Abstract
We find the optimal fire distribution for the one-against-many Lanchester aimed-fired model, in which a homogeneous Blue force fights a mixed Red force with several distinct types. Each unit of Blue force kills Red type i at rate bi, while each type-i Red unit kills Blue at rate ri. We show that Blue’s optimal dynamical policy is to, at any give time, allocate all its fire to the surviving Red type for which the value of biri is highest.
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