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Lanchester models for mixed forces with semi-dynamical target allocation

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  • N J MacKay

    (University of York)

Abstract

We consider the three standard Lanchester models of warfare (aimed-fire, unaimed-fire and asymmetric) with heterogeneous (mixed) forces on both sides. We begin by reviewing the homogeneous models, and then construct conserved quantities for the mixed models with separable kill-rates and random target allocation, commenting on the nature and allocation of unit types. Next we consider a more general semi-dynamical target allocation, construct a conserved quantity for the aimed-fire model and prove that the optimal strategy is to annihilate opposing unit types in succession. Finally, we make some comments on the optimal initial allocation of costed unit types in response to this.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:10:d:10.1057_jors.2008.97
    DOI: 10.1057/jors.2008.97
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    References listed on IDEAS

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    1. N E Ozdemirel & L Kandiller, 2006. "Semi-dynamic modelling of heterogeneous land combat," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(1), pages 38-51, January.
    2. 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.
    3. S. J. Deitchman, 1962. "A Lanchester Model of Guerrilla Warfare," Operations Research, INFORMS, vol. 10(6), pages 818-827, December.
    4. Robert L. Helmbold, 1965. "Letter to the Editor—A Modification of Lanchester's Equations," Operations Research, INFORMS, vol. 13(5), pages 857-859, October.
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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. 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.
    3. 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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