IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v51y2004i1p95-116.html
   My bibliography  Save this article

Fitting Lanchester equations to the battles of Kursk and Ardennes

Author

Listed:
  • Thomas W. Lucas
  • Turker Turkes

Abstract

Lanchester equations and their extensions are widely used to calculate attrition in models of warfare. This paper examines how Lanchester models fit detailed daily data on the battles of Kursk and Ardennes. The data on Kursk, often called the greatest tank battle in history, was only recently made available. A new approach is used to find the optimal parameter values and gain an understanding of how well various parameter combinations explain the battles. It turns out that a variety of Lanchester models fit the data about as well. This explains why previous studies on Ardennes, using different minimization techniques and data formulations, have found disparate optimal fits. We also find that none of the basic Lanchester laws (i.e., square, linear, and logarithmic) fit the data particularly well or consistently perform better than the others. This means that it does not matter which of these laws you use, for with the right coefficients you will get about the same result. Furthermore, no constant attrition coefficient Lanchester law fits very well. The failure to find a good‐fitting Lanchester model suggests that it may be beneficial to look for new ways to model highly aggregated attrition. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Suggested Citation

  • Thomas W. Lucas & Turker Turkes, 2004. "Fitting Lanchester equations to the battles of Kursk and Ardennes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(1), pages 95-116, February.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:1:p:95-116
    DOI: 10.1002/nav.10101
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.10101
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.10101?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. J. H. Engel, 1954. "A Verification of Lanchester's Law," Operations Research, INFORMS, vol. 2(2), pages 163-171, May.
    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. Jeffrey A. Appleget, 1995. "The combat simulation of desert storm with applications for contingency operations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(4), pages 691-713, June.
    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.
    5. M.P. Wiper & L.I. Pettit & K.D.S. Young, 2000. "Bayesian inference for a Lanchester type combat model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(7), pages 541-558, October.
    6. Ronald D. Fricker, 1998. "Attrition models of the Ardennes campaign," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(1), pages 1-22, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shawn C. McKay & Alok Chaturvedi & Douglas E. Adams, 2011. "A process for anticipating and shaping adversarial behavior," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(3), pages 255-280, April.
    2. Gerardo Minguela-Castro & Ruben Heradio & Carlos Cerrada, 2021. "Automated Support for Battle Operational–Strategic Decision-Making," Mathematics, MDPI, vol. 9(13), pages 1-15, June.
    3. Moshe Kress, 2020. "Lanchester Models for Irregular Warfare," Mathematics, MDPI, vol. 8(5), pages 1-14, May.
    4. Chad W. Seagren & Donald P. Gaver & Patricia A. Jacobs, 2019. "A stochastic air combat logistics decision model for Blue versus Red opposition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(8), pages 663-674, December.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ian R. Johnson & Niall J. MacKay, 2011. "Lanchester models and the battle of Britain," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(3), pages 210-222, April.
    2. Patrick S. Chen & Peter Chu, 2001. "Applying Lanchester's linear law to model the Ardennes campaign," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(8), pages 653-661, December.
    3. M.P. Wiper & L.I. Pettit & K.D.S. Young, 2000. "Bayesian inference for a Lanchester type combat model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(7), pages 541-558, October.
    4. C-Y Hung & G K Yang & P S Deng & T Tang & S-P Lan & P Chu, 2005. "Fitting Lanchester's square law to the Ardennes Campaign," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(8), pages 942-946, August.
    5. Gerardo Minguela-Castro & Ruben Heradio & Carlos Cerrada, 2021. "Automated Support for Battle Operational–Strategic Decision-Making," Mathematics, MDPI, vol. 9(13), pages 1-15, June.
    6. 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.
    7. Ronald D. Fricker, 1998. "Attrition models of the Ardennes campaign," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(1), pages 1-22, February.
    8. P.S. Sheeba & Debasish Ghose, 2008. "Optimal resource allocation and redistribution strategy in military conflicts with Lanchester square law attrition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(6), pages 581-591, September.
    9. Anelí Bongers & José L. Torres, 2021. "A bottleneck combat model: an application to the Battle of Thermopylae," Operational Research, Springer, vol. 21(4), pages 2859-2877, December.
    10. Kjell Hausken & John F. Moxnes, 2005. "Approximations and empirics for stochastic war equations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(7), pages 682-700, October.
    11. Luss, Hanan & Rosenwein, Moshe B., 1997. "Operations Research applications: Opportunities and accomplishments," European Journal of Operational Research, Elsevier, vol. 97(2), pages 220-244, March.
    12. Pettit, L. I. & Wiper, M. P. & Young, K. D. S., 2003. "Bayesian inference for some Lanchester combat laws," European Journal of Operational Research, Elsevier, vol. 148(1), pages 152-165, July.
    13. Chad W. Seagren & Donald P. Gaver & Patricia A. Jacobs, 2019. "A stochastic air combat logistics decision model for Blue versus Red opposition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(8), pages 663-674, December.
    14. 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.
    15. Sung Ha Hwang, 2009. "Larger groups may alleviate collective action problems," UMASS Amherst Economics Working Papers 2009-05, University of Massachusetts Amherst, Department of Economics.
    16. 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.
    17. Jesús Fernández-Villaverde & Mark Koyama & Youhong Lin & Tuan-Hwee Sng, 2023. "The Fractured-Land Hypothesis," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 138(2), pages 1173-1231.
    18. Kress, Moshe & Caulkins, Jonathan P. & Feichtinger, Gustav & Grass, Dieter & Seidl, Andrea, 2018. "Lanchester model for three-way combat," European Journal of Operational Research, Elsevier, vol. 264(1), pages 46-54.
    19. Miltiadis Chalikias & Michalis Skordoulis, 2017. "Implementation of F.W. Lanchester’s combat model in a supply chain in duopoly: the case of Coca-Cola and Pepsi in Greece," Operational Research, Springer, vol. 17(3), pages 737-745, October.
    20. McCartney, Mark, 2022. "The solution of Lanchester’s equations with inter-battle reinforcement strategies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:navres:v:51:y:2004:i:1:p:95-116. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.