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Optimal military strength allocation for campaign between single-kind arms and multi-kind arms

In the military conflict, the defending side may suffer threats from different attackers at the same time. This kind of situation is called campaign between single-kind arms and multi-kind arms in this article. By introducing the campaign superiority parameter(CSP), the optimal military strength allocation problem is studied for campaign between single-kind arms and multi-kind arms. Firstly, the general model for the campaign is established based on the Lanchester square law. Then, the defending force with enough strengths and with insufficient strengths are considered respectively, as well as the corresponding optimal military strength allocation principle given in theorems. Next, considering the tolerable maximum battle damage rate for the defending side, the optimal military strength allocation principle is modified on the basis of the previous conclusion. Numerical example is given to support the analytical results.