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Warfare command stratagem analysis for winning based on Lanchester attrition models

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Abstract

Lanchester equations and their extensions are widely used to calculate attrition in warfare models. The current paper addresses the warfare command decision-making problem for winning when the total combats capability of the attacking side is not superior to that of the defending side. For this problem, the corresponding warfare command stratagems, which can transform the battlefield situation, are proposed and analyzed quantitatively by considering the influence of the warfare information factor. The application examples in military conflicts show the feasibility and effectiveness of the proposed model and the warfare command stratagems for winning. The research results may provide a theoretical reference for warfare command decision making.

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References

  1. Bracken, J. (1995). Lanchester models of the Ardennes campaign. Naval Research Logistics, 42: 559–577

    Article  MATH  Google Scholar 

  2. Chen, H.M. (2002). An inverse problem of the Lanchester square law in estimating time-dependent attrition coefficients. Operations Research, 50(2): 389–394

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen, H.M. (2003). An optimal control problem in determining the optimal reinforcement schedules for the Lanchester equations. Computers and Operations Research, 30: 1051–1066

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen, P.S. & Chu, P. (2001). Applying Lanchester’s linear law to model the Ardennes campaign. Naval Research Logistics, 48: 653–661

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, S.S. & Ning, W.H. (2004). The model of situation assessment in anti-air fight. Journal of Air Force Engineering University (Natural Science Edition), 5(4): 54–57

    Google Scholar 

  6. Chen, X.Y., Jing, Y.W., Li, C.J. & Liu, X.P. (2009). Analysis of optimum strategy using Lanchester equation for naval battles like Trafalgar. Journal of Northeastern University, 30(4): 33–37

    Google Scholar 

  7. Chen, X.Y., Jing, Y.W., Li, C.J., Jiang, N. & Dimirovski, G.M. (2010). Effectiveness evaluation of warfare command systems with dissymmetric warfare information. In: Proceedings of the 2010 American Control Conference, 5556–5560, Baltimore, USA

  8. Chen, X.Y., Jing, Y.W. & Gong, M.S. (2011). An optimum seeking method of operation decision making schemes based on set pair analysis. Journal of Northeastern University, 32(8): 1033–1037

    Google Scholar 

  9. Chen, X.Y., Jing, Y.W., Li, C.J. & Liu, X.P. (2011a). Optimal strategies for winning in military conflicts based on Lanchester equation. Control and Decision, 26(7): 2011–2015

    MathSciNet  Google Scholar 

  10. Chen, X.Y., Jiang, N., Jing, Y.W., Stojanovski, G. & Dimirovski, G.M. (2011b). Differential game model and its solutions for force resource complementary via Lanchester square law equation. In: Proceeding of the 18th IFAC World Congress (IFAC WC), 1024–1030, Milano, Italy

  11. Cheng, Q.Y. (2004). Warfare Command Decision Making Analysis. Military Science Press

  12. Deitchman, S.J. (1962). A Lanchester model of guerrilla warfare. Operations Research, 10: 818–827

    Article  Google Scholar 

  13. Engel, J.H. (1954). A verification of Lanchester’s law. Journal of the Operations Research Society of America, 2(2): 163–171

    Google Scholar 

  14. Ghose, D., Krichman, M., Speyer, J.L. & Shamma, J.S. (2002). Modeling and analysis of air campaign resource allocation: a spatio-temporal decomposition approach. IEEE Transactions on Systems, Man and Cybernetics, Part A, 32(3): 403–418

    Article  Google Scholar 

  15. Johnson, I.R. & Mackay, N.J. (2008). Lanchester models and the battle of Britain. Naval Research Logistics, 58(3): 210–222

    Article  MathSciNet  Google Scholar 

  16. Ju, J.C. (2009). Improvement of Lanchester equation and its application in combat. Electronics Optics and Control, 16(10): 22–25

    Google Scholar 

  17. Lanchester, F.W. (1999). Aircraft in Warfare: the Dawn of the Fourth Arm. Lanchester Press

  18. Li, D.F., Tan, A.S. & Luo, F. (2002). Optimization model of reinforcements based on differential game and its solving method. Operations Research and Management Science, 11(4): 16–20

    Google Scholar 

  19. Li, D.F. & Chen, Q.H. (2004). Troops support differential game optimization model and solution. Fire Control and Command Control, 29(1): 41–43

    Google Scholar 

  20. Li, D.F. & Xu, T. (2007). Naval Operational Research Analysis and Application. Beijing: National Defence Industry Press

    Google Scholar 

  21. Li, D.F., Sun, T. & Wang, Y.C. (2008). Differential game model and its solution for the firepower-assignment in vessel formations in information war. Control Theory and Application, 25(6): 1163–1166

    MathSciNet  Google Scholar 

  22. Li, T., Bai, J.L. & Luan, Q.J. (2008). Research on situation assessment of air-defense warfare based on rough set theory and evidence theory. Aeronautical Computing Technique, 38(3): 46–48

    Google Scholar 

  23. Ling, Y.X., Ma, M.H. & Yuan, W.W. (2006). Wargame Models and Simulations. National University of Defense Technology Press, Changsha

    Google Scholar 

  24. Lucas, T.W. & Dinges, J.A. (2004). The effect of battlecircumstances on fitting Lanchester equations to the Battle of Kursk. Military Operations Research, 9: 17–30

    Article  Google Scholar 

  25. Lucas, T.W. & Turkes, T. (2004). Fitting Lanchester models to the battles of Kursk and Ardennes. Naval Research Logistics, 51: 95–116

    Article  MathSciNet  MATH  Google Scholar 

  26. Ning, W.H., Chen, S.S., Tian, X.H. & Chen, Y.G. (2004). Analysis on the stratagems for transforming the battlefield situation based on Lanchester Equation. Electronics Optics and Control, 11(4): 11–13

    Google Scholar 

  27. Peterson, R.H. (1967). On the algorithmic law of attrition and its application to tank combat. Operations Research, 15: 557–558

    Article  Google Scholar 

  28. Roberts, D.M. & Conolly, D.M. (1992). An extension of the Lanchester square law to inhomogeneous forces with an application to force allocation methodology. Journal of the Operational Research Society, 43(8): 741–752

    MATH  Google Scholar 

  29. Sha, J.C. & Zeng, A.J. (1994). Research on the warfare theory of Lanchester and tactics. In: Proceeding of Control and Decision Conference of China, 1134–1136, Xiamen

  30. Sha, J.C. (1994). The inner relations between Lanchester equations and the fire indexes. Journal of National University of Defense Technology, 12(3): 8–14

    Google Scholar 

  31. Sha, J.C. (2003). Mathematical Tactics. Beijing: Science Press

    Google Scholar 

  32. Sheeba, P.S. & Ghose, D. (2008). Optimal resource allocation and redistribution strategy in military conflicts with Lanchester square law attrition. Naval Research Logistics, 55: 581–591

    Article  MathSciNet  MATH  Google Scholar 

  33. Shi, Y.B., Gao, X.J. & Zhang, A. (2007). Effectiveness evaluation of information support based on the Lanchester equation. Aeronautical Computing Technique, 37(5): 21–24

    Google Scholar 

  34. Spradlin, C. & Spradlin, G. (2007). Lanchester’s equations in three dimensions. Computers and Mathematics with Applications, 53: 999–1011

    Article  MathSciNet  MATH  Google Scholar 

  35. Taylor, J.G. (1983). Lanchester Models of Warfare. Military Applications Section, Operations Research Society of America, Arlington, Virginia

    Google Scholar 

  36. Wang, J.S., Ren, B. & Pan, D. (2005). Analysis of an optimum strategy in the battle of Trafalgar. Journal of Hefei University of Technology, 28(2): 220–222

    MATH  Google Scholar 

  37. Wang, S.M. & Wang, B.S. (2004). Application of Bayesian networks in tactical situation assessment. Systems Engineering and Electronics, 11: 1620–1623

    Google Scholar 

  38. Wozencraft, J.M. & Moose, P.H. (1987). Characteristic trajectories of generalized Lanchester equations. Military Sciences: Military Operations, Strategy and Tactics, 6: A267581

    Google Scholar 

  39. Wu, J., Yang, F., Liang, Y., Cheng, Y.M. & Pan, Q. (2010). Generalized Lanchester combat model for information warfare. Fire Control and Command Control, 35(2): 50–53

    Google Scholar 

  40. Yu, B., Duan, C.Y., Zhou, M.L. & Mao, C.L. (2008). Military Operations Research. National University of Defense Technology Press, Changsha

    Google Scholar 

  41. Zhang, Y.P. (2006). Fundamentals of Military Operations Research. Higher Education Press, Beijing

    Google Scholar 

  42. Zeng, A.J. & Sha, J.C. (1995). Information war model based on differential game. Fire Control and Command Control, 20(4): 21–24

    Google Scholar 

  43. Zhou, Y., Zhou, J.P. & He, W.P. (2006). Air-combat effectiveness analysis of different information-supporting based on Lanchester equation. Aerospace Control, 24(2): 54–57

    Google Scholar 

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Correspondence to Xiangyong Chen.

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This work was partially supported by the National Natural Science Foundation of China under Grant No. 60774097 and 11171301, and by the Fundamental Research Funds for the Central Universities under Grant No. N100604019

Xiangyong Chen was born in 1983. He is currently working towards the Ph.D. degree in School of Information Science and Engineering in Northeastern University. His research interest focuses on warfare command decision making and game

Yuanwei Jing was born in 1956. He earned the Ph.D. degree in Northeastern University; currently he is a professor and doctoral supervisor. His research interests include analysis and control of large-scale complex systems and noncooperative games theory

Chunji Li was born in 1965. He earned the Ph.D. degree in Kyungpook National University in Korea in 2000. His research interests include decision making analysis, moment problem theory and control theory and application

Mingwei Li was born in 1982. She is currently working towards the Ph.D. degree in School of Information Science and Engineering in Northeastern University. Her research interest focuses on system theory and control

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Chen, X., Jing, Y., Li, C. et al. Warfare command stratagem analysis for winning based on Lanchester attrition models. J. Syst. Sci. Syst. Eng. 21, 94–105 (2012). https://doi.org/10.1007/s11518-011-5177-7

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