Mathematical Programs and Computations for a Class of Anti-aircraft Mission Planning Problems

摘要

The theater defense distribution is an important problem in the military that determines strategies against a sequence of offensive attacks in order to protect his targets. This study focuses on developing mathematical models for three important defense problems that generate anti-aircraft mission plans for a group of missile battalions. The simple Anti-aircraft Launching Assignment problem specifies number of missiles should be launched from each battalion to each fleet of attacking aircraft to maximize the defensive effectiveness, provided that the locations of missile battalions are given. On the other hand, the Anti-aircraft Mission Planning problem maximizes the defender's effectiveness using all his available battalions, while the Inverse Anti-aircraft Mission Planning problem computes necessary weapon resources (battalions and their missiles) to obtain a given defensive effectiveness value. The proposed formulations are Integer Programs and proved as NP-hard. A comprehensive set of experiments is then evaluated to show that these proposed programs can be applied to solve fast real-life instances to optimality.