Annihilation Prediction for Lanchester-Type Models of Modern Warfare

Taylor, James G.; Brown, Gerald G.

doi:10.1287/opre.31.4.752

Cited by 12 publications

(9 citation statements)

References 23 publications

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“…Rate‐based damage tracking has also been utilized in modeling combat attrition. For large‐scale battles between many units with constant attrition rates, the Lanchester Attrition model has been applied fruitfully to many situations since its inception in WWI (Taylor, ; Keane, ). More recently, the Hughes Salvo Model has been applied to simulate missile battles between ships (Hughes, ).…”

Section: Quantifying Rapid‐fire Combatmentioning

confidence: 99%

Optimal motion planning in rapid‐fire combat situations with attacker uncertainty

Walton

Lambrianides

Kaminer

et al. 2018

Naval Research Logistics

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This article provides a modeling framework for quantifying cost and optimizing motion plans in combat situations with rapid weapon fire, multiple agents, and attacker uncertainty characterized by uncertain parameters. Recent developments in numerical optimal control enable the efficient computation of numerical solutions for optimization problems with multiple agents, nonlinear dynamics, and a broad class of objectives. This facilitates the application of more realistic, equipment-based combat models, which track both more realistic models, which track both agent motion and dynamic equipment capabilities. We present such a framework, along with a described algorithm for finding numerical solutions, and a numerical example.autonomous vehicles, combat modeling, nonlinear control, path planning, trajectory planning

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Section: Quantifying Rapid‐fire Combatmentioning

confidence: 99%

Optimal motion planning in rapid‐fire combat situations with attacker uncertainty

Walton

Lambrianides

Kaminer

et al. 2018

Naval Research Logistics

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“…The rectangles in Figure 2 represent brigades (pale gray) and divisions (dark gray) as a whole. Attrition occurs if two enemy rectangles overlap, and it is calculated with Lanchester's differential equations [37,38].…”

Section: Functionalmentioning

confidence: 99%

Criteria for Decomposing Systems Into Components in Modeling and Simulation: Lessons Learned with Military Simulations

Hofmann¹

2004

SIMULATION

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A crucial decision within component-based modeling and simulation is the choice of the criterion or criteria to be used in decomposing the system. Many experiences with combat simulation systems indicate, first, that the optimal choice depends on the driving forces behind the decomposition or the goals that should be achieved by using components instead of monolithic systems. Second, the common criteria for decomposition in software design, information hiding, and “object picking”are sometimes inappropriate for model decomposition because they neglect the importance of so-called hidden assumptions of model abstraction and idealization, which are paramount to the modeling of every complex system.

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“…The conflict literature ( 11‐14 ) has mostly also considered static situations in the form of static contests where both contestants allocate their entire resources in one shot encounters. However, Sheeba ( 15 ) considered the optimal resource distribution among protections against different types of attacks based on a Lanchester ( 16 ) model that describes the dynamics of the resource attrition. Accounting for such continuous attrition, Taylor ( 17 ) considers this problem as a time sequential resource allocation problem and presents a solution as an optimal control problem.…”

Section: Introductionmentioning

confidence: 99%

Defense Resource Distribution Between Protection and Redundancy for Constant Resource Stockpiling Pace

Levitin

Hausken

2011

Risk Analysis

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The article considers the optimal resource distribution in a parallel system between increasing protection and providing redundancy in a situation when the attacker's and defender's resources are stockpiling and the resource increment rate is constant. It is assumed that the system must perform within an exogenously given time horizon and the attack time probability is uniformly distributed along this horizon. The defender optimizes the resource distribution in order to minimize the system destruction probability during the time horizon. First, we find the optimal pace of construction of the new redundant elements assuming that the construction must start in the initial stage of the stockpiling process. We show that starting construction of new elements in the beginning of the system's existence results in its high initial vulnerability. Introducing the time delay before starting the construction can reduce the initial system vulnerability and the entire system destruction probability. The problem of optimization of time delay and new element construction pace is considered with and without constraint on the initial system vulnerability. Examples illustrating the methodology of the optimal defense strategy analysis are presented.

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Annihilation Prediction for Lanchester-Type Models of Modern Warfare

Cited by 12 publications

References 23 publications

Optimal motion planning in rapid‐fire combat situations with attacker uncertainty

Optimal motion planning in rapid‐fire combat situations with attacker uncertainty

Criteria for Decomposing Systems Into Components in Modeling and Simulation: Lessons Learned with Military Simulations

Defense Resource Distribution Between Protection and Redundancy for Constant Resource Stockpiling Pace

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