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A Stochastic Salvo Model for Naval Surface Combat

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  • Michael J. Armstrong

    (Sprott School of Business, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada K1S 5B6)

Abstract

In this paper, we propose a stochastic version of the salvo model for modern naval surface combat. We derive expressions for the mean and variance of surviving force strengths and for the probabilities of the possible salvo outcomes in forms simple enough to be implemented in spreadsheet software. Numerical comparisons of the deterministic and stochastic models indicate that while the two models tend to provide similar estimates of the average number of ships surviving a salvo, this average by itself can be highly misleading with respect to the likely outcomes of the battle. Our results also suggest that a navy’s preferences for risk (variability) and armament (offensive versus defensive) will depend on not only its mission objectives but also on whether it expects to fight from a position of strength or of weakness.

Suggested Citation

  • Michael J. Armstrong, 2005. "A Stochastic Salvo Model for Naval Surface Combat," Operations Research, INFORMS, vol. 53(5), pages 830-841, October.
    • Handle: RePEc:inm:oropre:v:53:y:2005:i:5:p:830-841
    DOI: 10.1287/opre.1040.0195
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    References listed on IDEAS

    as
    1. 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.
    2. Glenn Kent, 2002. "Looking Back: Four Decades of Analysis," Operations Research, INFORMS, vol. 50(1), pages 122-124, February.
    3. Michael J. Armstrong, 2004. "Effects of lethality in naval combat models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(1), pages 28-43, February.
    4. 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.
    5. Thomas W. Lucas & John E. McGunnigle, 2003. "When is model complexity too much? Illustrating the benefits of simple models with Hughes' salvo equations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(3), pages 197-217, April.
    6. C. J. Ancker, 1995. "A proposed foundation for a theory of combat," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(3), pages 311-343, April.
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    Cited by:

    1. Michael J. Armstrong, 2007. "Effective attacks in the salvo combat model: Salvo sizes and quantities of targets," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(1), pages 66-77, February.
    2. Kjell Hausken & John F. Moxnes, 2026. "Modeling warfare between different kinds of military equipment," Annals of Operations Research, Springer, vol. 357(2), pages 1003-1019, February.
    3. Michael Armstrong, 2011. "A verification study of the stochastic salvo combat model," Annals of Operations Research, Springer, vol. 186(1), pages 23-38, June.
    4. Anelí Bongers & José L. Torres, 2017. "Revisiting the Battle of Midway: A counterfactual analysis," Working Papers 2017-01, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
    5. Michael Atkinson & Moshe Kress, 2025. "Hard and Soft Defense Against a Sequence of Aerial Threats," Operations Research, INFORMS, vol. 73(4), pages 1767-1784, July.
    6. 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.
    7. Michael J. Armstrong, 2013. "The salvo combat model with area fire," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 652-660, December.
    8. Younglak Shim & Michael P. Atkinson, 2018. "Analysis of artillery shoot‐and‐scoot tactics," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(3), pages 242-274, April.
    9. Timothy A. McLennan-Smith & Alexander C. Kalloniatis & Zlatko Jovanoski & Harvinder S. Sidhu & Dale O. Roberts & Simon Watt & Isaac N. Towers, 2021. "A Mathematical Model of Humanitarian Aid Agencies in Attritional Conflict Environments," Operations Research, INFORMS, vol. 69(6), pages 1696-1714, November.
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    11. 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.

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