Optimizing fire allocation in a Network Centric Warfare-type model

In this paper, we introduce a non-linear Lanchester's model of Network Centric Warfare type and investigate an optimization problem for this model, where only the Red force is supplied by several supply agents. Optimal fire allocation of the Blue force is sought in the form of a piece-wise constant function of time. A "threatening rate" is computed for the Red force and each of its supply agents at the beginning of each stage of the combat. These rates can be used to derive the optimal decision for the Blue force to focus its firepower to the Red force itself or one of its supply agents. This optimal fire allocation is derived and proved by considering an optimization problem of the number of Blue force troops. Numerical experiments are included to demonstrate the theoretical results.