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An operations research problem concerning the optimal surface-to-air-missile (SAM) firing pattern to defend a surface target is solved via applications of the concept of closed-loop (feedback) and open-loop optimal control. The SAM defense problem is formulated as a Markov decision process with the number of SAM's in each salvo as the decision variable. Interesting cases, including the presence of imperfect sensor observation and a bound on the number of SAM's available are considered. The principle of dynamic programming and the technique of nonlinear integer programming are applied to reach closed-loop and open-loop solutions. Numerical examples are given for illustration.