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A fire sequencing problem is considered. Fire sequencing problem is a kind of scheduling problem that seeks to minimize the overall time span under a result of weapon-target allocation problem. The assigned weapons should impact a target simultaneously and a weapon cannot transfer the firing against another target before all planned rounds are consumed. The computational complexity of the fire sequencing problem is strongly NP-complete even if the number of weapons is two, so it is difficult to get the optimal solution in a reasonable time by the mathematical programming approach. Therefore, a genetic algorithm is adopted as a solution method, in which the representation of the solution, crossover and mutation strategies are applied on a specific condition. Computational results using randomly generated data are presented. We compared the solutions given by CPLEX and the genetic algorithm. Above 7(weapon)15(target) size problems, CPLEX could not solve the problem even if we take enough time to solve the problem since the required memory size increases dramatically as the number of nodes expands. On the other hand, genetic algorithm approach solves all experimental problems very quickly and gives good solution quality.