Lanchester's differential equations as operational command decision making tools

Abstract

This paper investigates the application of Lanchester's equations as a scientific method and tool for examining the functioning of the armed forces as complex organizational systems in combat. It is important to assess the reliability of the knowledge obtained by this method, about the facts of the operational environment and the effectiveness of the use of forces, in order to support the process of planning and making optimal decisions, in conditions of uncertainty and risk, which are inherent in warfare. According to this hypothesis, a mathematical model was developed based on the wellknown Lanchester's equations, which defined the quadratic and linear law of combat between two opponents with a heterogeneous force structure (air force and army). The created model enables a correct simplified analysis in the decision-making process. Real war and combat operations are very complex and require the use of complex simulators, whose methodological background is often unknown to decision makers, which is why reliable approximate simulation and modeling methods are necessary and desirable.