THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY, SEVILLA, OCTOBER, 1986. 373 -
A Case Study in Army Combet Modelling
E. F, Wolstenholme
A.S. Al-Alusi
UNIVERSITY OF BRADFORD
ABSTRACT
This paper demonstrates en approach to army combat modelling using
system dynamics. A model is presented of an enemy ground advance which
is used to analyse how various edeptive strategies by the attacker and
defender during the advance can leed to different outcomes when the
combatants meet. Particuler attention is paid to the development of
performance measures and to the interpretation of results in terms of the
underlying feedbeck structure of the model.
INTRODUCTION
During the last two years, @ series of investigatons have been carried out
within the University of Bredford Menagement centre into the use of
system dynamics as @ modelling methodology for army defence analysis.
The objectives of the work have been to examine end demonstrete the use
of the approach for creating insights into situations involving complex
operational interactions between personnel and equipment. The purpose of
this paper is to communicate one particular model developed during this
Programme of work which captures the basic philosophy of the approach es
well es clearly demonstrating the type of insight which can be echieved.
This is referred to as the armoured advance model.
374 =~ THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTUBEK, 1986.
THE ARMOURED ADVANCE MODEL
Most traditional modelling of ground conflict has centred on essessing the
actual outcome resulting from the face to face confrontetion of two
combatants. Such low aggregation, high resolution modelling is not
considered here. Instead emphesis is placed upon assessing the use of
indirect strategies simed et avoiding situations occurring where face to
fece confrontation will lead to e defeat. That is, in the defenders terms,
the aim is to design indirect strategies which will result in reducing
those characteristics of the attacker (such es speed and force size) to on
‘acceptable level on arrival et the attackrs position. Conversely, in the
attackers terms the aim is to design strategies which will result in.
Preserving such characteristics. This approach is in line with @ growing
trend in defence enalysis towards the modelling of commend, control,
communication and intelligence interactions (Huber, RK. 1985), rether
thon detailed combat.
The objective of the emoured advance model was therefore to investigate
the merits of alternative defensive (blue) strategies for slowing down the
advance of an attacking force (red), under a number of edaptive strategies
by the latter concerning the timing of it's formation changes. General
defence thinking on this issue suggests thet basically red’s alternatives
‘ore to change to more widely dispersed formations eerly in the edvance, in
order to reduce their vunerability, or to maintain a dense formation for as
long as possible, since a higher speed is atteinable.
This is 6 diffuse, ambiguous and subjective question, in thet yunerability
‘and dispersion are concepts which are difficult to define and quantify. it
is also complicated by contsining both spacial and time dimensions.
A system dynamics model was developed using © stepwise epproach to
conceptuslisstion (Wolstenholme and Coyle 1983) end this resulted in a
sizeable quontitative model. Figure 1 shows © reosonably detoiled
qualitative diagram of this model which was used to communicate the
relationship between the model and reality. The actual movement of red's
‘advance can be treced by the variables across the top of the diagram.
Units for the advence are assembled in o pre-defined area and advance
tokes place firstly, in a dense ‘battalion’ formation, secondly in a slower
but more dispersed ‘company column’ formation and finally in a very slow,
very dispersed ‘platoon column’ formation. The key strategy variables for
red in this chain are the rates of deployment between formations, which
ore considered to take place at @ fixed distance (preplanned response) or a
Variable distance (adaptive response).
‘THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
375
te of deployment
number ii Bley! number red
number tv ‘i
advancing in a advancing rate of deployment ygvancing “gang Units
platoon platoon columns. in company into company columns inbattation rae "
Nut t solu assem!
, ’ J { columns in Bata ssembly
rate of dist. planned moment
ee cMied planned distance Bae at fateot distance am, rate
to platoon attrition to of
column deployment in Company company distance attrition
4 ‘columns 4 column covered
Cue A : deployment in battalion
defence fixed ae productivity formation
force. Planned 2 oer:
distance change shell fixed variable | rate | ogtetivit
of distance | (attrition) | planned planned ¢|P i
distance distance | change Las
speed eel
rate <— 5! scheduled of | attrition)
of + momentum’ distance
recovery — TOmparny
AS columns: scheduled
a number + speed
‘speee productivity advancing in
hath productivity}
ate PE iedated battalion per
schedoled of + (speed) sehe cae formation i
i speed
spre Secrease ¢ (speed)
in rate of recovery J | rate
speed density of speed oe t
decrease
Sompeny spre Gensits
speed columns criterion ShteO x
Spaley policy battalion
weapon weapon formation
delivery ————_—_J selivery
rate ———> rate
ce ammunition 4
ammunition «J stock
stock distance distance
criterion criterion
policy policy
FIG.L. INFLUENCE DIAGRAM
OF THE ARMOURED
ADVANCED MODEL
376 — THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
The veriable distance strotegy represents on attempt by red to deley
formation change to teke sdventage of the higher scheduled speed
associeted with the denser formations and a number of secondary
strategies for red exist by which to determine the variable distance.
These could be to base the decision on say speed or momentum (speed *
number advancing), with the formation change point being delayed more
end more @s these veriables fall behind schedule es @ result of blue fire.
Momentum is an often used concept in military analysis but is not often
used as 6 quanitetive measure es here. The key strategic variable from
blue’s point of view is of course the effectiveness of it's fire delivery, in
terms of both red speed reduction and red attrition. It will be seen thet
the effectiveness of fire is defined in Figure 1 in terms of both speed
reduction and attrition and thet it is itself mede to be 6 function of the
rote of weapon delivery and the productivity per delivery. Productivity of
fire is en interesting concept which is snalogous to managerial labour
productivity. This productivity is obviously a function of the distance
over which fire takes place (accuracy) and the density of the target, which
is in turn 6 function of the type of formation assumed by red. There are
verious strategies availeble to blue for the delivery of fire. Three.
possibilities for this might be to base fire on red distence or speed (shown
in Figure 1) or red momentum. It is assumed in Figure 1 that red can
recover speed where blue firing ceases.
The lower pert of the diagram in Figure 1, which displays variables
relating to blue fire delivery, speed and distance, ore replicated for the
bettelion end company column situations and various links between the
two are omitted for clarity. The most important of these ere, perhaps, the
constraints associated with the red decision to change between
formations. In the case of red using distance os a formation change
decision variable, it was assumed that there would be no point in red
holding on to a battalion formation beyond the point at which it's speed in
this formation fell below that achievable in company columns. The same
argument applied under a formation change decision based on momentum,
when the momentum in battalion formation fell below that ochievable in
company columns.
The above description is an overview outline of the model structure and
major strategy options which the model is capable of addressing. Some
examples of results from the model are contained in Tables 1 and 2. Here,
6 matrix output of results for each red/blue stretegy combinstion is
shown. The performance measures used were the time to company column
deployment, the total time for red to reach blue, the size of the red force
RED STRATEGY
Company Column Deployment at a Fixed Distance Company Column Deployment at @ Variable Distance
BLUE Time to jTime for | Size OF | Monentun || Tine to Time for Size of | Momentus
company | red to company red to
STRATEGY column reach on et | unite) colunn reach oe eres’? | cunits)
deployment | blue fositios deployment blue position
(hours) (hours) (anita) ours) (hours) (hours) (unite) (hours:
x
Zire 4.44 10,25 1598.50 155.37 4.75 9.25 1592.30 172.78
delivered on = = = .
a distance
criterion
Fire
delivered 5.88 13.19 1295.00 98.17 7.62 10.56 1098.00 103.99
on a speed
criterion
Fire .
delivered on
iB eoncataa’ 6.75 14,38 1219.00 84.80 9.06 10,81 1000.00 92.51
criterion : 3
TABLE 1 mple of model results for the o
light fire delivery by blue
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RED STRATEGY
Company Column Deployment at a Fixed Distance Company Column Deployment at a Variable Distance
Size or
BLUE Time to {Time for | sea torce | Momentum || Time to Time tor | Size of Momentum
ereatecy company red to ea érxival. company red to red ater
solus at blue (Waits) column reach ct blue | Cuntts)
deployment position deployment blue . aa iewea ——
(hours) (units) (hours) (hours) (hours) arene (hours)
Fire :
delivered
ev iitusce 4.38 10,25 1526.30 148.90 4,813 9,13 1517.20 168.46
criterion
Fire .
bipetien 6.32 14.63 726.00 49,70 4.87 16.38 864,00 52,00
eriterion
Fire
oe 6.56 13.50 787.00 58.34 8.25 9.56 707,00 73.97
criterion ‘
TABLE 2 Example of model results for the case of
heavy tire delivery by blue
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THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 379
on arrival and the momentum of the red force on errival (errival
size/arrivel time). In each table two red strategies are defined for
company column deployment and three blue strategies are defined for fire
delivery. Table 1 is for @ low rate of fire delivery and Table 2 for a high
rate of fire delivery. Some overall conclusions can be drawn for this set
of results. First from red’s point of view. When feced with a low rate of
blue fire delivery and if the major objective is to advance in the minimum
time, it would appear best for red to delay formation change for as long as
possible. However, to maximise the numbers arriving then red should
change formation as early as possible. in order to maximise the
momentum of errival then again red should defer formation change for as
long es possible. When faced with 0 higher rate of fire similar conclusions
follow except when the previously defined constraints come into play. In
particular the effect of the constraints can be seen in the second row of
results in Table 2, when fire is delivered on a speed criterion. Here, a very
early change of formation tekes place by red on the variable distance
strategy, the totel time of red to advance is increased but more units
arrive; again giving @ better arrival momentum.
From blue's point of view the results indicated that it was olways
Preferable to deliver fire on a red speed, rather than red distance,
criterion under eny of the performence measures. It would appear that it
was better still, for blue to deliver fire on @ criterion of red momentum.
However, this strategy did not ultimately generate as low a final level of
red momentum as that achieved when fire was delivered on 0 speed
criterion. This latter result, which is depicted in Table 2, is again
apperentiy associated with the activation of the speed constraint.
The ebove preferences in blue fire delivery criteria would appear to be
confirmed in terms of the efficiency of ammunition useage as shown in
Table 3. Table 3 also suggests that light fire is more economical than
heavy fire in reducing red’s momentum.
THE UNDERLYING FEEDBACK MODEL
Whilst the foregoing model and results presentation is perhaps adequate
and may answer some specific questions, it is possible to generate more
general insight and understanding by developing a simplified but very
explicit qualitative model of the feedback processes at work. Such a
model will now be developed and used to explain the previous results.
However, @ certain amount of abstraction is involved in the creation of
such 6 diagram in this case, and the resultent model will be seen to lose
it's one to one correspondence with the physical reality modelled which
existed in Figure 1.
RED STRATEGY
Company Column Deployment at a Fixed Distance
Company Column Deployment at a Variable Distance
‘Average ‘Average
BLUE ea Shella Reduction Bae fomeneun Shells Reduction
in momentum in momentum
STRATEGY Editors Delivered per a Pine Delivered per
eri 1000 shells osition 1000 shells
Fire
Delivered| light 155,37 ane 2.74 172.78 3308 4,39
on
Distance
Griterdon) heavy, 148.90 6656 6.10 168.46 5437 3.86
Fire
Delivered} light 98.17 8837 10.33 103.99 6956 12.20
on
Speed
Criterion} heavy 49.70 19406 7.20 52.10 22500 6.10
Fire
Delivered} light 84,80 9868 10.80 92.54 6912 14,00
on
Momentum
Criterion] heavy 58.34 16600 7.86 73.98 9281 a2i4a
TABLE 3 Comparison of the average reduction in red momentum
achieved per 1000 shells fired, for each combination
of red/blue strategy.
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THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986. 381
Figure 2 shows on influence diagram of the basic mode! feedbeck structure
focusing on the effectiveness of blue fire in reducing the speed of the red
advance, when the planned distence to each formation change is based ona
comparison of the actual to scheduled distance-achieved. it will be seen
from Figure 2 thet four major feedback loops exist. The one around the
left hand side of the diagram (loop A) is @ negative loop by which red
attempts to control (maintain) it's speed. As actual speed declines (os a
result of blue fire) and the achieved distance (relative to the scheduled
distance) falls, the planned distance to formation change is put beck;
resulting in @ leter formation change, higher density of formation and
higher scheduled speed. Speed erosion within a formation will, however,
take place because as Jong &s 4 high density formation is maintained the
productivity of blue fire and hence it's effectiveness, remoins high. This
effect can be traced at around the positive feedback loop on the right hand
side of the diagram (loop B). Ultimetely speed erosion will short circuit
both of these loops via the dotted constreint link, which will momentarily
reverse the polarity of both loops.
The other two feedback loops in Figure 2 relate to the effect of reds
distance of odvance on the productivity of blue fire (loop C; a negative
Joop) and the ‘rete of recovery of speed’ loop (loop D) by which red's speed
rises, whenever blue fire ceases.
It is importent to note here that red size as clearly indicated in Figure 2
does not pley 8 role in determining red strategy, but it is purely an output
voriable,
Figure 2 provides a clear explenation of the previously presented results
and conclusions for red stretegy, which centres on the effect of the
important but rather inconspicuous loop, in Figure 2, associated with
speed recovery (loop D), and the way in which this reletes to the strategy
of the combatants. The basic insight generated here is thet speed end s‘ze
as system variables have very different characteristics. The most
important of these differences is that the former is recoverable by red if
blue firing stops, but thet the letter is not. Consequentiy, momentum es 0
system veriable hes o recoverable ond @ non-recovereble component. As e
result, when momentum is used as a system performance measure, there is
on underlying downward trend in performance as blue fire tokes place.
This is recoverable, but then only in part, when firing stops. This expleins
why light (or more accurately, spasmodic) fire by blue is the least
effective strategy for blue and will result in high momentum being
achieved by red ond a preferred tendency by red to maintain e dense, higher
382 THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
DENSITY
OF RED
UNITS r
-A - SCHEDULED +B
T SPEED IN
PROPOSED +
RATE OF FORMATION ERE.
CHANGE ¢—_—J TOFORMATION —- PRODUCTIVITY
oFRED CHANGE POINT OF BLUE FIRE
+ PLANNED
‘ ¢ DISTANCE *
SCHEDULED \ TO FORMATION
SPEED OF t CHANGE POINT
RED | -
ADVANCE ‘
1 DISTANCE OF EFFECTIVENESS
; RED ADVANCE OF BLUE FIRE
. +
ACTUAL
+ SPEED OF RATE OF
RED ADVANCE BLUE
+ “ FIRE
&) SIZE OF _
- RED FORCE
RATE OF RECOVERY
OF RED SPEED OF
ADVANCE
*
TIME OF 4 MOMENTUM size oF
RED OF RED € RED
ARRIVAL ARRIVAL ARRIVAL
AT BLUE AT BLUE AT BLUE
POSITION POSITION POSITION
FIG.2. UNDERLYING FEEDBACK
STRUCTURE OF THE MODEL
(WITH RED FORMATION CHANGE DECISION
BASED ON THE DISTANCE OF THE RED ADVANCE.
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986. 383
speed formation. Conversely, heavy (or more accurately, continuous) fire
is the most effective strategy for blue and, if maintained, will result in
complete destruction of red unless the latter operates 6 constraint for
aborting from the denser formation, when an intolerable situation occurs.
Even when this results in an early formation change, however, it would
eppear thet red’s errivel momentum cen still be higher under @
veriable-distance, formation change strotegy, than under a fixed distance
strategy. However, not significantly so since, es indiceted in Figure 2, it
must elways be detrimental to red to eliminate it's opportunity to recover
speed. fi
Figure 3 shows 4 revised influence diagram which ceptures the effect of
red basing it’s planned distance to formation chenge on the product of the
red size and speed (momentum). This figure incorporates a momentum
constraint based on a scheduled momentum for the next formation, which
is 0 product of the scheduled speed and scheduled (minimum) size of force
tolerable for entry to the next formation. The purpose in showing this
figure is to emphasise the fact that the use of red size, os 6 product of
speed to create @ momentum decision veriable to determine the planned
distence is formation change, does in no way change the polerity of the
loops described in Figure 2. Figure 3 is therefore identical in feedback
terms to Figure 2.
Figure 3 aise includes the feedback loops associated with blue's strategies
for fire delivery. That is, based on red's achieved distance, speed or
momentum. These ere ol] negative feedback loops which attempt to
control red’s speed and size. This presentation focuses attention on the
different degrees of directness of these strategies ond implies, as born
out by the quantitative results, thet the most effective strategies will be
the most direct ones (speed or momentum besed). However, once again, on
important consideration is the consistency of fire delivery. It is
important to note here thet it is often the case that firing is deliberately
switched on and off os 4 result of the definition of the fire delivery
strategy itself; for example where firing is switched off when momentum
or speed ore reduced to pre-set lower limites and switched on again when
these variables reach pre-set upper limits. An intermittent blue fire
strategy constructed in such 6 seemingly logical wey will, in fact, be self
defeating as it facilitates recovery of speed and momentum by red. A
further factor brought to the fore here is that of the compatibility
between the criterion for fire delivery nd the performance measure used.
For example, if fire delivery is based on maintaining momentum at 6 given
target level and performance is messured in terms of momentum, then the
performence will be determined by the terget set by the strategy which
moy not be, ultimately, as low as intended.
Sa MM Sk ch cc tc ta al ad th lhc ich amin: Hilti: tailed
DENSITY
{— OF RED
UNITS
. SCHEDULED +B
tT MOMENTUM IN
PROPOSED +
SCHEDULED
RATE OF FORMATION MOMENTUM
CHANGE q——I TOFORMATION PRODUCTIVITY
OF RED —_ CHANGE POINT OF BLUE FIRE
FORMATION -
= s PLANNED
wv: DISTANCE
SCHEDULED ! TO FORMATION
SPEED OF CHANGE POINT
RED f .
ADVANCE © *
— — = momentum EFFECTIVENESS
OF RED ADVANCE OP BLUE FIRE
ACTUAL . , ae OF
Ny’ SPEED OF SIZE OF _ “SSUE
oo ADVANCE THE RED IRE ox
FORCE *mt
Vv.
RATE UF £) DISTANCE OF
OF RED SPEED OF + RED ADVANCE
ADVANCE
SE
FIG. 3 UNDERLYING FEEDBACK
_ STRUCTURE OF THE MODEL
(WITH RED FORMATION CHANGE DECISION
BASED ON THE MOMENTUM OF THE RED ADVANCE
AND SHOWING THE BLUE FIRE DELIVERY STRATEGIES.
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 385
FACILITATING MODEL DEVELOPMENT AND FURTHER INSIGHT
The parallel development of quantitative and qualitative models as used
here to aid and extend problem enalysis is formally and generally shown in
Figure 4. This figure also suggests that the insights gained can leed to
further model development.
An example of the use of this procedure in the current defence model
centres on the possibility of changing the assumption in the model
concerning the fact that @ change of formation would only take place
beyond a fixed distance. An elternative approach would be to allow
formation change earlier, if say, cumulative losses became intolerable.
This effect could be superimposed in peraliel with allowing the existing
deferral of formation change due to excessive speed loss. Such a
possibility is suggested directly as @ result of spotting the lack of 4
direct feedback link in the current model between red size of advance end
the rate of formation change in Figures 2 and 3. The inclusion of such a
negative link would create a more direct trade-off in the model between
the speed ond attrition effects of blue fire on the rate of red formation
change. A second example suggested by the existing queltiative model is
the possibility of introducing other alternative strategies by which red
could counter the effects of blue fire. One of these would be to introduce
a recoverable element to the size of the red force, say by reinforcement.
This would mean the advance of a second wave and have consequences for
the speed of advance of the first wave, which could be traced out using the
model. A third example might be to use the size of the red force as a
direct determinant of blue fire via 6 forme! surveillance sector of the
model.
CONCLUSIONS
This paper has presented a case study in the application of system
dynamics to the analysis of ground defence problems. It demonstrates how
low resolution, high aggregation models can be used effectively to analyse
the build up to situations of direct confrontation in terms of the indirect
ond adaptive strategies of combetents. Further, that the results from such
@ model can provide a quantitative assessment of the outcome from
selected strategy combinations. In addition to quantifying the effects of
specific strategies, however, it is also demonstrated that insight cen be
gained from wuch a model into e much more general and wider portfolio of
strategies available to both sides, by use of quelitative feedbeck analyers.
386 = THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
SIMPLIFIED
QUALITATIVE ————————_————-- 0 ABSTRACTED
FEEDBACK QUALITATIVE
MODEL
QUANTITATIVE > roveL
SIMULATION RESULTS
MODEL —>,
AND
CONCLUSIONS
SPECULATIONS ¢€——— EXPLANATIONS
AND INSIGHTS
FIG.4. THE PROCESS OF PARALLEL
DEVELOPMENT OF QUALITATIVE AND
QUANTITATIVE MODELS IN SYSTEM
DYNAMICS STUDIES
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 387
ACKNOWLEDGEMENT
This work hes been carried out with the support of the Procurement
Executive, Ministry of Defence.
388 = THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986
REFERENCES
Huber, R. K. (1985). On Current Issues in defence Systems Analysis and
Combet Modelling, OMEGA International Journal of Management
Science, vol. 13, no. 2, pp. 95-106.
Wolstenholme, E. F. and R. G. Coyle (1983). The Development of System
Dynamics as 6 Methodelogy for System Description end Quelitetive
Anelysis. Journal of the U.K. Operational Research Society, vol. 34,
no. 7, pp. 569-581.
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