Spatial Lanchester models

Lanchester equations have been widely used to model combat for many years, nevertheless, one of their most important limitations has been their failure to model the spatial dimension of the problems. Despite the fact that some efforts have been made in order to overcome this drawback, mainly through...

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Bibliographic Details
Published in:European journal of operational research 2011-05, Vol.210 (3), p.706-715
Main Authors: González, Eduardo, Villena, Marcelo
Format: Article
Language:English
Subjects:
Applied sciences
Attrition
Combat modeling
Consistency
Differential equations
Dynamical systems
Dynamics
Exact sciences and technology
Game theory
Lanchester theory
Mathematical analysis
Mathematical models
Mathematical problems
Movement
Numerical analysis
Operational research and scientific management
Operational research. Management science
Operations research
OR in military
OR in military Lanchester theory Combat modeling Partial differential equations
Partial differential equations
Similarity
Studies
War
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Description
Summary:Lanchester equations have been widely used to model combat for many years, nevertheless, one of their most important limitations has been their failure to model the spatial dimension of the problems. Despite the fact that some efforts have been made in order to overcome this drawback, mainly through the use of Reaction–Diffusion equations, there is not yet a consistently clear theoretical framework linking Lanchester equations with these physical systems, apart from similarity. In this paper, a spatial modeling of Lanchester equations is conceptualized on the basis of explicit movement dynamics and balance of forces, ensuring stability and theoretical consistency with the original model. This formulation allows a better understanding and interpretation of the problem, thus improving the current treatment, modeling and comprehension of warfare applications. Finally, as a numerical illustration, a new spatial model of responsive movement is developed, confirming that location influences the results of modeling attrition conflict between two opposite forces.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2010.11.009