This study proposes a McCormick-based mixed-integer linear programming (MILP) model for real-time dynamic weapon-target assignment (DWTA) in multi-layer missile defense systems. The proposed model simultaneously considers engagement time windows (ETWs), time-varying interception effectiveness, and inter-layer dependency based on the shoot-look-shoot (SLS) doctrine. To reflect operational engagement conditions, a K-factor-based effectiveness model is introduced by incorporating trajectory progress, engagement geometry, missile kinematics, and environmental conditions. Since the survival probability formulation results in nonlinear and nonconvex multilinear terms, the problem is reformulated into an MILP framework using binary-tree decomposition and McCormick linearization. In addition, a rolling horizon strategy and warm-start mechanism are applied to support real-time decision making under dynamically changing battlefield conditions. Numerical experiments on various threat scenarios demonstrate that the proposed approach significantly reduces computation time compared to nonlinear optimization methods while maintaining high solution quality. In particular, the proposed method achieves near optimal solutions within sub-second computation time even for large-scale instances.The results indicate that the proposed McCormick-based MILP framework provides an effective and practical solution for real-time DWTA problems in multi-layer missile defense systems.

1. 서 론
2. 이론적 고찰
    2.1 WTA 분야 관련 연구
    2.2 기존 연구의 한계 및 해법
3. 다층 미사일방어체계의 동적 WTA 모형 및해법
    3.1 탄도미사일의 비행특성
    3.2 DWTA 모형
    3.3 모형의 구현
    3.4 해법 개발
4. 실험결과 및 분석
    4.1 실험 환경 및 시나리오 설계
    4.2 문제 규모 분석
    4.3 시나리오 분석 및 확장성 평가
    4.4 McCormick 선형화 및 초기해 재활용 효과검증
    4.5 McCormick 완화 강도 및 Root Node Gap분석
    4.6 K-factor 가중치 민감도 분석
5. 결 론
Acknowledgement
References

• Joonha Jang(Department of Computer Science) | 장준하 (공군사관학교 컴퓨터과학과)
• Sangmin Lim(Department of Mechanical Engineering) | 임상민 (공군사관학교 기계공학과) Corresponding author
• Kwangjin Yang(Department of Mechanical Engineering) | 양광진 (공군사관학교 기계공학과)
• Hwajong Jin(Missile Systems Air and Missile Defense, System Development and Integration, LIG D&A, South Korea) | 진화종 (LIG 디펜스&에어로스페이스 미사일 시스템 대공체계연구소)
• Donghyouk Shim(Missile Systems Air and Missile Defense, System Development and Integration, LIG D&A, South Korea) | 심동혁 (LIG 디펜스&에어로스페이스 미사일 시스템 대공체계연구소)
• Kihoon Kwak(Department of Systems Engineering, Republic of Korea Air Force Academy) | 곽기훈 (공군사관학교 시스템공학과)