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Targeting, Deployment, and Loss-Tolerance in Lanchester Engagements

Author

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  • Michael P. Atkinson

    (Operations Research Department, Naval Postgraduate School, Monterey, California 93943)

  • Moshe Kress

    (Operations Research Department, Naval Postgraduate School, Monterey, California 93943)

  • Niall J. MacKay

    (Department of Mathematics, University of York, York YO10 5DD, United Kingdom)

Abstract

Existing Lanchester combat models focus on two force parameters: numbers (force size) and per-capita effectiveness (attrition rate). Whereas these two parameters are central in projecting a battle’s outcome, there are other important factors that affect the battlefield: (1) targeting capability, that is, the capacity to identify live enemy units and not dissipate fire on nontargets; (2) tactical restrictions preventing full deployment of forces; and (3) morale and tolerance of losses, that is, the capacity to endure casualties. In the spirit of Lanchester theory, we derive, for the first time, force-parity equations for various combinations of these effects and obtain general implications and trade-offs. We show that more units and better weapons (higher attrition rate) are preferred over improved targeting capability and relaxed deployment restrictions unless these are poor. However, when facing aimed fire and unable to deploy more than half of one’s force, it is better to be able to deploy more existing units than to have either additional reserve units or the same increase in attrition effectiveness. Likewise, more relaxed deployment constraints are preferred over enhanced loss-tolerance when initial reserves are greater than the force level at which withdrawal occurs.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:69:y:2021:i:1:p:71-81
    DOI: 10.1287/opre.2020.2022
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    References listed on IDEAS

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    1. Jerome Bracken, 1995. "Lanchester models of the ardennes campaign," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(4), pages 559-577, June.
    2. S. J. Deitchman, 1962. "A Lanchester Model of Guerrilla Warfare," Operations Research, INFORMS, vol. 10(6), pages 818-827, December.
    3. M Kress & I Talmor, 1999. "A new look at the 3:1 rule of combat through Markov Stochastic Lanchester models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(7), pages 733-744, July.
    4. Michèle Breton & Ramla Jarrar & Georges Zaccour, 2006. "A Note on Feedback Sequential Equilibria in a Lanchester Model with Empirical Application," Management Science, INFORMS, vol. 52(5), pages 804-811, May.
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    Cited by:

    1. Amir, Rabah & Machowska, Dominika & Troege, Michael, 2021. "Advertising patterns in a dynamic oligopolistic growing market with decay," Journal of Economic Dynamics and Control, Elsevier, vol. 131(C).

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    Keywords

    combat modeling; Lanchester equations;

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