On the problem of assigning multiple interceptors over multiple aerial threats

This article investigates the problem of assigning multiple identical interceptors over multiple identical aerial threats, where all interceptors are launched in a single salvo. For this problem, two strategies have been studied in the literature: (A) to spread all interceptors as evenly as possible over all threats, and (B) to randomly assign all interceptors over the threats. The main contributions of this article are as follows. First, the literature contains empirical evidence that Strategy A is more efficient than Strategy B in terms of the mean number of missed threats, when the number of interceptors is no less than the number of threats. This article gives a rigorous proof of this fact. Secondly, it demonstrates numerically that Strategy~A can be significantly more efficient than Strategy B. Thirdly, it shows that Strategy~A is not only superior to Strategy B, but also the bona fide optimal strategy. Finally, this article establishes that these conclusions also hold when the number of interceptors is less than the number of threats.