SDA:
System Dynamics Simulation of Inter Regional Risk Management
Using a Multi-Layered Model with Delays and Anticipation
Daniel M Dubois’, Stig C Holmberg?
"HEC Management School — University of Liége,
rue Louvrex 14, Liége, Belgium
+32 495 510419, daniel.dubois@ulg.ac.be
*Mid Sweden University, 83125 Ostersund, Sweden
+46 706 852885, shbg@ieee.org
Abstract-Even in inter regional risk management phenomena of retardation and adaptation
play an important role in the interplay between different logical management levels. In this
paper it is demonstrated that an System Dynamics (SD) approach may be very suitable for
modeling and simulating such phenomena. In some situations, however, SD approaches and
modeling tools may pose some unnecessary restrictions on the procedure. Hence, the authors
recommend a pragmatic and flexible attitude towards the choice of approach and tools.
Key Words: Anticipation, System Dynamics, Modeling, Simulation, Risk Management.
1 INTRODUCTION
Anticipatory modeling has proved itself as a fruitful approach for simulating phenomena
of delays and anticipation in management systems (Dubois and Holmberg, 2006a-b). Coming
to handling of anticipation, however, Asproth et al (2001) have stated that solutions based on
System Dynamics are “nor effective nor convenient and straightforward”. The main draw-
back being that in System Dynamic models everything is determined by the model's initial
conditions. New system states are calculated exclusively with help of earlier ones. This
procedure being quite contrary to an anticipatory approach. Nevertheless, Asproth et al
(2001) have also found that System Dynamics modeling can provide a good understanding of
the systems general behavior and properties. Finally they conclude that it may be necessary
with further investigations of anticipation in System Dynamics models. Hence, the purpose
of this paper is to clarify the possibilities of handling anticipation with help of System
Dynamics.
2 RISK MANAGEMENT SYSTEMS
Schwaninger (2000; 2001) has provided a model of the logical levels of management in
any organization. Figure 1 is a simplification of Schwaninger's model but anyhow it demon-
strates the existence of complex relations and interdependencies between levels. Due to those
relations decisions on one level may have surprising and unforeseen consequences on other
ones (Dubois and Holmberg, 2006a). Further, the status of higher levels may be taken as an
indicator or prediction of future status of lower levels. As a consequence, in taking decisions
on a higher level it is necessary to anticipate desirable future states on lower ones. Seen from
another perspective, any management system is a multi-level system with delays. It is those
delays that are the great challenge to management. Anticipation is here the main method to
handle those delays and to stabilize the system.
Normative management:
Visions, Fulfil the claims of
relevant stakeholders
i
Strategig management:
Research & Development, Doing
the right things
Delays
counteracted
by anticipation
Operative management: Future
Production, Doing things right operational states
T
>
Figure 1, Management model with interdependencies between logical levels of
organizational planning and decision making.
Let us take inter regional risk management as an example. Here, as outlined in figure 2, a
geographical region is divided between two nations, each governed by its own organizational
bodies. Those national bodies, however, tries to coordinate their actions in order to obtain
synergistic effects and an optimized security level over the whole region.
“Risk Mnt >
OrgA 7
Figure 2, Region governed by two coordinating national risk management organizations.
In mapping the generic model according to the interregional case according to figure 2 the
following couplings can be made:
* Normative management here stands for identification and admission of security
stakeholders and their relevant security claims.
* Strategic management besides research and development, training and other
preparations also stands for interregional coordination and communication with other
management centers.
* Operational management in the interregional security context means command and
control of concrete security operations.
For the simulation case the interdependencies between levels, which are shown in figure 3
are taken into account.
vty
R(t- tr)/(t- tr) f R(tyt NN
P(ty/t P(t+ Ta)/(t+ Ta)
Figure 3, Considered interdependencies in the simulation models.
The normative level (V) is influencing the two lower ones. The strategic level ( R ) is
influencing both its higher and lower level. Besides that, the strategic level from earlier time
steps is influencing the current operational level (P). The operational level in its turn has an
influence at the strategic one ( R ). A last influence goes from future operational levels back
to the current normative level.
Of course this is a big simplification compared with the real situation. As will be seen in
the forthcoming simulations, however, it is rich enough for providing good insights and
learning opportunities.
3 ORIGINAL APPROACH WITH ANTICIPATORY MODELING
The original multi layered model with anticipation and retardation was developed by
Dubois and Holmberg (2006b). It was not focusing specifically on security management.
Instead it handled a general management case. The basic part of the model will be shortly
recapitulated here.
3.1 From Model to Simulation Tool
The management situation expressed in figure 3 was initially represented with the
following differential equation system (Dubois and Holmberg, 2006b).
dP (t)/dt = [cR(t) + eV (t) - d]P (t) (eb)
dR(t)/dt = [f + bV (t) — cP (t)IR(t) (2)
dV (t)/dt = [a — bR(t) — eP (HIV(t) (3)
giving an explicit model at the current time t, with the set of parameters a, b, c, d, e, and f.
From that start in eqs. 1-3 a thorough mathematical analysis ended with a discretization
schema as result. So, with the development until the first order of the anticipated production,
the algorithm of this model with the Euler
schema is given by
eqs. 4-6.
P(t + At) = P(t) + At[cR(t — tR ) + eV (t) — d]P (t) (4)
R(t + At) = R(t) + At[f + (bV (t) — cP (t))R(H)] (5)
V (t+ At = V(t) + Atfa — bR(t) - e[P (t) +tA [P (t+ A -P(HVAtIV(t) (6)
With this algorithm, the retarded term is computed explicitly without the Taylor develop-
ment. It is to be pointed out that the Euler algorithm is numerically unstable. For example, a
system with an orbital stability becomes unstable with the Euler schema (Dubois, 2001). But,
with an incursive algorithm (Dubois, 2001), the orbital stability of a system is conserved. But
this question will not be further discussed here.
Next a software tool implementing the model was designed and built. The purpose of the
tool was to visualize the dynamics and to test the validity of the model. The computer tool,
which we named Multi-Level Management Support Simulation Tool with Anticipation and
Retardation (M2-STAR), was designed to meet the following criteria and requirements.
Firstly, M2-STAR has to be reachable over the Internet so everyone with access to the net
will be able to use and test the model. Secondly, M2-STAR has to be open source so
everyone will be able to change and improve the model. And Thirdly, M2-STAR will be
developed and run with free and commonly available development and run-time
environments. According to those specifications, M2-STAR was implemented as a web-
application based on an Apache web server and with PHP as programming milieu (Dubois
and Holmberg, 2006a).
M2-STAR, in its first version, was built with the following algorithm:
P (t+1) = P (t)+dt[cP (t)R(t-tau)+eP (t)V (t)-dP (t)]
R(t + 1) = R(t) + dt[f + bDR(DV (H) — cR(OP (H)]
V(t+ 1)=V(t) + dt[aV (t) — bV (DR(t) - eV (OP (t)]
-e(ant)V (t)(P (t+ 1) - P(t)
—[e(ant2 )/2dt](V (t)(P (t + 1) - 2P (t) + P(t- 1)
with a second order Taylor anticipation ant and retardation tau.
3.2 Experimental Simulation Runs
By running the simulations with different parameter settings a great diversity of results
were obtained (Dubois and Holmberg, 2006a). Here just a few glimpses of those results will
be given. In simulation 2, for example, there is no connection between the levels. As a
consequence, the research increases while production and vision decrease. Hence, we have a
got a demonstration that the three levels may not work independently of each other. Contrary,
they have to be carefully coordinated (Fig. 4).Figure 5 shows output from a run with great
retardation while figure 6 shows the result of introducing an anticipation factor in the same
retarded system.
Figure 4. Simulation with no connection between the three logical levels.
Figure 5. Simulation with great retardation.
Figure 6. Simulation with both retardation and anticipation.
4 SYSTEM DYNAMICS APPROACH
System dynamics (SD) as developed by Forrester in the fifties (1961) has by now evolved
into a well known methodology with wide application and with the most extensive impli-
cations (Forrester, 1994; Lane and Schwaninger, 2008; Schwaninger, 2011; Kljajic and
Borstnar, 2011).
For our purpose here, however, we just have to focus on the core concepts of SD. The
basic idea of SD modeling being based on the assumption that every system can be described
by a set of interconnected Flows (Rates) and Storages (Levels) according to fig. 7. Here Fin
and Fout are examples of flows in and out of the storage L. Further, there are influence
arrows going to, i.e. impacting, Fin and Fout and an auxiliary control variable v. The clouds,
at last, represent the system boundary, i.e. everything outside of the model or not being
considered in it.
ate
Fin L Fout
Figure 7. Core elements of System dynamics models.
For simulation purpose the dynamics of the model is translated into difference equations
of the following generic type:
L(k+1) = L(x) + dt{Fin(k) - Fout(k)] k= 0,1,2....n
Here k represents discrete time and dt the time interval of computation. L is the level
(system state) and F is the flow in and out. Initial values and values of Fin and Fout for each
time step being calculated in auxiliary functions.
4.1 A First System Dynamics Model with Simile
There are many software packages for design and simulation of SD models around'. For
this experiment we chose Simile’ mostly of pragmatic reasons.
A first attempt to translate the interdependencies outlined in figure 3 into a SD model is
shown in figure 8.
' http://www.vensim.com/sdmail/sdsoft.html (2012-02-03)
? — http://www.simulistics.com/ (2012-02-03)
First multi layred model with anticipation and retardation
subCnt
Figure 8. First SD model of the inter regional security system.
The flows in and out from the levels were defined in the following ways with the
algorithms taken directly from the original model (Figure 9).
‘© Derived: fProdin =
© Derived: fProdout ||Prod*vd|
i _. Derived: vf + vb*IResearch*lVision
fResearchin =
Pine |
vc*lProd*var_delay(IResearch,vRet) + ve*lProd*|Vision|
« _ Derived: |vc*lResearch*|Prod
fResearchout =
B
© Derived: fVisionin : va*IVision|
fVisionou
vb*lVision*IResearch + ve*lVision*IProd + antA
antP = |(ve*vAnt*var_delay(IVision, 1)*(IProd - var_delay(IProd, 1))) +
h ((ve*vAnt*vAnt*var_delay(IVision, 1) / 2) *
| |(\Prod - 2*var_delay(IProd, 1) + var_delay(IProd, 2)))|
Figure 9. Definition of algorithms in the model.
Below follows the output from some simulation runs with this model and with different
delays and anticipations (Figure 10-12).
Ww
Too Ea) ET) Z00
Time
Figure 10. Run with delay = 0 and anticipation = 0.
Figure 11. Run with delay 6 and anticipation 0.
50]
Time
Figure 12. Run with delay = 4 and anticipation = 2.
In short, it turned out that the original model could be transformed into a SD one with a
more or less identical behavior. The process was fast and straightforward. The SD-model,
however, is in this form not fully adapted to the intended context of inter regional security
management.
4.2 Possible Extensions
In the inter regional security context there are several security bodies active. Each of them
can be modeled and simulated in the way discussed above. The real challenge, however, is to
model the net result of their coordination and cooperation efforts. Here the sub model feature
of the Simile tool comes in handy.
Another challenge is to introduce a coupling between risk estimations and an anticipatory
approach into the model. By tradition rescue operations are based on a reactive paradigm.
Hence, there is always some sort of alarm that will trig the rescue work to start. With an
anticipatory approach, on the other hand, risk estimates could be used to start at least
preparatory rescue operations. In this way delays could be offset and considerable time could
be gained. So, having access to a model with anticipatory behavior would ease an upcoming
discussion concerning a possible shift toward an anticipatory paradigm with the responsible
security officers.
5 COMPARISON AND ASSESSMENT
From one point of view the most important contribution of this paper may be the
introduction of a multi-layered management model with retardation and anticipation into the
application area of inter regional security and crisis handling. On the other hand a large part
of the paper has been about translating an ad simulation model into one implemented with
System Dynamics (SD) methods and tools.
So in comparing the two approaches we have found the following:
* It is fast and straightforward to get the SD simulation model up and running. So here
the claims of the providers of SD-tools have been supported.
¢ The main model structure is well visualized in the graphical model display while the
most important properties of the model are hided in the algorithms (formulas).
* With the easiness to start modeling with the SD-tool it may be tempting to jump the
rigorous mathematical analysis underlaying the model. That may have a negative
impact on the final result.
* By using a known methodology and established tools there are also a given audience
or receivers of your work. Communication of results will with other words be
facilitated. On the other hand, when addressing a group of user within a specific
application area they probably have never heard about whatever modeling
methodology.
* Using a proprietary tool will always have as consequence that you become “locked
in”. Here Internet and open source tools have a clear advantage.
+ As a general rule: Basic tools provide the greatest freedom but are also more
cumbersome. Specialized tools are more fast and straightforward to use but also more
restricted.
* Based on this assessment we will not make a definite choice. We will be free to select
specialized tools for some tasks and basic ones for others.
6 CONCLUSIONS
In this paper we have demonstrated that the generic multi layered management model with
delay and retardation is also applicable on inter regional risk management. Further, it is
straightforward and reasonable easy to use System Dynamics (SD) methodology and tools
for conceptualizing and implementing a simulation model of such a management system.
There is also a potential in the SD approach for digging deeper into questions around
retardation and anticipation in inter regional risk management. There are, however, situations
there a SD approach may impose unnecessary restrictions on the work. For that reason we
would argue for a pragmatic and flexible attitude when coming to the choice of methodology
and tools.
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