## 2 Models and Methods
### RO Approach Using Scenario Concept  
The above RO model is an intractable problem with semi-infinite constraints. Thus, an approach using scenario concept is developed to reformulate the problem into a tractable problem and to identify a robust solution. We assume that the enemy's threat level and threat time are discrete parameters, occurring in sections \(\left[ \begin{matrix}f_{j},&\overline{f_{j}}\end{matrix} \right]\) and \(\left[ \begin{matrix}a_{j},&\overline{a_{j}}\end{matrix} \right]\), respectively. Let \(\mathsf{S}\) be the semi-infinite set of possible realizations of timings of threat and threat levels. A possible scenario \(\mathsf{s}\in\mathsf{S}\) represents a unique set of timings of threat and threat levels. The possible scenario \(\mathsf{s}\) can then be realized with an unknown probability. Let \(\mathsf{X}\) be the set of possible target firing schedules. A possible schedule \(\mathsf{x}\in\mathsf{X}\) represents a unique schedule of \(\mathsf{X}\). In addition, \(function\;f(X,\;S)\) is defined as a function that evaluates a performance of solution \(\mathsf{X}\) regarding scenario \(\mathsf{S}\). The deterministic optimization model can then be expressed as presented in Equation (12) because it searches for the optimal solution regarding a specific single scenario \(\mathsf{s}\). \[\underset{x\in\mathsf{X}}{\text{min}}f(x,\;s) \tag{12}\]  
Equation (12) searches for a firing sequence \(\mathsf{x}\) that minimizes \(function\;f(X,\;S)\) in scenario \(\mathsf{s}\) in which the enemy's threat level and threat time parameters are unique. The RO model is a method that searches for a robust solution that is immune to all scenarios, \(\mathsf{S}\), in which uncertain parameters are realized in a predefined section. In general, there are three measures of robustness: absolute robustness, absolute robust deviation, and relative robustness [19]. Absolute robustness helps minimize the maximum absolute cost in the possible outcome set. Absolute robust deviation helps minimize the maximum regret. Here, regret refers to an absolute difference between the realized result and the optimal solution that corresponds to the realized result. Relative robustness helps minimize the maximum relative deviation of the realized outcome from the corresponding optimal solution. In this firing sequence determination model, absolute robustness is selected as the metric for robustness. This is because uncertain parameters considered in this problem are determined by the opponent's will and enemies strive to ensure that the opponents are at a disadvantage as much as possible in a special situation, such as war. Here, if absolute robustness is selected as the measure of robust, the robust optimal solution searches for the worst scenario from all scenarios sets where uncertain parameters are realized for any solution, and it makes the objective equation optimal (best) among those solutions. Finding the worst scenario in any solution (scheduling) \(x\) can be expressed as follows:  
\[f^{WORST}(x)=\max_{s\in S}\ f(x,s) \tag{13}\]  
When all scenarios are realized, the best solution is searched for from all feasible solutions, which can be expressed as follows:  
\[\min_{x\in X}f^{WORST}(x)=\min_{x\in X}\ \max_{s\in S}f(x,\ s) \tag{14}\]  
We search for the best worst-case solutions for all scenarios.