Modeling of combat operations

Introduction/purpose: The goal of the research in this paper is to present and evaluate the method of modeling operations by aggregating forces by simulating the battle process with Lanchester's equations. This method is the software basis of a certain number of programs used in NATO, in war simulations, and in the planning and analysis of operations. Its value is in understanding the consequences of decisions made with outcomes and results of combat actions. Methods: The case study of the well-known Operation Desert Storm gathered the necessary data on operational parameters and the way forces are used in battles. The obtained data were transformed into operational variables of the combat model using the force aggregation method, whose simulation was carried out using the method of differential Lanchester's equations (quadratic law). Results: By simulating the modeled operation, the parameters of the outcome of the conflict were obtained with numerical indicators of success, consumption of resources, etc. The results were analyzed and a certain correlation with the parameters of the real operation was determined, which enables the validation of the model. Conclusion: The partial validity of the model describing the conflict on a practical historical example from a case study was confirmed. There are objective limitations in the application of modeling of military operations and optimization of the use of forces. The value of this method is the possibility of a reliable strategic assessment of the adversary's military power at the strategic level

Refighting Pickett’s Charge: mathematical modeling of the Civil War battlefield

Objective. We model Pickett’s Charge at the Battle of Gettysburg to see whether the Confederates could have achieved victory by committing more infantry, executing a better barrage, or facing a weaker defense. Methods. Our mathematical modeling is based on Lanchester equations, calibrated using historical army strengths. We weight the Union artillery and infantry two different ways using two sources of data, and so have four versions of the model. Results. The models estimate that a successful Confederate charge would have required at least 1 to 3 additional brigades. An improved artillery barrage would have reduced these needs by about 1 brigade. A weaker Union defense could have allowed the charge to succeed as executed. Conclusions. The Confederates plausibly had enough troops to take the Union position and alter the battle’s outcome, but likely too few to further exploit such a success

Uncertainty and Error in Combat Modeling, Simulation, and Analysis

Due to the infrequent and competitive nature of combat, several challenges present themselves when developing a predictive simulation. First, there is limited data with which to validate such analysis tools. Secondly, there are many aspects of combat modeling that are highly uncertain and not knowable. This research develops a comprehensive set of techniques for the treatment of uncertainty and error in combat modeling and simulation analysis. First, Evidence Theory is demonstrated as a framework for representing epistemic uncertainty in combat modeling output. Next, a novel method for sensitivity analysis of uncertainty in Evidence Theory is developed. This sensitivity analysis method generates marginal cumulative plausibility functions (CPFs) and cumulative belief functions (CBFs) and prioritizes the contribution of each factor by the Wasserstein distance (also known as the Kantorovich or Earth Movers distance) between the CBF and CPF. Using this method, a rank ordering of the simulation input factors can be produced with respect to uncertainty. Lastly, a procedure for prioritizing the impact of modeling choices on simulation output uncertainty in settings where multiple models are employed is developed. This analysis provides insight into the overall sensitivities of the system with respect to multiple modeling choices