Modeling the Lanchester Laws with System Dynamics

Artelli, Michael J.; Deckro, Richard F.

doi:10.1177/154851290800500101

Cited by 16 publications

(10 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Several works discussed the validity of the laws [ 42 , 43 ]. Other contributions extended the original framework introducing concepts such as spatial structure or system dynamics [ 44 , 45 ]. The utility of the model was also expanded beyond its initial purpose, and has been successfully applied to study competition dynamics in ecology [ 46 – 48 ], evolutionary biology [ 49 ] or economics [ 50 ].…”

Section: Methodsmentioning

confidence: 99%

Model Selection in Historical Research Using Approximate Bayesian Computation

Rubio-Campillo

2016

PLoS ONE

View full text Add to dashboard Cite

Formal Models and HistoryComputational models are increasingly being used to study historical dynamics. This new trend, which could be named Model-Based History, makes use of recently published datasets and innovative quantitative methods to improve our understanding of past societies based on their written sources. The extensive use of formal models allows historians to re-evaluate hypotheses formulated decades ago and still subject to debate due to the lack of an adequate quantitative framework. The initiative has the potential to transform the discipline if it solves the challenges posed by the study of historical dynamics. These difficulties are based on the complexities of modelling social interaction, and the methodological issues raised by the evaluation of formal models against data with low sample size, high variance and strong fragmentation.Case StudyThis work examines an alternate approach to this evaluation based on a Bayesian-inspired model selection method. The validity of the classical Lanchester’s laws of combat is examined against a dataset comprising over a thousand battles spanning 300 years. Four variations of the basic equations are discussed, including the three most common formulations (linear, squared, and logarithmic) and a new variant introducing fatigue. Approximate Bayesian Computation is then used to infer both parameter values and model selection via Bayes Factors.ImpactResults indicate decisive evidence favouring the new fatigue model. The interpretation of both parameter estimations and model selection provides new insights into the factors guiding the evolution of warfare. At a methodological level, the case study shows how model selection methods can be used to guide historical research through the comparison between existing hypotheses and empirical evidence.

show abstract

Section: Methodsmentioning

confidence: 99%

Model Selection in Historical Research Using Approximate Bayesian Computation

Rubio-Campillo

2016

PLoS ONE

View full text Add to dashboard Cite

show abstract

“…Lanchester's (1916) seminal work continues to inspire a rich and varied literature that includes analyses of combat on the ground (Bonder, 1967;Taylor, 1983), at sea (Hughes, 1995), in the air (Gilbert, 2011;McLemore, Gaver, & Jacobs, 2016), and in more general terms (Brackney, 1959). Researchers have extended the original deterministic model to include stochastic varieties (Ancker, 1967;Karr, 1974;Kress & Talmor, 1999) and have developed simulation models with Lanchestarian qualities (eg, Artelli and Deckro (2008) as well the US Army and Marine Corps' Combat XXI leverage Lanchester [Balogh & Harless, 2003]). Still others have extended such models to consider counterinsurgency (Saie & Ahner, 2018), guerilla warfare (Deitchman, 1962;Schaffer, 1968), and cyberwarfare (Schramm & Gaver, 2013).…”

Section: A Review Of the Literaturementioning

confidence: 99%

A stochastic air combat logistics decision model for Blue versus Red opposition

Seagren

Gaver

Jacobs

2019

Naval Research Logistics

View full text Add to dashboard Cite

Technologically advanced aircraft rely on robust and responsive logistics systems to ensure a high state of operational readiness. This paper fills a critical gap in the literature for combat models by closely relating effectiveness of the logistics system to determinants of success in combat. We present a stochastic diffusion model of an aerial battle between Blue and Red forces. The number of aircraft of Blue forces aloft and ready to be aloft on combat missions is limited by the maximum number of assigned aircraft, the reliability of aircraft subsystems, and the logistic system's ability to repair and replenish those subsystems. Our parsimonious model can illustrate important trade‐offs between logistics decision variables and operational success.

show abstract

“…A similar idea has been used by Artelli and Deckro (2008) to introduce fatigue into a Lanchester-like battle.…”

Section: Lanchester Models With Discontinuities: An Application To Nementioning

confidence: 99%