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The Lanchester (n, 1) problem

Author

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  • G T Kaup

    (University of Central Florida)

  • D J Kaup

    (University of Central Florida)

  • N M Finkelstein

    (Simulation Technology Center)

Abstract

We discuss the background of the Lanchester (n, 1) problem, in which a heterogeneous force of n different troop types faces a homogeneous force. We also present a more general set of equations for modelling this problem, along with its general solution. As an example of the consequences of this model, we take the (2, 1) case and solve for the optimal force allocation and fire distribution in a (2, 1) battle. Next, we present examples that demonstrate our model's advantages over a previous formulation. In particular, we point out how different forces may win a battle, depending on the handling and interpretation of the model's solution. Lastly, we present a variant of the Lanchester square law which applies to the (2, 1) case.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:56:y:2005:i:12:d:10.1057_palgrave.jors.2601936
    DOI: 10.1057/palgrave.jors.2601936
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Kangaspunta, Jussi & Liesiö, Juuso & Salo, Ahti, 2012. "Cost-efficiency analysis of weapon system portfolios," European Journal of Operational Research, Elsevier, vol. 223(1), pages 264-275.
    2. N J MacKay, 2009. "Lanchester models for mixed forces with semi-dynamical target allocation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(10), pages 1421-1427, October.
    3. 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.
    4. González, Eduardo & Villena, Marcelo, 2011. "Spatial Lanchester models," European Journal of Operational Research, Elsevier, vol. 210(3), pages 706-715, May.
    5. 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.

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    Keywords

    Lanchester problem; optimisation;

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