A theory of ideal linear weights for heterogeneous combat forces

Howes, David R.; Thrall, Robert M.

doi:10.1002/nav.3800200406

Cited by 17 publications

(7 citation statements)

References 12 publications

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“…Thirdly, we have a motivation for valuing enemy target types in direct proportion to their kill capability (fire effectiveness) from the fact that the optimal policy is both intuitively appealing and also very simple in this case. The Howes and Thrall concept of "ideal" linear weights [12] is an extension of this idea to cases of heterogeneous forces on both sides. Thus, we have a motivation for Howes and…”

Section: Discussionmentioning

confidence: 99%

On the treatment of force‐level constraints in times‐equential combat problems

Taylor

1975

Naval Research Logistics

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The treatment of force-level constraints in time-sequential combat optimization problems is illustrated by further studying the fire-programming problem of Isbell and Marlow. By using the theory of state variable inequality constraints from modern optimal control theory, sharper results are obtained on necessary conditions of optimality for an optimal fire-distribution policy (in several cases justifying conjectures made in previous analysis). This leads to simplification of the determination of the domains of controllability for extremals leading to the various terminal states of combat. (Additionally, some new results for the determination of boundary conditions for the adjomt variables in optimal control problems with state variable inequality constraints have arisen from this work.) Some further extensions of previous analysis of the fire-programming problem are also given. These clarify some key points in the solution synthesis. Some important military principles for target selection and the valuation of combat resources are deduced from the solution. As a result of this work, more general time-sequential combat optimization problems can be handled, and a more systematic solution procedure is developed.

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Section: Discussionmentioning

confidence: 99%

On the treatment of force‐level constraints in times‐equential combat problems

Taylor

1975

Naval Research Logistics

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“…The main reasons for their concern are that the aggregated force strengths represent the destructive potential of weapons but do not incorporate any estimate of their vulnerability, and that the aggregation of heterogeneous forces violates the basic assumption of force homogeneity in the derivation of the Lanchester equations. One way which could be considered for the aggregation of heterogeneous forces is described by Howes and Thrall [7] and is applied in the war game IDAHEX [9].…”

Section: A New Square Lawmentioning

confidence: 99%

A note on Dupuy's QJM and new square law

Geldenhuys¹,

Botha²

2003

ORiON

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SOUTH AFRICA T.N. Dupuy has developed various operations research models in an attempt to quantify lessons that can be learned from military history. We discuss two of his models, the Quantified Judgment Model (QJM), and the "new square law". The QJM was developed by Dupuy for the analysis of military operations. We point out mathematical discrepancies in a part of the model and make suggestions to remove these discrepancies. Dupuy's new square law is an attempt to modify the well-known Lanchester equations for aimed fire, taking into account some results that were obtained in the OJM. We show that the new square law cannot be accepted as a valid mathematical model of combat attrition.

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“…Eigenvalue methods (which include antipotential potential) are discussed much further in Anderson [l], Anderson et al [ll], Howes and Thrall [12], Johnsrud [13], and Spudich [22]. Antipotential potential has been used in several dynamic models-e.g., IDAGAM, INBATIM.…”

Section: Antipotential Potentialmentioning

confidence: 99%

On weapons scores and force strengths

Anderson¹,

Miercort²

1995

Naval Research Logistics

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Quantitative comparisons of the combat forces on two opposing sides are virtually always formed as follows. First, all of the resources on each of the two sides are grouped into a set of categories. Each of the resources in each category is assigned a (nonnegative) value or score, where these scores are constant within categories, can vary across categories, and can be functions of the numbers and effectiveness parameters of the resources on both sides. These categories need not be the same for the two sides. Force strengths are then formed for each side by summing, over all of its categories, the product of the number of resources in each category times the score given to the resources in that category. Quantitative comparisons of the two forces are then calculated using (real‐valued) functions of these strengths and, perhaps, of exogenous input parameters. Thus, such force comparisons depend on the number and effectiveness of the weapons in the forces only through these force strengths. Accordingly, if this type of quantitative comparison of the forces on two opposing sides is desired, then it is reasonable to consider the questions of how to calculate scores for the resources of each type, and of how to combine the resulting scores to form force strengths that can be used to calculate measures of the relative effectiveness of the forces involved. This article addresses these questions. © 1995 John Wiley & Sons, Inc.

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A theory of ideal linear weights for heterogeneous combat forces

Cited by 17 publications

References 12 publications

On the treatment of force‐level constraints in times‐equential combat problems

On the treatment of force‐level constraints in times‐equential combat problems

A note on Dupuy's QJM and new square law

On weapons scores and force strengths

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