Letter to the Editor—The Mean Lanchester Attrition Rate

Bonder, Seth

doi:10.1287/opre.18.1.179

Cited by 17 publications

(13 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Other forms of Lanchester-type equations appear in the literature, but we will not consider them here (see Dolansky [1964], Taylor [1974Taylor [ , 1979aTaylor [ , 1980a). The Lanchester attrition-rate coefficients a(t) and b(t) depend on such variables as force separation, tactical posture of targets, rate of target acquisition, firing doctrine, firing rate, and so forth (e.g, see Bonder [1965Bonder [ , 1967Bonder [ , 1970; Bonder and Farrell). Bonder [1965J (see also Bonder and Farrell) has stressed the importance for evaluating weapon systems of such variable coefficient differential combat models to represent temporal variations in firepower on the battlefield.…”

Section: Modern Warfarementioning

confidence: 99%

See 1 more Smart Citation

Annihilation Prediction for Lanchester-Type Models of Modern Warfare

Taylor

Brown

1983

Operations Research

View full text Add to dashboard Cite

I N AN EARLIER paper (Taylor and Brown (1976]), we showed how to solve variable-coefficient Lanchester-type equations of modern warfare for combat between two homogeneous forces. In that paper, we introduced canonical hyperbolic-like Lanchester functions for constructing the solution. Unfortunately, with only these previous resu lts one is limited to computing force-level trajectories and cannot gain a real understanding of qualitative model behavior (e.g. force annihilation) without extensive numerical computations (and only then for specific values of model parameters). Si nce the appearance of our earl ier work, several mathematical discoveries Comstock [1977], Taylor [1979b]) have provided new qualitative insight about the behavior of this combat model. We wish to show here how these new results allow parametric analysis of combat modeled by power attrition-rats coefficients with somewhat the same facility as allowed by F. W. Lanchester's classic constant-coefficient model. In order to obtain this analysis capaSubj«t d o_i{icolion: 434 Lanc~r· type equationa, «9 (orce-annihiLatio n prediction .

show abstract

Section: Modern Warfarementioning

confidence: 99%

“…Work by Bonder [1965Bonder [ , 1967Bonder [ , 1970, Clark (1969], Barfoot [1969J, and • t--9.32 minutes and X, = x( r = 0) -1.35.…”

Section: Final Remarksmentioning

confidence: 99%

Annihilation Prediction for Lanchester-Type Models of Modern Warfare

Taylor

Brown

1983

Operations Research

View full text Add to dashboard Cite

show abstract

“…When Y loses, he may switch from firing at XI entirely to firing at X2 entirely before the XI force has been annihilated. This happens in Case (2) (R -VR (R -1) 6 < 1 ) when survivors of force-type Xp are assigned utility in excess of their Lanchester attrition-rate coefficient as compared with force-type XI, and certain relationships hold between initial force strengths. Thus, in contrast to the prescribed duration battle (Problem l), the optimal policy for Problem 2 may depend on initial force levels.…”

Section: Terminal Control Battle (Twomentioning

confidence: 99%

“…These factors themselves may be range dependent or change over time. S. Bonder [5], [6] has developed explicit formulas for relating the Lanchester attrition-rate coefficient to weapons system performance characteristics such as those mentioned above.…”

Section: Some Special Cases Of Time Dependent Attrition-rate Coefficimentioning

confidence: 99%

See 1 more Smart Citation

Lanchester‐type models of warfare and optimal control

Taylor¹

1974

Naval Research Logistics

View full text Add to dashboard Cite

The optimization of the dynamics of combat (optimal distribution of fire over enemy target types) is studied through a sequence of idealized models by use of the mathematical theory of optimal controL The models are for combat over a period of time described by Lanchester-type equations with a choice of tactics available to one side and subject to change with time. The structure of optimal fire distribution policies is discussed with reference to the influence of combatant objectives, termination conditions of the conflict, type of attrition process, and variable attrition-rate coefficients. Implications for intelligence, command and control systems, and human decision making are pointed out. The use of such optimal control models for guiding extensions to differential games is discussed.

show abstract

A theory of ideal linear weights for heterogeneous combat forces

Howes

Thrall

1973

Naval Research Logistics

View full text Add to dashboard Cite

Detailed combat simulations can produce effectiveness tables which measure the effectiveness of each weapon class on one side of an engagement, battle, or campaign to each weapon class on the other. Effectiveness tables may also be constructed in other ways.This paper assumes that effectiveness tables are given and shows how to construct from them a system of weapon weights each of which is a weighted average of the effects of a given weapon against each of the enemy's weapons. These weights utilize the PerronFrobenius theory of eigenvectors of nonnegative matrices. Methods of calculation are discussed and some interpretations are given for both the irreducible and reducible cases.

show abstract

Letter to the Editor—The Mean Lanchester Attrition Rate

Cited by 17 publications

References 2 publications

Annihilation Prediction for Lanchester-Type Models of Modern Warfare

Annihilation Prediction for Lanchester-Type Models of Modern Warfare

Lanchester‐type models of warfare and optimal control

A theory of ideal linear weights for heterogeneous combat forces

Contact Info

Product

Resources

About