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An efficient approximate solution for stochastic Lanchester models

Author

Listed:
  • Donghyun Kim

    (KAIST)

  • Hyungil Moon

    (KAIST)

  • Donghyun Park

    (KAIST)

  • Hayong Shin

    (KAIST)

Abstract

Combat modeling is one of the essential topics for military decision making. The Lanchester equation is a classic method for modeling warfare, and many variations have extended its limitations and relaxed its assumptions. As a model becomes more complex, solving it analytically becomes intractable or computationally expensive. Hence, we propose two approximation methods: moment-matching scheme and a supporting method called battle-end approximation. These methods give an approximate solution in a short amount of time, while maintaining a high level of accuracy in simulation results in terms of hypothesis testing and numerical verification. They can be applied to computationally intensive problems, such as optimal resource allocation and analysis with asymmetric power like snipers or stealth aircrafts.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:68:y:2017:i:11:d:10.1057_s41274-016-0163-6
    DOI: 10.1057/s41274-016-0163-6
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    References listed on IDEAS

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    1. 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.
    2. Jerome Bracken, 1995. "Lanchester models of the ardennes campaign," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(4), pages 559-577, June.
    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. 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.
    5. Michael J. Armstrong, 2005. "A Stochastic Salvo Model for Naval Surface Combat," Operations Research, INFORMS, vol. 53(5), pages 830-841, October.
    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. Amacher, M. & Mandallaz, D., 1986. "Stochastic versions of Lanchester equations in wargaming," European Journal of Operational Research, Elsevier, vol. 24(1), pages 41-45, January.
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    Cited by:

    1. Young-Jun Jee & Tae-Gyung Lee & Sang-Ho Park & Jun-Ho Cho & Hee-Soo Kim & Tae-Eog Lee, 2022. "A multiresolution simulation system and simulation development processes," The Journal of Defense Modeling and Simulation, , vol. 19(3), pages 325-338, July.
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    3. Moshe Kress, 2020. "Lanchester Models for Irregular Warfare," Mathematics, MDPI, vol. 8(5), pages 1-14, May.

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