Journal of Korean Institute of Industrial Engineers (대한산업공학회지)

Korean Institute of Industrial Engineers (대한산업공학회)
권호 표지
DOI QR코드

DOI QR Code

Gaussian Approximation of Stochastic Lanchester Model for Heterogeneous Forces

혼합 군에 대한 확률적 란체스터 모형의 정규근사

  • Park, Donghyun (Department of Industrial and Systems Engineering, KAIST) ;
  • Kim, Donghyun (Department of Industrial and Systems Engineering, KAIST) ;
  • Moon, Hyungil (Department of Industrial and Systems Engineering, KAIST) ;
  • Shin, Hayong (Department of Industrial and Systems Engineering, KAIST)
  • 박동현 (KAIST 산업 및 시스템 공학과) ;
  • 김동현 (KAIST 산업 및 시스템 공학과) ;
  • 문형일 (KAIST 산업 및 시스템 공학과) ;
  • 신하용 (KAIST 산업 및 시스템 공학과)
  • Received : 2015.10.28
  • Accepted : 2016.01.06
  • Published : 2016.04.15
Download PDF
⟨ Previous Next ⟩

Abstract

We propose a new approach to the stochastic version of Lanchester model. Commonly used approach to stochastic Lanchester model is through the Markov-chain method. The Markov-chain approach, however, is not appropriate to high dimensional heterogeneous force case because of large computational cost. In this paper, we propose an approximation method of stochastic Lanchester model. By matching the first and the second moments, the distribution of each unit strength can be approximated with multivariate normal distribution. We evaluate an approximation of discrete Markov-chain model by measuring Kullback-Leibler divergence. We confirmed high accuracy of approximation method, and also the accuracy and low computational cost are maintained under high dimensional heterogeneous force case.

Keywords

References

  1. Amacher, M. and Mandallaz, D. (1986), Stochastic version of Lanchester equations in wargamiming, European Journal of Operational Research, 24(1), 41-45. https://doi.org/10.1016/0377-2217(86)90008-1
  2. Ancker Jr, C. J. and Gafarian, A. V. (1988), The validity of assumptions underlying current uses of Lanchester attrition rates, Technical Report TRAC-WSMR-TD-7-88. US Army TRADOC Analysis Command-WSMR, White Sands Missile Range, New Mexico.
  3. Baek, S. W. and Hong, S. P. (2013), A pragmatic method on multi-weapon Lanchester's law, Journal of the Korean Operations Research and Management Science Society, 38(4), 1-9. https://doi.org/10.7737/JKORMS.2013.38.4.001
  4. Kaup, G. T., Kaup, D. J., and Finkelstein, N. M. (2005), The Lanchester (n, 1) problem, Journal of the Operational Research Society, 56(12), 1399-1407. https://doi.org/10.1057/palgrave.jors.2601936
  5. Karmeshu, and Jaiswal, N. K. (1986), A Lanchester-type model of combat with stochastic rates, Naval Research Logistics Quarterly, 33(1), 101-110. https://doi.org/10.1002/nav.3800330109
  6. Kress, M. and Talmor, I. (1999), A new look at the 3 : 1 rule of combat through Markov stochastic Lanchester models, Journal of the Operational Research Society, 50(7), 733-744. https://doi.org/10.1057/palgrave.jors.2600758
  7. Kingman, J. F. C. (2002), Stochastic aspects of Lanchester's theory of warfare, Journal of applied probability, 455-465.
  8. Lanchester, F. W. (1916), Aircraft in warfare : The dawn of the fourth arm., Constable and Company, London.
  9. Lappi, E., Pakkanen, M. S., and Åkesson, B. (2012), An approximative method of simulating a duel, Proceedings of the Winter Simulation Conference, Winter Simulation Conference, 208.
  10. Strickland, J. (2011), Fundamentals of Combat Modeling, Lulu.com.
  11. Strickland, J. (2011), Mathematical Modeling of Warfare and Combat Phenomenon, Lulu.com.
  12. Taylor, J. G. (1983), Lanchester models of warfare, Military Applications Section, Operations Research Society of America, Alexandria, VA, I/II.