Some properties of nonlinear Lanchester equations with an application in military

Kim, Dong Hyun; Moon, Hyun-Joo; Shin, Hayong

doi:10.1080/00949655.2017.1296441

Cited by 7 publications

(9 citation statements)

References 12 publications

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“…al. [15] or by Lin and Mackay [8]. Thus, by the first case in our proof, in order that B (t) is always maximal, for the first stage B should focus its firepower to N .…”

Section: Optimal Fire Allocationmentioning

confidence: 71%

“…By the third case in our proof, B will focus its firepower on A. The second stage in this case has been considered in [15]. The fourth case is analyzed similarly as the third case.…”

Section: Optimal Fire Allocationmentioning

confidence: 99%

“…In many historical battles, firepower was not only aimed at the direct rivals but also their supply units, see [9]. In 2017, Kim and his colleagues [15] considered a Lanchester's model where Blue force B fights against Red force R supported by a supply unit N and called this a NCW model. This model can be denoted by (B vs (R, N )).…”

Section: Introductionmentioning

confidence: 99%

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Optimal fire allocation in a combat model of mixed NCW type

Vu,

Nguyen,

Nguyen

et al. 2021

Preprint

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In this work, we introduce a nonlinear Lanchester model of NCW-type and study a problem of finding the optimal fire allocation for this model. A Blue party B will fight against a Red party consisting of A and R, where A is an independent force and R fights with supports from a supply unit N . A battle may consist of several stages but we consider the problem of finding optimal fire allocation for B in the first stage only. Optimal fire allocation is a set of three non-negative numbers whose sum equals to one, such that the remaining force of B is maximal at any instants. In order to tackle this problem, we introduce the notion of threatening rates which are computed for A, R, N at the beginning of the battle. Numerical illustrations are presented to justify the theoretical findings.

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“…al. [15] or by Lin and Mackay [8]. Thus, by the first case in our proof, in order that B (t) is always maximal, for the first stage B should focus its firepower to N .…”

Section: Optimal Fire Allocationmentioning

confidence: 71%

“…By the third case in our proof, B will focus its firepower on A. The second stage in this case has been considered in [15]. The fourth case is analyzed similarly as the third case.…”

Section: Optimal Fire Allocationmentioning

confidence: 99%

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Optimal fire allocation in a combat model of mixed NCW type

Vu,

Nguyen,

Nguyen

et al. 2021

Preprint

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“…On the other hand, the optimal decision making problem in military field is interesting itself and fire allocating problem is one of the most common problems. In this regard, Donghyun Kim (16) set up and investigated a non-linear Lanchester-type model where one of the parties is supported by a network consisting of all kinds of supply such as intelligence, ammunition,…”

Section: Introductionmentioning

confidence: 99%

Optimizing fire allocation in a NCW-type model

Nguyen¹,

Vu²,

Dinh³

et al. 2020

Preprint

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In this paper, we introduce a non-linear Lanchester's model of NCW-type and investigate an optimization problem for this model, where only the Red force is supplied by several supply agents. Optimal fire allocation of the Blue force is sought in the form of a piece-wise constant function of time. A "threatening rate" is computed for the Red force and each of its supply agents at the beginning of each stage of the combat. These rates can be used to derive the optimal decision for the Blue force to focus its firepower to the Red force itself or one of its supply agents. This optimal fire allocation is derived and proved by considering an optimization problem of number of Blue force's troops. Numerical experiments are included to demonstrate the theoretical results.

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“…This increase in complexity has driven recent developments in the literature to advance the Lanchester equations e.g. multiple combatants [Kress et al, 2018], geographically distributed combat interactions [McLemore et al, 2016], and network centric warfare [Kim et al, 2017] to name but a few. This paper will present a new approach to modelling the presence of non-combatant groups, drawing upon recent developments in ecological systems modelling [Fontaine et al, 2011;Kéfi et al, 2012Kéfi et al, , 2016.…”

Section: Introductionmentioning

confidence: 99%

Exploiting ecological non-trophic models in representations of warfare

2019

El Sawah, S. (Ed.) MODSIM2019, 23rd International Congress on Modelling and Simulation.

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Traditional combat models such as the Lanchester model are typically limited to two competing populations and exhibit either exponential growth or decay solutions. Although these early models were well suited to the type of warfare in the early twentieth century, they are no longer as directly applicable to the complex modern military operating environment. Despite these shortcomings, the Lanchester model was used in the Operations Research of Force Design even in World War II, as evidenced in the classic work Methods of Operations Research of Morse and Kimball [1950]. Our work seeks to enrich such models to account for modern and future complexities, particularly around the role of inter-agency engagement in operations. To this end, we account for the presence of civilian or non-combatant populations, which have long been an unfortunate part of the combat setting as they are directly impacted by the warfare surrounding them. Typically this non-combatant group consists of the host population in the space where combat occurs. The other type of non-combatant groups, a development since the 19th century and with ongoing evolution today, are agencies, be they governmental or non-governmental, that undertake work in conflict e nvironments t o s upport local populations. Depending on whether they are governmental or otherwise, these agencies have a range of formal and informal relationships with both sides of the conflict. As the agency non-combatant populations play no direct role in combat, their interactions with the two combatant forces are well suited to be modelled through the recent developments in non-trophic ecological models. The networked non-trophic ecological model is one of the most recent developments in ecological modelling that incorporates a great number of positive and negative interactions, both trophic (consumptive) and nontrophic (non-consumptive), between multiple species in a "multiplex" network. In a similar manner in which the Lanchester combat model can be viewed as an adaptation of the Lotka-Volterra model for two species in a predator-prey relationship, the networked non-trophic ecological model can be exploited as a viable representation of modern combat in which non-combatant groups exist. The combat model presented in this paper provides a global representation of asymmetrical combat between two forces in the modern setting where non-combatant populations are present. In our model, the noncombatant population is present as a neutral agency supporting the native population to the extent that they are non-combatants, but where there can be leakage from this group to the insurgent fighting f orce. Correspondingly, the opposing intervention force is under obligations to enable an environment where the neutral agency may undertake its work. A key result of our model is that, in contrast to the typical exponential growth or decay solutions of the Lanchester system, with the inclusion of a third group limit cycles and bifurcations can now occur which we interpret in light of the warfighting app...

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Some properties of nonlinear Lanchester equations with an application in military

Cited by 7 publications

References 12 publications

Optimal fire allocation in a combat model of mixed NCW type

Optimal fire allocation in a combat model of mixed NCW type

Optimizing fire allocation in a NCW-type model

Exploiting ecological non-trophic models in representations of warfare

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