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Approximations and empirics for stochastic war equations

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  • Kjell Hausken
  • John F. Moxnes

Abstract

The article develops a theorem which shows that the Lanchester linear war equations are not in general equal to the Kolmogorov linear war equations. The latter are time‐consuming to solve, and speed is important when a large number of simulations must be run to examine a large parameter space. Run times are provided, where time is a scarce factor in warfare. Four time efficient approximations are presented in the form of ordinary differential equations for the expected sizes and variances of each group, and the covariance, accounting for reinforcement and withdrawal of forces. The approximations are compared with “exact” Monte Carlo simulations and empirics from the WWII Ardennes campaign. The band spanned out by plus versus minus the incremented standard deviations captures some of the scatter in the empirics, but not all. With stochastically varying combat effectiveness coefficients, a substantial part of the scatter in the empirics is contained. The model is used to forecast possible futures. The implications of increasing the combat effectiveness coefficient governing the size of the Allied force, and injecting reinforcement to the German force during the Campaign, are evaluated, with variance assessments. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:52:y:2005:i:7:p:682-700
    DOI: 10.1002/nav.20105
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    References listed on IDEAS

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    1. 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.
    2. Jerome Bracken, 1995. "Lanchester models of the ardennes campaign," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(4), pages 559-577, June.
    3. 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.
    4. Hausken, Kjell & Moxnes, John F., 2002. "Stochastic conditional and unconditional warfare," European Journal of Operational Research, Elsevier, vol. 140(1), pages 61-87, July.
    5. 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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    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. 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.
    3. Michael J Armstrong, 2014. "The salvo combat model with a sequential exchange of fire," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(10), pages 1593-1601, October.

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