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Defence operational analysis using system dynamics
10
European Journal of Operational Research 34 (1988) 10-18 North-Holland
Defence operational analysis using system dynamics E.F. W O L S T E N H O L M E
System Dynamics Research Group, University of Bradford, Management Centre, Emm Lane, Bradford, West Yorkshire BD9 4JL, UK Abstract: This paper reflects on experiences gained in applying system dynamics as a modelling methodology to create a feedback perspective of army defence situations. The ideas of the approach are outlined, and a case study model presented to demonstrate the type of insight which can be generated by the method. This example is further used to make a comparison between system dynamics and other methods of defence operational analysis. Keywords: Computers, control, military, simulation, practice
Introduction There is a growing trend in defence analysis away from the modelling of combat related process and towards the modelling of command, control, communication and intelligence interactions [1]. This trend has been exemplified during the last 18 months by investigations carried out at Bradford University Management Centre into the use of system dynamics as a modelling methodology for army defence analysis. The objectives of this work have been to examine and demonstrate 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 some of the experiences gained from this work and to contrast the approach with main stream defence operational analysis. The methodology of system dynamics was conceived and developed during the late 1950's [2], and, although early work was in policy design in the management field [3], the subject became primarily known during the late 1960's for it's application at the macro level to global and urban modelling [4]. Although macro applications are
Received April 1986; revised November 1986
still in evidence [5], the scale of applications has generally reduced and diversified during the 1970's. More recent work has seen an expansion on the development of sub-techniques and philosophy of the subject [6,7,8]. In particular the method has recently been communicated as a full scale systems methodology [9], capable of providing the much sought after compromise between the systemic ideals of holism and the practical necessities of real world problem solving. This definition is as follows: " A rigorous method of system description, which facilitates feedback analysis, usually via a continuous simulation model, of the effects of alternative system structure and control policies on system behaviour". System dynamics focuses on the conceptualisation of models in a feedback perspective, which views a system from a 'stand-off' position, as being composed of a series of processes, where physical resources more through the system over time under the control of information feedback from the states of the processes. This facility of the method of explicitly and continuously model the control or self adaptiveness of systems is a unique characteristic of the approach, and allows the concept of strategy to be built into models. The procedure for applying the method is to
0377-2217/88/$3.50 © 1988, ElsevierSciencePublishers B.V. (North-Holland)
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E.F. Wolstenholme / Defence operational analysis using system dynamics
develop a cause and effect diagram (influence or causal loop diagram) of the major flows of resources and information in the system, which relate to an observed cause for concern. These qualitative diagrams are a first step in moving towards a quantitative model and attempt to capture the underlying major feedback structure of the model. This is a key issue in retaining understanding and simplicity. There are a variety of approaches by which to arrive at such diagrams. If the real behaviour of major system variables is available (a reference mode), it may be possible to immediately hypothesise the feedback structure of the system which is responsible for the observed behaviour. However, if such information is not available a more systematic, stepwise procedure for the development feedback structure must be followed [10]. Irrespective of the method of conceptualisation, a major strength of the method lies in the fact that the qualitative model can be validated and developed to quantitatively test out the effects of strategy options on the behaviour of the system. This is achieved by taking advantage of the rigorous nature of the diagrams and the ease with which they can be translated into simulation models. This translation usually involves the building of more detail into the diagrams; the end point being a flow diagram for the computer model. One of the major problems with developing computer models of complex systems is that the models themselves become more and more complex. This frequently results in them assuming a life and purpose of their own, quite separate from their role in facilitating understanding of the system which they represent. This tendency is minimised in system dynamics by maintaining, in parallel, with the complex simulation model a simplified diagrammatic, qualitative model of the underlying feedback structure of the quantitative model. This might be an updated version of the original diagram from which the qualitative model was developed or an abstracted version of it. The important point is that the two models must be developed together and it is only when the quantitative model development rate outstrips the qualitative that confusion arises. The qualitative model promotes a means to interpret the results of the quantitative model to create a lasting explanation of the operation of the system and a basis for further qualitative or quantitative analysis. The
SIMPLIFIED QUALITATIVE
OR ABSTRACTED
FEEDBACK MODEL *
QUANTITATIVE ~SIMULATION
/
~nuv~lb~n~EL
• QUALITATIVE r MODEL I I •
RESULTS
I
CONCLUSION
~'~
SPECULATIONS
~
EXPLANATIONSql ~ AND INSIGHTS
Figure 1. The process of parallel development of qualitative and quantitative models in system dynamics studies
cycle of model development suggested by these procedures is shown in Figure 1. The use of such ideas are, in practice, quite subtle and the remainder of this paper is concerned with a case study to demonstrate their application. Firstly, the purpose of the study will be presented together with the development of a qualitative and quantitative model for it's analysis and some specific results and conclusions. That is following the conventional route through the inner loop of Figure 1. Secondly, an abstract qualitative model will be developed to assist the interpretation and generalisation of the results. That is, following the outer loop in Figure 1.
A demonstration model
One of the major advantages of the system dynamics methodology is that it facilitates a modular approach to model creation. Individual pieces of the total system can be modelled tested and subjected to strategy experimentation prior to their integration into a composite system model. This facility has been well used in the current study. A highly aggregated low resolution model was first constructed of the general indirect fire command control cycle. This model captured the general essence of the major composite activities of this cycle (namely enemy advance, surveillance, fire request, fire despatch and fire effects) and investigated various fire allocation policies over a number of axes of advance. Subsequent work has been involved with increasing the degree of resolution of each of these activities in turn in a modular fashion. In order to demonstrate the capability of the methodology, a simplified description of one of
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E.F. Wolstenholme / Defence operationalanalysis using system dynamics
the models developed concerning enemy advance will be presented here. The objective of the model was to investigate the merits of alternative defensive (blue) strategies for slowing down the advance of an attacking force (red), under a number of adaptive strategies by the latter concerning the timing of it's formation changes. General defence thinking on this issue suggests that basically red's alternatives are to change to more widely dispersed formations early in the advance, in order to reduce their vulnerability, or to maintain a dense formation for as long as possible, since a higher speed is attainable.
number advancing in platoon columns •
of breakthrough rate
rate of deplogrnerlt in to platoon columns
number number advancif~g rate of deployment advancing in company into compan9 columns in battalion columns ~ L.
' 1
,
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istanc
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,4W
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rateI
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I productivity per
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"~'I"
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tl I'
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ammunition ~ stock
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t
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~--A'I
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speed criterion policy
in speed I weapon delivery
, ammunition stock
•
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•
dlslance
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Figure 2. Influencediagram of the armoured advancemodel
productivity per
shell (attrition)
speed
advancing " I
weapon
~ delivery ~_r rate
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÷
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This is a diffuse, ambiguous and subjective question, in that vulnerability and dispersion are concepts which are difficult to define and quantify. It is also complicated by containing both spacial and time dimensions. A system dynamics model was developed using a stepwise approach to conceptualisation and this resulted in a sizeable quantitative model. Figure 2 shows a reasonably detailed 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 traced by the variables across the top of the diagram. Units for the advance are assembled in a pre-
policy
productivitl per shell (speed)
density in battalion formation
E.F Wolstenholme / Defenee operational analysis using system dynamics
13
a function of the distance over which fire takes place (accuracy) and the density of the target, which is in turn a function of the type of formation assumed by red. There are various strategies available to blue for the delivery of fire. Three possibilities for this might be to base first on red distance or speed (shown in Figure 2) or red momentum. It is assumed in Figure 2 that red can recover speed where blue firing ceases. The lower part of the diagram in Figure 2, which displays variables relating to blue fire delivery, speed and distance, are replicated for the battalion and company column situations and various links between the two are omitted for clarity. The most important of these are, perhaps, the constraints associated with the red decision to change between formations. In the case of red using distance as 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 m o m e n t u m in battalion formation fell below that achievable 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. The model was programmed as a quantitative model using DYSMAP (Dynamic System Model Analysis Programme) [11].
defined area and advance takes place firstly, in a dense 'battalion' formation, secondly in a slower but more dispersed ' c o m p a n y column' formation and finally in a very slow, very dispersed ' p l a t o o n column' formation. The key strategy variables for red in this chain are the rates of deployment between formations, which are considered to take place at a fixed distance (preplanned response) or a variable distance (adaptive response). The variable distance strategy represents an attempt by red to delay formation change to take advantage of the higher scheduled speed associated 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 m o m e n t u m (speed * number advancing), with the formation change point being delayed more and more as these variables fall behind schedule as a result of blue fire. M o m e n t u m is an often used concept in military analysis but is not often used as a quantitative measure as 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 that the effectiveness of fire is defined in Figure 2 in terms of both speed reduction and attrition and that it is itself made to be a function of the rate of weapon delivery and the productivity per delivery. Productivity of fire is an interesting concept which is analogous to managerial labour productivity. This productivity is obviously
Table 1 Example of model results for the case of light firing delivery by blue Blue strategy
Red strategy Company column deployment at a fixed distance
Company column deployment at a ,variable distance
Time to company column deployment (hours)
Time for red to reach blue (hours)
Size of red force on arrival (units)
Momentum on arrival (units) (hours)
Time to company column deployment (hours)
Fire delivered on a distance criterion
4.44
10.25
1598.50
155.37
4.75
Fire delivered on a speed criterion
5.88
13.19
1295.00
98.17
Fire delivered on a momentum criterion
6.75
14.38
1219.00
84.00
Times for red to reach blue (hours)
Size of red force on arrival (units)
Momentum on arrival (units) (hours)
9.25
1592.30
172.78
7.62
10.56
1098.00
103.99
9.06
10.81
1000.00
92.51
E.F.. Wolstenholme / Defence operational analysis using system dynamics
14
Table 2 Example of model results for the case of heavy firing delivery by blue Blue strategy
Red strategy Company column deployment at a fixed distance
Company column deployment at a variable distance
Time to company column deployment (hours)
Time for red to reach blue (hours)
Size of red force on arrival (units)
Momentum on arrival (units) (hours)
Time to company column depolyment (hours)
Fire delivered on a distance criterion
4.38
10.25
1526.30
148,.90
4.813
Fire delivered on a speed criterion
6.32
14.63
726.00
49.70
Fire delivered on a momentum criterion
6.56
13.50
878.00
58.34
Times for red to reach blue (hours)
Size of red force on arrival (units)
Momentum on arrival (units) (hours)
9.13
1517.20
168.46
4.87
16.38
864.00
52.00
8.25
9.56
707.00
73.97
can be drawn for this set of results. First from red's point of view. When faced 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 m o m e n t u m of arrival then again red should defer formation change for as long as possible. When faced with a higher rate of fire similar conclusions follow ex-
Some examples of results from the model are contained in Tables 1 and 2. Here, a matrix output of results for each r e d / b l u e strategy combination 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 on arrival and the m o m e n t u m of the red force on arrival (arrival size/arrival time). In each table two red strategies are defined for company column deployment and three blue strategies are defined for fire delivery. Some overall conclusions
Table 3 Comparison of the average reduction in red momentum achieved per 1000 shells fired, for each combination of r e d / b l u e strategy Blue strategy
Red strategy Company column deployment at a fixed distance Red momentum on arrival at blue position
Fire delivered on distance criterion Fire delivered on speed criterion Fire delivered on momentum criterion
Shells delivered
Company column deployment at a variable distance Average reduction in momentum per 1000 shells
Red momentum on arrival at blue position
Shells delivered
Average reduction in momentum per 1000 shells
light
155.37
4418
7.71
172.78
3306
4.39
heavy
148.90
6656
6.10
168.46
5437
3.86
light
98.17
8837
10.33
103.99
6956
12.20
heavy
49.70
19406
7.20
52.10
22500
6.10
light
84.80
9668
10.80
92.51
6912
14.00
heavy
58.34
16688
7.86
73.98
9281
12.44
E.F. Wolstenholme / Defence operational analysis using system dynamics
cept 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 takes place by red on the variable distance strategy, the total time of red to advance is increased but more units arrive; again giving a better arrival momentum. From blue's point of view the results indicated that it was always preferable to deliver fire on a red speed, rather than red distance, criterion under any of the performance measures. It would appear that it was better still, for blue to deliver fire on a 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 a speed criterion. This latter result, which is depicted in Table 2, is again apparently associated with the activation of the speed constraint. The above 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, the analysis of a system dynamics model does not terminate at this point. 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, a certain amount of abstraction is involved in the creation of such a diagram in this case, and the resultant model will be seen to lose it's one to one correspondence with the physical reality modelled which existed in Figure 2. Figure 3 shows an influence diagram of the basic model feedback structure focusing on the effectiveness of blue fire in reducing the speed of the red advance, when the planned distance to each formation change is based on a comparison of the actual to scheduled distance achieved. The polarity convention used in the diagram is that a
15
DENSITY
-
RATE OF CHANGE •
SCHEDULED SPEED IN PROPOSED FORMATION i
TO FORMATION
-
CHANGE POINT
• FORMATION
-
PRODUCTIVITY OF BLUE FIRE
~
DISTANCE
*~
I
DIST E OF RED ADVANCE
Q
I NESS OF BLUE g~RE
ACTUAL L ÷ SPEED OF • RED ADVANCE •
'
"Y
RATE JF RECOVERy OF RED SPEED OF ADVANCE TIME OF ÷ MOMENTUM RED OF RED ARRIVAE---~ARRIVAL ~ ~ AT BLUE AT BLUE POSITION POSITION
SIZE OF RED FORCE I
1
RATE OF BLUE
SIZE OF RED ARRIVAL AT BLUE POSITION
Figure 3. Underlying feedback structure of the model (with red formation change decision based on the distance of the red advance
positive link indicates that the head and tail variables of each arrow change magnitude in the same direction, and that a negative link indicates that they change magnitude in the opposite direction. The polarity of feedback loops are determined by multiplying together the polarity of the individual links of which they are composed. It will be seen from Figure 3 that four major feedback loops exist. The one around the left hand side of the diagram (loop A) is a negative loop by which red attempts to control (maintain) it's speed. As actual speed declines (as a result of blue fire) and the achieved distance (relative to the scheduled distance) falls, the planned distance to formation change is put back; resulting in a later formation change, higher density of formation and higher scheduled speed. Speed erosion within a formation will, however, take place because as long as a high density formation is maintained the productivity of blue fire and hence it's effectiveness, remains high. This effect can be traced out around the positive feedback loop on the right hand side of the diagram (loop B). Ultimately speed erosion will short circuit both of these loops via the dotted constraint link, which will momentarily reverse the polarity of both loops.
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E.F. Wolstenholme / Defence operational analysis using system dynamics
The other two feedback loops In Figure 3 relate to the effect of red's distance of advance on the productivity of blue fire (loop C; a negative loop) and the 'rate of recovery of speed' loop (loop D) by which red's speed rises, whenever blue fire ceases. It is important to note here that red size as clearly indicated in Figure 3 does not play a role in determining red strategy, but it is purely an output variable. Figure 3 provides a clear explanation of the previously presented results and conclusions for red strategy, which centres on the effect of the important but rather inconspicuous loop, in Figure 3, associated with speed recovery, and the way in which this relates to the strategy of the combatants. The basic insight generated here is that speed and size 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 that the latter is not. Consequently, m o m e n t u m as a system variable has a recoverable and a non-recoverable component. As a result, when m o m e n t u m is used as a system performance measure, there is an underlying downward trend in performance as blue fire takes place. This is recoverable, but then only in part, when firing stops. This explains why light (or more accurately, spasmodic) fire by blue is the least effective strategy for blue and will result in high m o m e n t u m being achieved by red and a preferred tendency by red to maintain a dense, higher 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 a constraint for aborting from the denser formation, when an intollerable situation occurs. Even when this results in an early formation change, however, it would appear that red's arrival m o m e n t u m can still be higher under a variabledistance, formation change strategy, than under a fixed distance strategy. However, not significantly so since, as indicated in Figure 3, it must always be detrimental to red to eliminate it's opportunity to recover speed. Figure 4 shows a revised influence diagram which captures the effect of red basing it's planned distance to formation change on the product of the red size and speed (momentum). This figure incorporates a m o m e n t u m constraint based on a
DENSITY OF RED UNITS -
SCHEDULED MOMENTUM IN PROPOSED RATE OF FORMATION CHANGE •• • I OF RED • ~ FORMATION i SCHEDULED SPEED OF RED ADVANCE
I
~*~lw SCHEDULED MOMENTUM PRODUCTIVITV TO FORMATION CHANGE POINT OF BLUEFIRE
PLANNED ~~EFFEC~! CHANGEdiIIOINT C
I NESS OE BLUEFIRE
-- -- " MOMENTUM OF RED ADVANCE I%~
ACTUAL • * SPEED OF • RED ADVANCE
-r-OT-T L AOV.NE
[,,l
-
DISTANCE 0E ÷ RED ADVANCE
RATE OF BLUE
÷~}il
Figure 4. 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
scheduled m o m e n t u m for the next formation, which is a 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 emphasize the fact that the use of red size, as a product of speed to create a m o m e n t u m decision variable to determine the planned distance is formation change, does in no way change the polarity of the loops described in Figure 3. Figure 4 is therefore identical in feedback terms to Figure 3. Figure 4 also includes the feedback loops associated with blue's strategies for the fire delivery. That is, based on red's achieved distance, speed or momentum. These are all 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 and implies, as born out by the quantitative results, that the most effective strategies will be the most direct ones (speed or m o m e n t u m based). However, once again, an important consideration is the consistency of fire delivery. It is important to note here that it is often the case that firing is deliberately switched on and off as a result of the definition of the fire delivery strategy itself; for example where firing is switched off when m o m e n t u m or speed are reduced to pre-set lower
E.F. Wolstenholme / Defence operational analysis using system dynamics
limites and switched on again when these variables reach pre-set upper limits. An intermittant blue fire strategy constructed in such a seemingly logical way 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 and the performance measure used. For example, if fire delivery is based on maintaining momentum at a given target level and performance is measured in terms of momentum, then the performance will be determined by the target set by the strategy which may not be, ultimately, as low as intended.
Facilitating model development and further insight One of the most important consequences of being able to communicate an explanation of model results in terms of a simplified underlying feedback structure of the model, is that it is possible to generate further insights into what might happen in other experiments on the model or under different modelling assumptions. A certain amount of speculation is always possible outside the boundaries of the model results by using the framework of the qualitative model. These modifications can later be built into the quantitative model and the cycle of model refinement continued. 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 a change of formation would only take place beyond a fixed distance. An alternative approach would be to allow formation change earlier, if say, cumulative losses became intolerable. This effect could be superimposed in parallel with allowing the existing deferral of formation change due to excessive speed loss. Such a possibility is suggested directly as a result of spotting the lack of a direct feedback link in the current model between red size of advance and the rate of formation change in Figures 3 and 4. The inclusion of such a negative link would create a more direct trade-off in the model between the speed and attrition effects of blue fire on the rate of red formation change. A second example suggested by the existing qualitative model is the possibility of introducing other alternative strategies by which
17
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 a formal surveillance sector of the model.
The role of system dynamics in defence Defence operation analysis, certainly in the procurement area (12), is characterized by a mixture of modelling and gaming methodologies, with recent trends strongly reinforcing the role of the former. The overall purpose of such analysis is to test out the operational usefullness of equipment, based on optimized field trial data, both relative to and in combination with other equipment and under a tactical and threat setting set of scenarios. The general tendency is to model in the greatest detail and at the highest level of resolution possible, which results in very large models, often requiting a hierarchical structure. Simulation is clearly seen and used as a tool within the modelling area. The type of simulation models most commonly used are discrete event, stochastic simulation models which do not have inbuilt adaptive feedback and control. To incorporate these features usually necessitates the use of hand simulation perhaps involving user intervention. and this type of hand simulation creates a link between the modelling and gaming methodologies. The work to date on system dynamics would appear to indicate that it's most likely future role in the defence operational analysis field would appear to be in formalising the link between games and models. The incorporation of strategic rules directly into a computer simulation as facilitated by system dynamics allows two important developments in analysis. Firstly, by building blue command and control elements into the analysis, the system and the hardware can be designed and tested in terms of how it will be 'managed' in addition to the more usual determination of capacity requirements. There is, additionally, the possibility of examining the trade-off between capacity and control. Secondly, however, similar
18
E.F. Wolstenholme / Defence operationalanalysis using system dynamics
adaptive strategies can be built into the same models from ted's point of view. It is felt that current defence modelling analysis might benefit substantially from studies which incorporate adaptive rather than static opponents. Since system dynamics by definition attempts to create a systemic viewpoint linking the elements and strategies of a given situation together, it must, by necessity, be created at a lower level of resolution and at a higher level of aggregation than in conventional defence simulation models. However, as clearly shown in the demonstration model here, higher resolution can be progressively introduced into models in a controlled manner and simplified feedback structure diagrams can be used to retain understanding. In general the role of system dynamics in defence operational analysis can be currently perceived as being one of creating initial insights into problems situations prior to detailed conventional modelling. This is considered as an important role. It is only too easy in practice to develop models in detail and expound much effort before components of models are integrated together at the next level of the modelling hierarchy. If some restrictive interaction is discovered at this time much abortive work could result. It is felt that there is a great need to model higher level interactions, particularly between hardware and strategy at a much earlier stage, and that the system dynamics methodology is suited to this task.
Conclusions This paper has attempted to present, by means of a case study, how the methodology of system dynamics can provide insight into defence problems by modular model construction and b y the parallel development of sophisticated quantitative models and simplified, qualitative feedback di-
agrams. These procedures overcome m a n y of the problems associated with model complexity as well as providing a means of assessing adaptive strategic options between combatants.
Acknowledgement This work has been carried out with the support of the Procurement Executive, Ministry of Defence.
References [1] Huber, R.K., "On current issues in defence systemsanalysis and combat modelling", OMEGA InternationalJournal of Management Science 13(2) (1985) 95-106. [2] Forrester, J.W., Principals of Systems, MIT Press, Cambridge, MA, 1958. [3] Forrester, J.W., Industrial Dynamics, MIT Press, Cambridge, MA, 1962. [4] Meadows, D.H., Limits to Growth, Earth Island Press, 1972. [5] Forrester, J.W. et al., "The United States national economic model", Proceedings of the 1984 System Dynamics Conference, Oslo.
[6] Coyle, R.G., Management System Dynamics, Wiley, New York, 1979. [7] Randers, J., Elements of the System Dynamics Methods, MIT Press, Cambridge, MA. [8] Richardson, G.P., and Pugh, A.L., Introduction to System Dynamics Modelling with D~7~AMO, MIT Press, Cambridge, MA. [9] Wolstenholme, E.F., "System dynamics in perspective", Journal of the UK Operational Research Society 33 (36) (1982) 547-556. [10] Wolstenholme, E.F., and Coyle, R.G., "The development of system dynamics as a methodology for system description and qualitative analysis", Journal of the UK Operational Research Society 34 (7) (1983) 569-581. [11] Cavana, R.Y., and Coyle, R.G., DYSM~O, User Manual, University of Bradford, 1982. [12] Bailey, R.J.M., "Operational analysis in the UK Ministry of Defence--A personal view", R.A.R.D.E. internal working paper.
European Journal of Operational Research 34 (1988) 10-18 North-Holland
Defence operational analysis using system dynamics E.F. W O L S T E N H O L M E
System Dynamics Research Group, University of Bradford, Management Centre, Emm Lane, Bradford, West Yorkshire BD9 4JL, UK Abstract: This paper reflects on experiences gained in applying system dynamics as a modelling methodology to create a feedback perspective of army defence situations. The ideas of the approach are outlined, and a case study model presented to demonstrate the type of insight which can be generated by the method. This example is further used to make a comparison between system dynamics and other methods of defence operational analysis. Keywords: Computers, control, military, simulation, practice
Introduction There is a growing trend in defence analysis away from the modelling of combat related process and towards the modelling of command, control, communication and intelligence interactions [1]. This trend has been exemplified during the last 18 months by investigations carried out at Bradford University Management Centre into the use of system dynamics as a modelling methodology for army defence analysis. The objectives of this work have been to examine and demonstrate 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 some of the experiences gained from this work and to contrast the approach with main stream defence operational analysis. The methodology of system dynamics was conceived and developed during the late 1950's [2], and, although early work was in policy design in the management field [3], the subject became primarily known during the late 1960's for it's application at the macro level to global and urban modelling [4]. Although macro applications are
Received April 1986; revised November 1986
still in evidence [5], the scale of applications has generally reduced and diversified during the 1970's. More recent work has seen an expansion on the development of sub-techniques and philosophy of the subject [6,7,8]. In particular the method has recently been communicated as a full scale systems methodology [9], capable of providing the much sought after compromise between the systemic ideals of holism and the practical necessities of real world problem solving. This definition is as follows: " A rigorous method of system description, which facilitates feedback analysis, usually via a continuous simulation model, of the effects of alternative system structure and control policies on system behaviour". System dynamics focuses on the conceptualisation of models in a feedback perspective, which views a system from a 'stand-off' position, as being composed of a series of processes, where physical resources more through the system over time under the control of information feedback from the states of the processes. This facility of the method of explicitly and continuously model the control or self adaptiveness of systems is a unique characteristic of the approach, and allows the concept of strategy to be built into models. The procedure for applying the method is to
0377-2217/88/$3.50 © 1988, ElsevierSciencePublishers B.V. (North-Holland)
11
E.F. Wolstenholme / Defence operational analysis using system dynamics
develop a cause and effect diagram (influence or causal loop diagram) of the major flows of resources and information in the system, which relate to an observed cause for concern. These qualitative diagrams are a first step in moving towards a quantitative model and attempt to capture the underlying major feedback structure of the model. This is a key issue in retaining understanding and simplicity. There are a variety of approaches by which to arrive at such diagrams. If the real behaviour of major system variables is available (a reference mode), it may be possible to immediately hypothesise the feedback structure of the system which is responsible for the observed behaviour. However, if such information is not available a more systematic, stepwise procedure for the development feedback structure must be followed [10]. Irrespective of the method of conceptualisation, a major strength of the method lies in the fact that the qualitative model can be validated and developed to quantitatively test out the effects of strategy options on the behaviour of the system. This is achieved by taking advantage of the rigorous nature of the diagrams and the ease with which they can be translated into simulation models. This translation usually involves the building of more detail into the diagrams; the end point being a flow diagram for the computer model. One of the major problems with developing computer models of complex systems is that the models themselves become more and more complex. This frequently results in them assuming a life and purpose of their own, quite separate from their role in facilitating understanding of the system which they represent. This tendency is minimised in system dynamics by maintaining, in parallel, with the complex simulation model a simplified diagrammatic, qualitative model of the underlying feedback structure of the quantitative model. This might be an updated version of the original diagram from which the qualitative model was developed or an abstracted version of it. The important point is that the two models must be developed together and it is only when the quantitative model development rate outstrips the qualitative that confusion arises. The qualitative model promotes a means to interpret the results of the quantitative model to create a lasting explanation of the operation of the system and a basis for further qualitative or quantitative analysis. The
SIMPLIFIED QUALITATIVE
OR ABSTRACTED
FEEDBACK MODEL *
QUANTITATIVE ~SIMULATION
/
~nuv~lb~n~EL
• QUALITATIVE r MODEL I I •
RESULTS
I
CONCLUSION
~'~
SPECULATIONS
~
EXPLANATIONSql ~ AND INSIGHTS
Figure 1. The process of parallel development of qualitative and quantitative models in system dynamics studies
cycle of model development suggested by these procedures is shown in Figure 1. The use of such ideas are, in practice, quite subtle and the remainder of this paper is concerned with a case study to demonstrate their application. Firstly, the purpose of the study will be presented together with the development of a qualitative and quantitative model for it's analysis and some specific results and conclusions. That is following the conventional route through the inner loop of Figure 1. Secondly, an abstract qualitative model will be developed to assist the interpretation and generalisation of the results. That is, following the outer loop in Figure 1.
A demonstration model
One of the major advantages of the system dynamics methodology is that it facilitates a modular approach to model creation. Individual pieces of the total system can be modelled tested and subjected to strategy experimentation prior to their integration into a composite system model. This facility has been well used in the current study. A highly aggregated low resolution model was first constructed of the general indirect fire command control cycle. This model captured the general essence of the major composite activities of this cycle (namely enemy advance, surveillance, fire request, fire despatch and fire effects) and investigated various fire allocation policies over a number of axes of advance. Subsequent work has been involved with increasing the degree of resolution of each of these activities in turn in a modular fashion. In order to demonstrate the capability of the methodology, a simplified description of one of
12
E.F. Wolstenholme / Defence operationalanalysis using system dynamics
the models developed concerning enemy advance will be presented here. The objective of the model was to investigate the merits of alternative defensive (blue) strategies for slowing down the advance of an attacking force (red), under a number of adaptive strategies by the latter concerning the timing of it's formation changes. General defence thinking on this issue suggests that basically red's alternatives are to change to more widely dispersed formations early in the advance, in order to reduce their vulnerability, or to maintain a dense formation for as long as possible, since a higher speed is attainable.
number advancing in platoon columns •
of breakthrough rate
rate of deplogrnerlt in to platoon columns
number number advancif~g rate of deployment advancing in company into compan9 columns in battalion columns ~ L.
' 1
,
t'-~planned !
istanc
distance in company__
,4W
blue
rateI
defence
of
distance
change of distance
1,,
I productivity per
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"~'I"
to " I I ,
attrition
columns %
LM colomn l i
company
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of ~ recovery of
A
_
T
T
tl I'
in compamy columns
r•aate
of change of listance
t scheduled speed
decrease in speed
F
density
T
policy
company columns
ammunition ~ stock
t
scheduled__J
t
speed
in battalion formation
~--A'I
=
rate of recovery T I rate of s p e e d ~ of "v" decrease
speed criterion policy
in speed I weapon delivery
, ammunition stock
•
Irate
•
dlslance
distance
criterion policy
criterion
Figure 2. Influencediagram of the armoured advancemodel
productivity per
shell (attrition)
speed
advancing " I
weapon
~ delivery ~_r rate
,I,
tl
number _J I
÷
T in
speed criterion
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I
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- reds advance41-'-unit ~tart ~ in rate assembly
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This is a diffuse, ambiguous and subjective question, in that vulnerability and dispersion are concepts which are difficult to define and quantify. It is also complicated by containing both spacial and time dimensions. A system dynamics model was developed using a stepwise approach to conceptualisation and this resulted in a sizeable quantitative model. Figure 2 shows a reasonably detailed 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 traced by the variables across the top of the diagram. Units for the advance are assembled in a pre-
policy
productivitl per shell (speed)
density in battalion formation
E.F Wolstenholme / Defenee operational analysis using system dynamics
13
a function of the distance over which fire takes place (accuracy) and the density of the target, which is in turn a function of the type of formation assumed by red. There are various strategies available to blue for the delivery of fire. Three possibilities for this might be to base first on red distance or speed (shown in Figure 2) or red momentum. It is assumed in Figure 2 that red can recover speed where blue firing ceases. The lower part of the diagram in Figure 2, which displays variables relating to blue fire delivery, speed and distance, are replicated for the battalion and company column situations and various links between the two are omitted for clarity. The most important of these are, perhaps, the constraints associated with the red decision to change between formations. In the case of red using distance as 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 m o m e n t u m in battalion formation fell below that achievable 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. The model was programmed as a quantitative model using DYSMAP (Dynamic System Model Analysis Programme) [11].
defined area and advance takes place firstly, in a dense 'battalion' formation, secondly in a slower but more dispersed ' c o m p a n y column' formation and finally in a very slow, very dispersed ' p l a t o o n column' formation. The key strategy variables for red in this chain are the rates of deployment between formations, which are considered to take place at a fixed distance (preplanned response) or a variable distance (adaptive response). The variable distance strategy represents an attempt by red to delay formation change to take advantage of the higher scheduled speed associated 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 m o m e n t u m (speed * number advancing), with the formation change point being delayed more and more as these variables fall behind schedule as a result of blue fire. M o m e n t u m is an often used concept in military analysis but is not often used as a quantitative measure as 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 that the effectiveness of fire is defined in Figure 2 in terms of both speed reduction and attrition and that it is itself made to be a function of the rate of weapon delivery and the productivity per delivery. Productivity of fire is an interesting concept which is analogous to managerial labour productivity. This productivity is obviously
Table 1 Example of model results for the case of light firing delivery by blue Blue strategy
Red strategy Company column deployment at a fixed distance
Company column deployment at a ,variable distance
Time to company column deployment (hours)
Time for red to reach blue (hours)
Size of red force on arrival (units)
Momentum on arrival (units) (hours)
Time to company column deployment (hours)
Fire delivered on a distance criterion
4.44
10.25
1598.50
155.37
4.75
Fire delivered on a speed criterion
5.88
13.19
1295.00
98.17
Fire delivered on a momentum criterion
6.75
14.38
1219.00
84.00
Times for red to reach blue (hours)
Size of red force on arrival (units)
Momentum on arrival (units) (hours)
9.25
1592.30
172.78
7.62
10.56
1098.00
103.99
9.06
10.81
1000.00
92.51
E.F.. Wolstenholme / Defence operational analysis using system dynamics
14
Table 2 Example of model results for the case of heavy firing delivery by blue Blue strategy
Red strategy Company column deployment at a fixed distance
Company column deployment at a variable distance
Time to company column deployment (hours)
Time for red to reach blue (hours)
Size of red force on arrival (units)
Momentum on arrival (units) (hours)
Time to company column depolyment (hours)
Fire delivered on a distance criterion
4.38
10.25
1526.30
148,.90
4.813
Fire delivered on a speed criterion
6.32
14.63
726.00
49.70
Fire delivered on a momentum criterion
6.56
13.50
878.00
58.34
Times for red to reach blue (hours)
Size of red force on arrival (units)
Momentum on arrival (units) (hours)
9.13
1517.20
168.46
4.87
16.38
864.00
52.00
8.25
9.56
707.00
73.97
can be drawn for this set of results. First from red's point of view. When faced 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 m o m e n t u m of arrival then again red should defer formation change for as long as possible. When faced with a higher rate of fire similar conclusions follow ex-
Some examples of results from the model are contained in Tables 1 and 2. Here, a matrix output of results for each r e d / b l u e strategy combination 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 on arrival and the m o m e n t u m of the red force on arrival (arrival size/arrival time). In each table two red strategies are defined for company column deployment and three blue strategies are defined for fire delivery. Some overall conclusions
Table 3 Comparison of the average reduction in red momentum achieved per 1000 shells fired, for each combination of r e d / b l u e strategy Blue strategy
Red strategy Company column deployment at a fixed distance Red momentum on arrival at blue position
Fire delivered on distance criterion Fire delivered on speed criterion Fire delivered on momentum criterion
Shells delivered
Company column deployment at a variable distance Average reduction in momentum per 1000 shells
Red momentum on arrival at blue position
Shells delivered
Average reduction in momentum per 1000 shells
light
155.37
4418
7.71
172.78
3306
4.39
heavy
148.90
6656
6.10
168.46
5437
3.86
light
98.17
8837
10.33
103.99
6956
12.20
heavy
49.70
19406
7.20
52.10
22500
6.10
light
84.80
9668
10.80
92.51
6912
14.00
heavy
58.34
16688
7.86
73.98
9281
12.44
E.F. Wolstenholme / Defence operational analysis using system dynamics
cept 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 takes place by red on the variable distance strategy, the total time of red to advance is increased but more units arrive; again giving a better arrival momentum. From blue's point of view the results indicated that it was always preferable to deliver fire on a red speed, rather than red distance, criterion under any of the performance measures. It would appear that it was better still, for blue to deliver fire on a 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 a speed criterion. This latter result, which is depicted in Table 2, is again apparently associated with the activation of the speed constraint. The above 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, the analysis of a system dynamics model does not terminate at this point. 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, a certain amount of abstraction is involved in the creation of such a diagram in this case, and the resultant model will be seen to lose it's one to one correspondence with the physical reality modelled which existed in Figure 2. Figure 3 shows an influence diagram of the basic model feedback structure focusing on the effectiveness of blue fire in reducing the speed of the red advance, when the planned distance to each formation change is based on a comparison of the actual to scheduled distance achieved. The polarity convention used in the diagram is that a
15
DENSITY
-
RATE OF CHANGE •
SCHEDULED SPEED IN PROPOSED FORMATION i
TO FORMATION
-
CHANGE POINT
• FORMATION
-
PRODUCTIVITY OF BLUE FIRE
~
DISTANCE
*~
I
DIST E OF RED ADVANCE
Q
I NESS OF BLUE g~RE
ACTUAL L ÷ SPEED OF • RED ADVANCE •
'
"Y
RATE JF RECOVERy OF RED SPEED OF ADVANCE TIME OF ÷ MOMENTUM RED OF RED ARRIVAE---~ARRIVAL ~ ~ AT BLUE AT BLUE POSITION POSITION
SIZE OF RED FORCE I
1
RATE OF BLUE
SIZE OF RED ARRIVAL AT BLUE POSITION
Figure 3. Underlying feedback structure of the model (with red formation change decision based on the distance of the red advance
positive link indicates that the head and tail variables of each arrow change magnitude in the same direction, and that a negative link indicates that they change magnitude in the opposite direction. The polarity of feedback loops are determined by multiplying together the polarity of the individual links of which they are composed. It will be seen from Figure 3 that four major feedback loops exist. The one around the left hand side of the diagram (loop A) is a negative loop by which red attempts to control (maintain) it's speed. As actual speed declines (as a result of blue fire) and the achieved distance (relative to the scheduled distance) falls, the planned distance to formation change is put back; resulting in a later formation change, higher density of formation and higher scheduled speed. Speed erosion within a formation will, however, take place because as long as a high density formation is maintained the productivity of blue fire and hence it's effectiveness, remains high. This effect can be traced out around the positive feedback loop on the right hand side of the diagram (loop B). Ultimately speed erosion will short circuit both of these loops via the dotted constraint link, which will momentarily reverse the polarity of both loops.
16
E.F. Wolstenholme / Defence operational analysis using system dynamics
The other two feedback loops In Figure 3 relate to the effect of red's distance of advance on the productivity of blue fire (loop C; a negative loop) and the 'rate of recovery of speed' loop (loop D) by which red's speed rises, whenever blue fire ceases. It is important to note here that red size as clearly indicated in Figure 3 does not play a role in determining red strategy, but it is purely an output variable. Figure 3 provides a clear explanation of the previously presented results and conclusions for red strategy, which centres on the effect of the important but rather inconspicuous loop, in Figure 3, associated with speed recovery, and the way in which this relates to the strategy of the combatants. The basic insight generated here is that speed and size 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 that the latter is not. Consequently, m o m e n t u m as a system variable has a recoverable and a non-recoverable component. As a result, when m o m e n t u m is used as a system performance measure, there is an underlying downward trend in performance as blue fire takes place. This is recoverable, but then only in part, when firing stops. This explains why light (or more accurately, spasmodic) fire by blue is the least effective strategy for blue and will result in high m o m e n t u m being achieved by red and a preferred tendency by red to maintain a dense, higher 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 a constraint for aborting from the denser formation, when an intollerable situation occurs. Even when this results in an early formation change, however, it would appear that red's arrival m o m e n t u m can still be higher under a variabledistance, formation change strategy, than under a fixed distance strategy. However, not significantly so since, as indicated in Figure 3, it must always be detrimental to red to eliminate it's opportunity to recover speed. Figure 4 shows a revised influence diagram which captures the effect of red basing it's planned distance to formation change on the product of the red size and speed (momentum). This figure incorporates a m o m e n t u m constraint based on a
DENSITY OF RED UNITS -
SCHEDULED MOMENTUM IN PROPOSED RATE OF FORMATION CHANGE •• • I OF RED • ~ FORMATION i SCHEDULED SPEED OF RED ADVANCE
I
~*~lw SCHEDULED MOMENTUM PRODUCTIVITV TO FORMATION CHANGE POINT OF BLUEFIRE
PLANNED ~~EFFEC~! CHANGEdiIIOINT C
I NESS OE BLUEFIRE
-- -- " MOMENTUM OF RED ADVANCE I%~
ACTUAL • * SPEED OF • RED ADVANCE
-r-OT-T L AOV.NE
[,,l
-
DISTANCE 0E ÷ RED ADVANCE
RATE OF BLUE
÷~}il
Figure 4. 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
scheduled m o m e n t u m for the next formation, which is a 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 emphasize the fact that the use of red size, as a product of speed to create a m o m e n t u m decision variable to determine the planned distance is formation change, does in no way change the polarity of the loops described in Figure 3. Figure 4 is therefore identical in feedback terms to Figure 3. Figure 4 also includes the feedback loops associated with blue's strategies for the fire delivery. That is, based on red's achieved distance, speed or momentum. These are all 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 and implies, as born out by the quantitative results, that the most effective strategies will be the most direct ones (speed or m o m e n t u m based). However, once again, an important consideration is the consistency of fire delivery. It is important to note here that it is often the case that firing is deliberately switched on and off as a result of the definition of the fire delivery strategy itself; for example where firing is switched off when m o m e n t u m or speed are reduced to pre-set lower
E.F. Wolstenholme / Defence operational analysis using system dynamics
limites and switched on again when these variables reach pre-set upper limits. An intermittant blue fire strategy constructed in such a seemingly logical way 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 and the performance measure used. For example, if fire delivery is based on maintaining momentum at a given target level and performance is measured in terms of momentum, then the performance will be determined by the target set by the strategy which may not be, ultimately, as low as intended.
Facilitating model development and further insight One of the most important consequences of being able to communicate an explanation of model results in terms of a simplified underlying feedback structure of the model, is that it is possible to generate further insights into what might happen in other experiments on the model or under different modelling assumptions. A certain amount of speculation is always possible outside the boundaries of the model results by using the framework of the qualitative model. These modifications can later be built into the quantitative model and the cycle of model refinement continued. 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 a change of formation would only take place beyond a fixed distance. An alternative approach would be to allow formation change earlier, if say, cumulative losses became intolerable. This effect could be superimposed in parallel with allowing the existing deferral of formation change due to excessive speed loss. Such a possibility is suggested directly as a result of spotting the lack of a direct feedback link in the current model between red size of advance and the rate of formation change in Figures 3 and 4. The inclusion of such a negative link would create a more direct trade-off in the model between the speed and attrition effects of blue fire on the rate of red formation change. A second example suggested by the existing qualitative model is the possibility of introducing other alternative strategies by which
17
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 a formal surveillance sector of the model.
The role of system dynamics in defence Defence operation analysis, certainly in the procurement area (12), is characterized by a mixture of modelling and gaming methodologies, with recent trends strongly reinforcing the role of the former. The overall purpose of such analysis is to test out the operational usefullness of equipment, based on optimized field trial data, both relative to and in combination with other equipment and under a tactical and threat setting set of scenarios. The general tendency is to model in the greatest detail and at the highest level of resolution possible, which results in very large models, often requiting a hierarchical structure. Simulation is clearly seen and used as a tool within the modelling area. The type of simulation models most commonly used are discrete event, stochastic simulation models which do not have inbuilt adaptive feedback and control. To incorporate these features usually necessitates the use of hand simulation perhaps involving user intervention. and this type of hand simulation creates a link between the modelling and gaming methodologies. The work to date on system dynamics would appear to indicate that it's most likely future role in the defence operational analysis field would appear to be in formalising the link between games and models. The incorporation of strategic rules directly into a computer simulation as facilitated by system dynamics allows two important developments in analysis. Firstly, by building blue command and control elements into the analysis, the system and the hardware can be designed and tested in terms of how it will be 'managed' in addition to the more usual determination of capacity requirements. There is, additionally, the possibility of examining the trade-off between capacity and control. Secondly, however, similar
18
E.F. Wolstenholme / Defence operationalanalysis using system dynamics
adaptive strategies can be built into the same models from ted's point of view. It is felt that current defence modelling analysis might benefit substantially from studies which incorporate adaptive rather than static opponents. Since system dynamics by definition attempts to create a systemic viewpoint linking the elements and strategies of a given situation together, it must, by necessity, be created at a lower level of resolution and at a higher level of aggregation than in conventional defence simulation models. However, as clearly shown in the demonstration model here, higher resolution can be progressively introduced into models in a controlled manner and simplified feedback structure diagrams can be used to retain understanding. In general the role of system dynamics in defence operational analysis can be currently perceived as being one of creating initial insights into problems situations prior to detailed conventional modelling. This is considered as an important role. It is only too easy in practice to develop models in detail and expound much effort before components of models are integrated together at the next level of the modelling hierarchy. If some restrictive interaction is discovered at this time much abortive work could result. It is felt that there is a great need to model higher level interactions, particularly between hardware and strategy at a much earlier stage, and that the system dynamics methodology is suited to this task.
Conclusions This paper has attempted to present, by means of a case study, how the methodology of system dynamics can provide insight into defence problems by modular model construction and b y the parallel development of sophisticated quantitative models and simplified, qualitative feedback di-
agrams. These procedures overcome m a n y of the problems associated with model complexity as well as providing a means of assessing adaptive strategic options between combatants.
Acknowledgement This work has been carried out with the support of the Procurement Executive, Ministry of Defence.
References [1] Huber, R.K., "On current issues in defence systemsanalysis and combat modelling", OMEGA InternationalJournal of Management Science 13(2) (1985) 95-106. [2] Forrester, J.W., Principals of Systems, MIT Press, Cambridge, MA, 1958. [3] Forrester, J.W., Industrial Dynamics, MIT Press, Cambridge, MA, 1962. [4] Meadows, D.H., Limits to Growth, Earth Island Press, 1972. [5] Forrester, J.W. et al., "The United States national economic model", Proceedings of the 1984 System Dynamics Conference, Oslo.
[6] Coyle, R.G., Management System Dynamics, Wiley, New York, 1979. [7] Randers, J., Elements of the System Dynamics Methods, MIT Press, Cambridge, MA. [8] Richardson, G.P., and Pugh, A.L., Introduction to System Dynamics Modelling with D~7~AMO, MIT Press, Cambridge, MA. [9] Wolstenholme, E.F., "System dynamics in perspective", Journal of the UK Operational Research Society 33 (36) (1982) 547-556. [10] Wolstenholme, E.F., and Coyle, R.G., "The development of system dynamics as a methodology for system description and qualitative analysis", Journal of the UK Operational Research Society 34 (7) (1983) 569-581. [11] Cavana, R.Y., and Coyle, R.G., DYSM~O, User Manual, University of Bradford, 1982. [12] Bailey, R.J.M., "Operational analysis in the UK Ministry of Defence--A personal view", R.A.R.D.E. internal working paper.