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Applying Lanchester's linear law to model the Ardennes campaign

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  • Patrick S. Chen
  • Peter Chu

Abstract

In modern warfare, many believe the decisive factor in winning a battle is seizing the right moment to shift from defense to attack, or vice versa. This paper attempts to bring that perspective to Lanchester's differential equations of warfare, and continues the application of Lanchester's linear law to the analysis of the World War II battle of Ardennes, as reported in earlier issues of Naval Research Logistics by Bracken and by Fricker. A new variable, shift time, accounting for the timing of the shift between defense and attack is explicitly included in our version of the model, and it helps obtain improved goodness of fit to historical data. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:653–661, 2001

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:48:y:2001:i:8:p:653-661
    DOI: 10.1002/nav.1040
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    References listed on IDEAS

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    1. J. H. Engel, 1954. "A Verification of Lanchester's Law," Operations Research, INFORMS, vol. 2(2), pages 163-171, May.
    2. John S. Maybee, 1985. "The theory of combined‐arms lanchester‐type models of warfare," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 32(2), pages 225-237, May.
    3. Jerome Bracken, 1995. "Lanchester models of the ardennes campaign," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(4), pages 559-577, June.
    4. 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.
    5. S. J. Deitchman, 1962. "A Lanchester Model of Guerrilla Warfare," Operations Research, INFORMS, vol. 10(6), pages 818-827, December.
    6. Protopopescu, V. & Santoro, R. T. & Dockery, J., 1989. "Combat modeling with partial differential equations," European Journal of Operational Research, Elsevier, vol. 38(2), pages 178-183, January.
    7. Ronald D. Fricker, 1998. "Attrition models of the Ardennes campaign," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(1), pages 1-22, February.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.

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