Recent conflicts have renewed focus on missile defense systems, presenting a resource allocation problem that is NP-complete. The U.S. Ground-Based Midcourse Defense system exemplifies these challenges, with interceptors costing approximately $75 million each but achieving only a 56% Single Shot Probability of Kill. This creates complex mathematical trade-offs between cost and effectiveness.

Kill probability improves with multiple interceptors per warhead, reaching 96% with four interceptors against a single target. However, this model assumes perfect tracking capability. The probability of successfully tracking a target (P(track)) significantly impacts effectiveness. When P(track) drops to 0.90, the kill probability with four interceptors falls to just 87%, demonstrating how tracking capability is critical.

When facing multiple incoming missiles, systems face the Weapon-Target Assignment (WTA) problem - optimally allocating limited interceptors against various targets with different values. Recent conflicts have demonstrated how radar targeting can be destroyed, eliminating tracking coverage entirely. The 1991 Patriot missile failure illustrates how tracking system errors can render interceptors useless.