Warfare command stratagem analysis for winning based on Lanchester attrition models

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.

Keywords

Lanchester attrition models / warfare command stratagems / battle situation / warfare information system

References

[1] Bracken J.. Lanchester models of the Ardennes campaign. Naval Research Logistics, 1995, 42: 559-577.

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

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

[4] Chen P.S., Chu P.. Applying Lanchester’s linear law to model the Ardennes campaign. Naval Research Logistics, 2001, 48: 653-661.

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

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

[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.. An optimum seeking method of operation decision making schemes based on set pair analysis. Journal of Northeastern University, 2011, 32(8): 1033-1037.

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

[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.. A Lanchester model of guerrilla warfare. Operations Research, 1962, 10: 818-827.

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

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

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

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

[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.. Optimization model of reinforcements based on differential game and its solving method. Operations Research and Management Science, 2002, 11(4): 16-20.

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

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

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

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

[23] Ling Y.X., Ma M.H., Yuan W.W.. Wargame Models and Simulations, 2006, Changsha: National University of Defense Technology Press

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

[25] Lucas T.W., Turkes T.. Fitting Lanchester models to the battles of Kursk and Ardennes. Naval Research Logistics, 2004, 51: 95-116.

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

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

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

[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.. The inner relations between Lanchester equations and the fire indexes. Journal of National University of Defense Technology, 1994, 12(3): 8-14.

[31] Sha J.C.. Mathematical Tactics, 2003, Beijing: Science Press

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

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

[34] Spradlin C., Spradlin G.. Lanchester’s equations in three dimensions. Computers and Mathematics with Applications, 2007, 53: 999-1011.

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

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

[37] Wang S.M., Wang B.S.. Application of Bayesian networks in tactical situation assessment. Systems Engineering and Electronics, 2004, 11: 1620-1623.

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

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

[40] Yu B., Duan C.Y., Zhou M.L., Mao C.L.. Military Operations Research, 2008, Changsha: National University of Defense Technology Press

[41] Zhang Y.P.. Fundamentals of Military Operations Research, 2006, Beijing: Higher Education Press

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

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