Optimal commitment of forces in some Lanchester-type combat models
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Authors
Taylor, James G.
Subjects
Lanchester Theory of Combat
Tactical Decision Making
Military Decision Analysis
Combat Dynamics
Deterministic Combat Attrition
Tactical Decision Making
Military Decision Analysis
Combat Dynamics
Deterministic Combat Attrition
Advisors
Date of Issue
1977
Date
September 1976 - December 1976
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
This paper shows that one can determine whether or not it is beneficial for
the victor to initially commit as many forces as possible to battle in
Lanchester-type combat between two homogeneous forces by considering the
instantaneous casualty-exchange ratio. It considers the initial-commitment
decison as a one-sided static optimization problem and examines this nonlinear
program for each of three decision criteria (victor's losses, loss
ratio, and loss difference) and for each of two different battle-termination conditions (given force-level breakpoint and given force-ratio breakpoint)
.
The paper's main contribution is to show how to determine the sign of the
partial derivative of the decision criterion with respect to the victor's
initial force level for general combat dynamics without explicitly solving the
Lanchester-type combat equations. Consequently, the victor's optimal initialcommitment
decision many times may be determined from how the instantaneous
casualty-exchange ratio varies with changes in the victor's force level and
time. Convexity of the instantaneous casualty-exchange ratio is shown to
imply convexity of the decision criterion so that conditions of decreasing
marginal returns may be identified also without solving the combat equations.
The optimal initial-commitment decision is shown to be sensitive to the decision
criterion for fixed force-ratio breakpoint battles.
Type
Technical Report
Description
Series/Report No
Department
Organization
Graduate School of Operational and Information Sciences (GSOIS)
Identifiers
NPS Report Number
NPS 55-77-2
Sponsors
supported by the Foundation Research Program of the Naval Postgraduate School with funds provided by the Chief of Naval Research
Funder
N0001477WR70044
Format
Citation
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.