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A bottleneck combat model: an application to the Battle of Thermopylae

Author

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  • Anelí Bongers

    (University of Malaga)

  • José L. Torres

    (University of Malaga)

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.

Suggested Citation

  • Anelí Bongers & José L. Torres, 2021. "A bottleneck combat model: an application to the Battle of Thermopylae," Operational Research, Springer, vol. 21(4), pages 2859-2877, December.
    • Handle: RePEc:spr:operea:v:21:y:2021:i:4:d:10.1007_s12351-019-00513-0
    DOI: 10.1007/s12351-019-00513-0
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    References listed on IDEAS

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    1. Hirshleifer, Jack, 1991. "The Technology of Conflict as an Economic Activity," American Economic Review, American Economic Association, vol. 81(2), pages 130-134, May.
    2. Israel David, 1995. "Lanchester modeling and the biblical account of the battles of gibeah," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(4), pages 579-584, June.
    3. N. C. G. Campbell & K. J. Roberts, 1986. "Lanchester market structures: A. Japanese approach to the analysis of business competition," Strategic Management Journal, Wiley Blackwell, vol. 7(3), pages 189-200, May.
    4. Kjell Hausken & John F. Moxnes, 2005. "Approximations and empirics for stochastic war equations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(7), pages 682-700, October.
    5. Kress, Moshe & Caulkins, Jonathan P. & Feichtinger, Gustav & Grass, Dieter & Seidl, Andrea, 2018. "Lanchester model for three-way combat," European Journal of Operational Research, Elsevier, vol. 264(1), pages 46-54.
    6. Wayne P. Hughes, 1995. "A salvo model of warships in missile combat used to evaluate their staying power," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(2), pages 267-289, March.
    7. Flores, J.C. & Bologna, Mauro, 2013. "Troy: A simple nonlinear mathematical perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4683-4687.
    8. Jerome Bracken, 1995. "Lanchester models of the ardennes campaign," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(4), pages 559-577, June.
    9. S. J. Deitchman, 1962. "A Lanchester Model of Guerrilla Warfare," Operations Research, INFORMS, vol. 10(6), pages 818-827, December.
    10. Kjell Hausken & Gregory Levitin, 2011. "Shield versus sword resource distribution in K-round duels," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(4), pages 589-603, December.
    11. Hausken, Kjell & Moxnes, John F., 2002. "Stochastic conditional and unconditional warfare," European Journal of Operational Research, Elsevier, vol. 140(1), pages 61-87, July.
    12. Miltiadis Chalikias & Michalis Skordoulis, 2017. "Implementation of F.W. Lanchester’s combat model in a supply chain in duopoly: the case of Coca-Cola and Pepsi in Greece," Operational Research, Springer, vol. 17(3), pages 737-745, October.
    13. Shanahan, Linda & Sen, Surajit, 2011. "Dynamics of stochastic and nearly stochastic two-party competitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1800-1810.
    14. Michael J. Armstrong, 2014. "Modeling Short-Range Ballistic Missile Defense and Israel's Iron Dome System," Operations Research, INFORMS, vol. 62(5), pages 1028-1039, October.
    15. Ronald D. Fricker, 1998. "Attrition models of the Ardennes campaign," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(1), pages 1-22, February.
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