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Annihilation Prediction for Lanchester-Type Models of Modern Warfare

Author

Listed:
  • James G. Taylor

    (Naval Postgraduate School, Monterey, California)

  • Gerald G. Brown

    (Naval Postgraduate School, Monterey, California)

Abstract

This paper introduces important new functions for analytic solution of Lanchester-type equations of modem warfare for combat between two homogeneous forces modeled by power attrition-rate coefficients with “no offset.” Tabulations of these Lanchester-Clifford-Schläfli (or LCS) functions allow one to study this particular variable-coefficient model almost as easily and thoroughly as Lanchester's classic constant-coefficient one. LCS functions allow one to obtain important information (in particular, force-annihilation prediction) without having to spend the time and effort of computing force-level trajectories. The choice of these particular functions is based on theoretical considerations that apply in general to Lanchester-type equations of modern warfare and provide guidance for developing other canonical functions. Moreover, our new LCS functions also provide valuable information about related variable-coefficient models. Also, we introduce an important transformation of the battle's time scale that not only simplifies the force-level equations, but also shows that relative fire effectiveness and intensity of combat are the only two weapon-system parameters determining the course of such variable-coefficient Lanchester-type combat.

Suggested Citation

  • James G. Taylor & Gerald G. Brown, 1983. "Annihilation Prediction for Lanchester-Type Models of Modern Warfare," Operations Research, INFORMS, vol. 31(4), pages 752-771, August.
    • Handle: RePEc:inm:oropre:v:31:y:1983:i:4:p:752-771
    DOI: 10.1287/opre.31.4.752
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    Citations

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    Cited by:

    1. Moshe Kress, 2020. "Lanchester Models for Irregular Warfare," Mathematics, MDPI, vol. 8(5), pages 1-14, May.
    2. González, Eduardo & Villena, Marcelo, 2011. "Spatial Lanchester models," European Journal of Operational Research, Elsevier, vol. 210(3), pages 706-715, May.
    3. Israel David, 1995. "Lanchester modeling and the biblical account of the battles of gibeah," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(4), pages 579-584, June.
    4. David Connors & Michael J. Armstrong & John Bonnett, 2015. "A Counterfactual Study of the Charge of the Light Brigade," Historical Methods: A Journal of Quantitative and Interdisciplinary History, Taylor & Francis Journals, vol. 48(2), pages 80-89, June.
    5. N. K. Jaiswal & Meena Kumari & B. S. Nagabhushana, 1995. "Optimal force mix in heterogeneous combat," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(6), pages 873-887, September.
    6. Gregory Levitin & Kjell Hausken, 2012. "Resource Distribution in Multiple Attacks with Imperfect Detection of the Attack Outcome," Risk Analysis, John Wiley & Sons, vol. 32(2), pages 304-318, February.
    7. G T Kaup & D J Kaup & N M Finkelstein, 2005. "The Lanchester (n, 1) problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(12), pages 1399-1407, December.
    8. Chad W. Seagren & Donald P. Gaver & Patricia A. Jacobs, 2019. "A stochastic air combat logistics decision model for Blue versus Red opposition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(8), pages 663-674, December.
    9. Ian R. Johnson & Niall J. MacKay, 2011. "Lanchester models and the battle of Britain," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(3), pages 210-222, April.
    10. Gregory Levitin & Kjell Hausken, 2010. "Resource Distribution in Multiple Attacks Against a Single Target," Risk Analysis, John Wiley & Sons, vol. 30(8), pages 1231-1239, August.
    11. M.P. Wiper & L.I. Pettit & K.D.S. Young, 2000. "Bayesian inference for a Lanchester type combat model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(7), pages 541-558, October.
    12. Wayne P. Hughes, 1995. "A salvo model of warships in missile combat used to evaluate their staying power," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(2), pages 267-289, March.
    13. David L. Bitters, 1995. "Efficient concentration of forces, or how to fight outnumbered and win," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(3), pages 397-418, April.
    14. Michael J. Armstrong, 2004. "Effects of lethality in naval combat models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(1), pages 28-43, February.
    15. Hausken, Kjell & Moxnes, John F., 2002. "Stochastic conditional and unconditional warfare," European Journal of Operational Research, Elsevier, vol. 140(1), pages 61-87, July.
    16. Patrick S. Chen & Peter Chu, 2001. "Applying Lanchester's linear law to model the Ardennes campaign," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(8), pages 653-661, December.
    17. Kjell Hausken & John F. Moxnes, 2005. "Approximations and empirics for stochastic war equations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(7), pages 682-700, October.
    18. Stephen Biddle & Stephen Long, 2004. "Democracy and Military Effectiveness," Journal of Conflict Resolution, Peace Science Society (International), vol. 48(4), pages 525-546, August.
    19. Michael J. Armstrong & Steven E. Sodergren, 2015. "Refighting Pickett's Charge: Mathematical Modeling of the Civil War Battlefield," Social Science Quarterly, Southwestern Social Science Association, vol. 96(4), pages 1153-1168, December.

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