Abstract
This paper proposes a Lanchester-type combat model to simulate battles in which one or two of the opposing sides cannot use all the forces simultaneously due to some physical restriction (i.e., topographic constraints, transforming the battlefield into a bottleneck). We show that this model, when the bottleneck restriction applies to both sides, leads to the Lanchester’s linear law for both aimed- and unaimed-fire, but the rate of change over time is a constant. The main characteristics of the bottleneck combat model are the following: (1) the topographic constraint makes the quality (fighting effectiveness) and size of the restriction the more relevant factors for the outcome of the battle, reducing the relative importance of quantity; (2) the bottleneck transforms the Lanchester’s square law into the linear law under direct-fire; and (3) if quality is similar among foes, the topographic bottleneck restriction is irrelevant for victory. The model is used to simulate the Battle of Thermopylae and shows that if the bottleneck restriction had persisted and was not removed, the Persian army would have been defeated.
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Acknowledgements
We are grateful to three anonymous referees and the editor for very helpful comments and suggestions on a previous version of the paper. Funding was provided by Spanish Ministry of Science and Tecnology (Grant No. ECO2016-76818-C3-2-P).
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Bongers, A., Torres, J.L. A bottleneck combat model: an application to the Battle of Thermopylae. Oper Res Int J 21, 2859–2877 (2021). https://doi.org/10.1007/s12351-019-00513-0
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DOI: https://doi.org/10.1007/s12351-019-00513-0