Air defense is a crucial area for all naval combat systems. In this study, we consider a warship equipped with an air-defense weapon that targets incoming threats using surface-to-air missiles. We define the weapon scheduling problem as the optimal scheduling of a set of surface-to-air missiles of a warship to a set of attacking air threats. The optimal scheduling of the weapon results in an increase in the probability of successful targeting of all incoming threats. We develop a heuristic method to obtain a very fast and acceptable solution for the problem. In addition, a branch and bound algorithm is developed to find the optimal solution. In order to increase the efficiency of this algorithm, a lower bound, an upper bound and a set of dominance rules have been developed. Using randomly generated test problems, the performance of the proposed solution approaches is analyzed. The results indicate that in all practical situations, the branch-and-bound algorithm is able to solve the problem optimally in less than a second.