A Study on the Allocation and Engagement Scheduling of Air Defense Missiles by Using Mixed Integer Programming

- Journal title : Korean Management Science Review
- Volume 32, Issue 4, 2015, pp.109-133
- Publisher : The Korean Operations and Management Science Society
- DOI : 10.7737/KMSR.2015.32.4.109

Title & Authors

A Study on the Allocation and Engagement Scheduling of Air Defense Missiles by Using Mixed Integer Programming

Lee, Dae Ryeock; Yang, Jaehwan;

Lee, Dae Ryeock; Yang, Jaehwan;

Abstract

This paper considers the allocation and engagement scheduling of air defense missiles by using MIP (mixed integer programming). Specifically, it focuses on developing a realistic MIP model for a real battle situation where multiple enemy missiles are headed toward valuable defended assets and there exist multiple air defense missiles to counteract the threats. In addition to the conventional objective such as the minimization of surviving target value, the maximization of total intercept altitude is introduced as a new objective. The intercept altitude of incoming missiles is important in order to minimize damages from debris of the intercepted missiles and moreover it can be critical if the enemy warhead contains an atomic or chemical bomb. The concept of so called the time window is used to model the engagement situation and a continuous time is assumed for flying times of the both missiles. Lastly, the model is extended to simulate the situation where the guidance radar, which guides a defense missile to its target, has the maximum guidance capacity. The initial mathematical model developed contains several non-linear constraints and a non-linear objective function. Hence, the linearization of those terms is performed before it is solved by a commercially available software. Then to thoroughly examine the MIP model, the model is empirically evaluated with several test problems. Specifically, the models with different objective functions are compared and several battle scenarios are generated to evaluate performance of the models including the extended one. The results indicate that the new model consistently presents better and more realistic results than the compared models.

Keywords

Weapon Target Allocation Problem;Missile Allocation Problem;Mixed Integer Programming;Optimization;

Language

Korean

References

1.

권용수, 김정희, 이경행, "성공적 하층 미사일방어 수행을 위한 시스템 요구능력 도출", 한국국방경영분석학회지, 제37권, 제2호(2011), pp.21-22.

2.

김민구, "한국형 미사일 방어체계 발전방안 연구-미사일 방어체계 구축을 위한 선결조건을 중심으로", 한성대학교 대학원 석사학위논문, (2014), p.32.

3.

김민석, "뉴스를 점령한 미사일 KAMD & Kill Chain", 근두운, LIG 넥스원(주), 제59권(2013), p.14.

4.

김민욱, "공군 방공유도탄사령부, '13년 방공유도탄 실사격 대회", 국방과 기술, 제417호(2013), p.32.

5.

대한민국 국방부, 국방백서, 2014, pp.58-59.

6.

이상헌, 정인철, "미사일 방어를 위한 KDX 최적 배치모형 연구", 한국시뮬레이션학회 논문지, 제15권, 제4호(2006), pp.69-77.

7.

이준복, "다수무장-다수표적에 대한 실시간 동적 교전 할당 알고리즘 연구", KAIST 대학원 박사학위논문, 2009.

8.

이진호, 김종현, 김우람, 협동성 강화를 위한 무기체계, 북코리아, (2013), p.226.

9.

이재영, 곽기훈, "복합-휴리스틱 알고리즘을 이용한 지대공 유도무기(SAM)최적배치 방안 : 탄도미사일 방어를 중심으로", IE interfaces, 제21권, 제3호(2008), pp.262-273.

10.

장준건, 최봉완, 김경택, "미사일 탄도궤적 시뮬레이션을 이용한 핵탄도미사일 방어체계 요구능력 분석", 군사과학연구지, 제7권, 제1호(2014), pp.11-24.

11.

정치영, "IP를 이용한 패트리어트 최적배치모형에 관한 연구", 국방대학교 국방관리대학원 석사학위논문, 2006.

12.

정치영, 이재영, 이상헌, "격추확률 최대화를 위한 미사일 최적배치 문제", 경영과학, 제27권, 제1호(2010), pp.75-90.

13.

정형석, "Ballistic Missile Defense(탄도미사일방어)", 국방과학기술정보, 제40호(2013), p.169.

14.

Bertsekas, D.P., M.L. Homer, D.A. Logan, S.D. Patek, and N.R. Sandell, "Missile defense and interceptor allocation by Neuro-Dynamic Programming," IEEE Transactions on Systems, Man, and Cybernetics-Part A : Systems and Humans, Vol.30, No.1(2000), pp.42-51.

15.

Burr, S.A., J.E. Falk, and A.F. Karr, "Integer Prim-Read solutions to a class of target defense problems," Operations Research, Vol.33, No.4(1985), pp.726-745.

16.

Cai, H., J. Liu, Y. Chen, and H.Wang, "Survey of the research on dynamic weapon-target assignment problem," Journal of Systems Engineering and Electronics, Vol.17, No.3(2006), pp.559-565.

17.

Chen, J., B. Xin, Z.H. Peng, L.H. Dou, and J. Zhang, "Evolutionary decision-makings for the dynamic weapon-target assignment problem," Science in China Series F : Information Sciences, Vol.52, No.11(2009), pp.2006-2018.

18.

He, Y. and Y. Qiu, "THAAD-like high altitude theater missile defense : Strategic defense capability and certain countermeasures analysis," Science and Global Security, Vol.11, No.2-3(2003), p.153.

19.

Headquarters Department of the Army, FM 3-01.85 Patriot battalion and battery operations, (2002), pp.5.24-5.31.

20.

Hosein, P., "A class of dynamic nonlinear resource allocation problems," Ph.D. Thesis, Massachusetts Institute of Technology, (1989), pp.23-199.

21.

Hosein, P.A. and M. Athans, "An asymptotic result for the multi-stage weapon-target allocation problem," Proceedings of the 29th Conference on Decision and Control, Honolulu, Hawaii, (1990), pp.240-245.

22.

Karasakal, O., "Optimal air defense strategies for a naval task group," Ph.D. Thesis, Middle East Technical University, (2004), pp.17-73.

23.

Khosla, D., "Hybrid genetic approach for the dynamic weapon-target allocation problem. in Proceedings of SPIE, Vol.4396(2001), pp.244-259.

24.

Li, J., R. Cong, and J. Xiong, "Dynamic WTA optimization model of air defense operation of warships' formation," Journal of Systems Engineering and Electronics, Vol.17, No.1(2006), pp.126-131.

25.

Matlin, S., "A review of the literature on the missile-allocation problem," Operations Research, Vol.18, No.2(1970), pp.334-373.

26.

Soland, R.M., "Optimal terminal defense tactics when several sequential engagements are possible," Operations Research, Vol.35, No.4(1987), pp.537-542.

27.

Wikipedia, .