An optimal assignment of multi-type weapons to single-target

The weapon target assignment (WTA) problem is to find a proper assignment of weapons to the enemy´s targets with the objective of minimizing the total expected survival value of the targets. The problem can be formulated as a nonlinear integer programming problem, and is proven to be NP-hard. In this paper, we focus on the case where the defense has multi-type weapons and the offense (the enemy) has only one target. We first formulate this problem as a nonlinear integer programming model. Then we demonstrate that this model can be equivalently transformed as a linear integer problem. Thus the optimal solution can be easily obtained via solving this linear integer problem. Finally, we illustrate this problem and its solving method via a concrete example.