JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Gaussian Approximation of Stochastic Lanchester Model for Heterogeneous Forces
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Gaussian Approximation of Stochastic Lanchester Model for Heterogeneous Forces
Park, Donghyun; Kim, Donghyun; Moon, Hyungil; Shin, Hayong;
  PDF(new window)
 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
Combat Modelling;Stochastic Lanchester Model;Heterogeneous Forces;
 Language
Korean
 Cited by
 References
1.
Amacher, M. and Mandallaz, D. (1986), Stochastic version of Lanchester equations in wargamiming, European Journal of Operational Research, 24(1), 41-45. crossref(new window)

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.

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. crossref(new window)

5.
Karmeshu, and Jaiswal, N. K. (1986), A Lanchester-type model of combat with stochastic rates, Naval Research Logistics Quarterly, 33(1), 101-110. crossref(new window)

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. crossref(new window)

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.