will be available by reducing the time to determine firing scheduling. In this study, the fire scheduling model was divided into master and subproblems to identify the most robust solution. In the master problem, GA was utilized to overcome the complexity of global search and to shorten the solution search time. The commercial optimization program CPLEX was unable to identify the solution within three hours when the target number (n) was eight or larger in the numerical experiment, whereas the methodology proposed in this study was able to identify the solution even if the target number was large.  
Fire scheduling is a special circumstance that requires decision making in a relationship with enemies as competitors. In such war scenarios, parameters that affect decision making are uncertain and worse cases are likely to occur. For competitors, it would be advantageous to create the worst situations for opponents. Thus, a robust solution for fire scheduling must be found regardless of uncertain circumstances. The model proposed in this study provides the best solution in the worst situation. The RS performance obtained using the proposed methodology was verified through numerical experiments, which indicated that RS always had better results than those of NS in the worst case, regardless of uncertainty level and problem size.  
For future research, a model that determines fire scheduling will be developed to consider realistic limitations such as preparation time for changing targets during artillery firing and uncertainty of the enemy's intangible combat power. Next, studies on air defense weapon scheduling and missile scheduling should also consider uncertainty as a similar field of this study. Thus, a methodology based on the methodology proposed in this study must be developed to solve problems by considering unique operation situations and constraints that should be considered for each field.  
Figure 3: The maximum value of the objective value among 150,000 simulation results for each given uncertain level value (n = 15).  
**Author Contributions:** [PERSON] developed the model and wrote the majority of the manuscript. [PERSON] and [PERSON] performed the experiments and wrote the experimental section of the paper. [PERSON] reviewed and edited the manuscript. [PERSON] developed the overall idea and the basic outline of the paper.  
**Funding:** This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea. (NRF-2017S1A5B8060156).  
**Conflicts of Interest:** The authors declare no conflict of interest.