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An Inverse Problem of the Lanchester Square Law in Estimating Time-Dependent Attrition Coefficients

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  • Hsi-Mei Chen

    (Department of Information Management, Kung Shan University of Technology, 949 Da Wan Road, Tainan Hsien, Taiwan 710, Republic of China)

Abstract

This paper considers the inverse problem of estimating time-varying attrition coefficients in Lanchester's square law with reinforcements, using observed data on some or all of the battle's strength histories and the reinforcement schedules. The method employed is a nonparametric extension of the parametric conjugate gradient method (P-CGM). We use hypothetical strength histories and reinforcement schedules that are known to be without error at several points in time to illustrate the method. However, the method has application in other circumstances. The problem of estimating the time-dependent attrition coefficients that best fit a set of given strength histories is inherently a nonparametric inverse problem. In this paper we cast it into a nonlinear optimization problem, and show how to solve it numerically by using a nonparametric conjugate gradient method (NP-CGM). Two numerical test cases are provided to illustrate the application of the method.

Suggested Citation

  • Hsi-Mei Chen, 2002. "An Inverse Problem of the Lanchester Square Law in Estimating Time-Dependent Attrition Coefficients," Operations Research, INFORMS, vol. 50(2), pages 389-394, April.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:2:p:389-394
    DOI: 10.1287/opre.50.2.389.422
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    References listed on IDEAS

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    1. Helmbold, Robert L., 1994. "Direct and inverse solution of the Lanchester square law with general reinforcement schedules," European Journal of Operational Research, Elsevier, vol. 77(3), pages 486-495, September.
    2. J. H. Engel, 1954. "A Verification of Lanchester's Law," Operations Research, INFORMS, vol. 2(2), pages 163-171, May.
    3. J. D. Bueil & H. H. Kagiwada & R. E. Kalaba, 1968. "Letter to the Editor—Quasilinearization and Inverse Problems for Lanchester Equations of Conflict," Operations Research, INFORMS, vol. 16(2), pages 437-442, April.
    4. Dean S. Hartley & Robert L. Helmbold, 1995. "Validating Lanchester's square law and other attrition models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(4), pages 609-633, June.
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    Cited by:

    1. González, Eduardo & Villena, Marcelo, 2011. "Spatial Lanchester models," European Journal of Operational Research, Elsevier, vol. 210(3), pages 706-715, May.
    2. Chen, Hsi-Mei, 2007. "A non-linear inverse Lanchester square law problem in estimating the force-dependent attrition coefficients," European Journal of Operational Research, Elsevier, vol. 182(2), pages 911-922, October.

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    Keywords

    Military: warfare models;

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