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Lanchester models of the ardennes campaign

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  • Jerome Bracken

Abstract

A detailed data base of the Ardennes campaign of World War II (December 15, 1944 through January 16, 1945) has recently been developed. The present article formulates four Lanchester models of the campaign and estimates their parameters for these data. Two‐sided time histories of warfare on battles and campaigns are very rare, so Lanchester models have seldom been validated with historical data. The models are homogeneous in that tanks, armored personnel carriers, artillery, and manpower are weighted to yield a measure of strength of the Allied and German forces. This weighting is utilized for combat power and for losses. The models treat combat forces in the campaign (including infantry, armor, and artillery manpower) and total forces in the campaign (including both combat manpower and support manpower.) Four models are presented. Two models have five parameters (Allied individual effectiveness, German individual effectiveness, exponent of shooting force, exponent of target force, and a tactical parameter reflecting which side is defending and attacking.) The other two models remove the tactical parameter, which is not generally known prior to warfare, and estimate the other parameters without the tactical parameter. The main results of the research are (a) the Lanchester linear model fits the Ardennes campaign data in all four cases, and (b) when combat forces are considered Allied individual effectiveness is greater than German individual effectiveness, whereas when total forces are considered Allied and German individual effectiveness is the same. The interpretation of the latter result is that the two sides had essentially the same individual capabilities but were organized differently—the Allies chose to have more manpower in the support forces, which yielded greater individual capabilities in the combat forces. The overall superiority of the Allies in the campaign led to the attrition to the Allies being a smaller portion of their forces. © 1995 John Wiley & Sons, Inc. This article is a US Government work and, as such, is in the public domain in the United States of America.

Suggested Citation

  • Jerome Bracken, 1995. "Lanchester models of the ardennes campaign," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(4), pages 559-577, June.
  • Handle: RePEc:wly:navres:v:42:y:1995:i:4:p:559-577
    DOI: 10.1002/1520-6750(199506)42:43.0.CO;2-R
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    1. Robert L. Helmbold, 1964. "Letter to the Editor—Some Observations on the Use of Lanchester's Theory for Prediction," Operations Research, INFORMS, vol. 12(5), pages 778-781, October.
    2. James G. Taylor, 1971. "Technical Note—A Note on the Solution to Lanchester-Type Equations with Variable Coefficients," Operations Research, INFORMS, vol. 19(3), pages 709-712, June.
    3. Ladislav Dolanský, 1964. "Present State of the Lanchester Theory of Combat," Operations Research, INFORMS, vol. 12(2), pages 344-358, April.
    4. Herbert K. Weiss, 1966. "Combat Models and Historical Data: The U.S. Civil War," Operations Research, INFORMS, vol. 14(5), pages 759-790, October.
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    Cited by:

    1. McCartney, Mark, 2022. "The solution of Lanchester’s equations with inter-battle reinforcement strategies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).
    2. Gerardo Minguela-Castro & Ruben Heradio & Carlos Cerrada, 2021. "Automated Support for Battle Operational–Strategic Decision-Making," Mathematics, MDPI, vol. 9(13), pages 1-15, June.
    3. N. Cangiotti & M. Capolli & M. Sensi, 2023. "A generalization of unaimed fire Lanchester’s model in multi-battle warfare," Operational Research, Springer, vol. 23(2), pages 1-19, June.
    4. Ronald D. Fricker, 1998. "Attrition models of the Ardennes campaign," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(1), pages 1-22, February.
    5. Pettit, L. I. & Wiper, M. P. & Young, K. D. S., 2003. "Bayesian inference for some Lanchester combat laws," European Journal of Operational Research, Elsevier, vol. 148(1), pages 152-165, July.
    6. P.S. Sheeba & Debasish Ghose, 2008. "Optimal resource allocation and redistribution strategy in military conflicts with Lanchester square law attrition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(6), pages 581-591, September.
    7. Kress, Moshe & Caulkins, Jonathan P. & Feichtinger, Gustav & Grass, Dieter & Seidl, Andrea, 2018. "Lanchester model for three-way combat," European Journal of Operational Research, Elsevier, vol. 264(1), pages 46-54.
    8. Miltiadis Chalikias & Michalis Skordoulis, 2017. "Implementation of F.W. Lanchester’s combat model in a supply chain in duopoly: the case of Coca-Cola and Pepsi in Greece," Operational Research, Springer, vol. 17(3), pages 737-745, October.
    9. Michael P. Atkinson & Moshe Kress & Niall J. MacKay, 2021. "Targeting, Deployment, and Loss-Tolerance in Lanchester Engagements," Operations Research, INFORMS, vol. 69(1), pages 71-81, January.
    10. Donghyun Kim & Hyungil Moon & Donghyun Park & Hayong Shin, 2017. "An efficient approximate solution for stochastic Lanchester models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1470-1481, November.
    11. 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.
    12. 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.
    13. Anelí Bongers & José L. Torres, 2021. "A bottleneck combat model: an application to the Battle of Thermopylae," Operational Research, Springer, vol. 21(4), pages 2859-2877, December.
    14. 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.
    15. 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.
    16. C-Y Hung & G K Yang & P S Deng & T Tang & S-P Lan & P Chu, 2005. "Fitting Lanchester's square law to the Ardennes Campaign," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(8), pages 942-946, August.
    17. Zhao Qingsong & Zhang Xiaoke & Yang Zhiwei, 2016. "Capability Oriented Combat System of Systems Networked Modeling and Analyzing," Journal of Systems Science and Information, De Gruyter, vol. 4(3), pages 195-211, June.
    18. Chen, Hsi-Mei, 2007. "A non-linear inverse Lanchester square law problem in estimating the force-dependent attrition coefficients," European Journal of Operational Research, Elsevier, vol. 182(2), pages 911-922, October.
    19. Thomas W. Lucas & Turker Turkes, 2004. "Fitting Lanchester equations to the battles of Kursk and Ardennes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(1), pages 95-116, February.
    20. 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.

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