Lanchester models for mixed forces with semi-dynamical target allocation

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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. Journal of the Operational Research Society (2009) 60, 1421-1427. doi:10.1057/jors.2008.97 Published online 24 September 2008

Original languageEnglish
Pages (from-to)1421-1427
Number of pages7
JournalJournal of the Operational Research Society
Issue number10
Early online date24 Sept 2008
Publication statusPublished - Oct 2009


  • military
  • combat modelling
  • Lanchester problem

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