Air defense is a crucial matter 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 an optimal scheduling of a set of surface-to-air missiles of a warship to a set of attacking air threats. 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 the algorithm, a lower bound, an upper bound and a set of dominance rules are proposed. Using randomly generated test problems, the performances of the proposed solution approaches are analyzed. The results indicate that in all practical situations, the branch-and-bound algorithm is able to solve the problem in less than a second.

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