Table of Contents
TEACHING SYSTEM DYNAMICS IN A FRENCH
SCHOOL OF ENGINEERING
Michel Karsky, KBS', Paris France
Hakim Remita, Ecole Centrale Paris”, France
1- INTRODUCTION
We shall describe here the development of the System Dynamics teaching content at
ECP (Ecole Centrale Paris), following some 25 years of teaching this subject in
various French Universities, Institutes of Technology and Business Schools. The
ideas and experience accumulated in previous years have been applied at ECP, one
of the top French engineering schools, and will be described in this chapter.
This course was created three years ago, at the same time as, and within a new
specialization program in Industrial Engineering whose aim is to give a global but in
depth view of Industrial Processes. System Dynamics was considered as particularly
suited to take into consideration all the numerous closed loop Processes.
The Industrial Engineering specialization, with some 60 students, deals with three
subjects :
- Design Processes
- Logistic Processes
- Economic Processes
As it stands now, System Dynamics is an optional course within the Design
Processes sector.
‘BS, 340 rue Saint Jacques, 75005 Paris, France
? Koole Centrale Paris, Grande Voie des ‘Vignes, 92295 Chatenay Malabry, France
2-A SHORT PRESENTATION OF ECOLE CENTRALE PARIS
(ECP)
GENERAL:
Ecole Centrale Paris is one of the most prestigious engineering school in France.
Founded in 1829 to train multidisciplinary engineers for industry, ECP is considered
as one of the leading engineering “Grandes Ecoles” in Europe.
It is accessed through a very selective competitive process, at least 2, generally three
years after high school. 400 students enter each year, of whom 100 coming from
European Universities.
Educational project :
First two years 3 Basic scientific and technical education.
3rd year :“Area of specialization” in a specific field, chosen amongst 8 scientific or
industry-related sectors : Civil & Environnemental Engineering, Industral
Engineering, Information technology, Applied mathematics, Mecanical & Aerospace
Engineering, Applied Physics, Process & environemental Engineering, Electrical
Engineering.
Partnership : ECP is in parmership with prestigious technological Universities in
Europe creating the ‘TIME NETWORK”, and it has developed a “Master's Degree"
Network involving American Universities like Harvard University, MIT, Stanford
University, Georgia Tech....
@ TIME Network
—— © "Master's Degree" Universities
e" © Double Degree Universities
3 - Teaching System Dynamics
How to teach System Dynamics ?
When faced with students in their early twenties, eager to learn, full of imagination,
with a strong desire to change the world, but disorderly, impulsive, often lacking
method in their approach to problems, what meaning should be given, and how
should one teach System Dynamics so that these students become and remain
interested in this approach, while “keeping their feet on the ground” ?
A tentative answer to this question leads to defining several aspects of the teaching
approach :
1 - System Dynamics is to be considered as both a philosophical approach to
complex dynamic problems, but also as a practical quantitative method without which
any analysis remains of litte use.
2 - students are often imaginative - and it is a quality which we must develop rather
than quelch - but they are also required, particularly as future scientists, engineers,
managers - to be practical, to obtain, show and analyze meaningful results.
Hence we try to develop four complementary aspects of our teaching :
1- The philosophical aspects of SD, which we feel are twofold :
Feedback Loops
- SD deals with - and only with - systems which contain feedback loops. This
is hardly a limitation, since most systems contain feedback loops which are the
essential cause of the complexity of their dynamic modes of behavior. On the other
hand, this sets SD apart from other modelling and simulation techniques which deal
with and are applicable to structures without feedback loops. This is an important
initial criterion for choosing the system which the students will study, model and
simulate. Although the students at ECP have had courses in feedback systems and
have no difficulty with the concept, we unfortunately find, again and again, that they
often have difficulties in recognizing the presence of feedback loops in ‘soft’ systems,
or on the contrary realizing the absence of such loops.
It is one of our aims, and main tasks to have them look systematically for feedback
loops in whatever system they want to study and analyze.
Causality
- we repeatedly insist on the necessity to explain the cause(s) of results
obtained through simulation, that “why” is at least as important as the “how” of future
behavior. Explaining results, behaviors, proposing intelligent changes should be
more important than predicting uncertain (even if likely) future developments, and
these causal explanations should be based on the complementary and interacting
notions of state vector which caracterizes a system and the vector of force which
cause change in that same system.
Here again, the natural tendency of many students, which we systematically ty to
correct, is to present simulation results, whether normal or surprising and
counterintuitive, without much effort to explain the intemal (system) reasons for such
behaviors, and without searching for policy changes or even new policies which could
modify these results.
In order to favor the search for causes and develop the awareness of the effects and
importance of closed loops, we systematically ask students to start - and finish, we'll
see later why - by drawing a causal diagram of the problem they chose to tackle. In
our experience, we have seen that starting analyzing a problem by means of a causal
diagram, has many advantages :
- it gives a global view of the system, and avoids jumping immediately into
details,
- it brings out very quickly at least some feedback loops within the system,
thus justifying the u se of SD, or on the contrary, showing that the latter is not
the appropriate approach,
- itallows a better immediate dialog with the client, in this case the professor,
- it gives a good start for the next step, namely the construction of a dynamic
quantitative model.
We shall also develop later in this paper the notion of “a posteriori” causal diagrams,
drawn after the model has been developed, thoroughly studied and used. The idea is
to help develop tools for showing dynamic behaviors of complex systems in a way
that can be easily understood by managers and policy makers, without having to get
into lengthy and detailed explanations about the model. But showing only the main
causal feedback loops, those which act in the long term, whose effects are not
evident to understand, nor to forecast, requires a deep knowledge of the system, a
knowledge based on an extensive use of the model.
The philosophical aspects of System Dynamics are introduced right at the begining of
our course. But we have come to realize, again and again, that these concepts are
quickly forgotten, and we must come back to them throughout our teaching, whether
it be theoretical - main concepts and examples of SD - or practical - models
developed by students or large models realized outside the course -.
2 - The practical aspect of SD
As mentioned earlier, we consider that beyond its philosophical aspects, SD is a
practical quantitative tool meant for the analysis of complex time evolving systems,
and this attitude does suit scientifically minded future engineers and managers.
Hence we pass very quickly to the practical aspects of SD :
- separation of variables into levels, rates and information - decision - influence
variables, explaining with a few very simple examples, the reason and the
need for this decomposition,
- delays, non-linearities, graphs and mathematical or logical functions, etc.,
- the use of some specific softwares such as ithink or Stella, Vensim,
Powersim (not yet much in use in France).
At the Ecole Centrale Paris, where most students are bright, fast and highly
scientifically oriented, all these elements pose no problem. There remains, however,
one recurring question more or less openly asked by most students : how to start a
dynamic model on the basis of the causal diagram built previously ? We try to show
that in principle, the answer to this question is simple and quite general. We suggest
looking within the causal diagram for a few level variables (don’t try to be exhaustve,
a few such levels will do, to start with) which can be characterized as follows : if and
when everything stops brutally (vacation period, for example, when the company
closes, with neither sales, nor production nor ordering taking place), level variables
are the only ones not to vary at all, to remain fixed at the last evolving value. All other
variables will either fall to zero or become inexistant and/or useless. This has proven
to be an effective way to start modelling, whatever the problem, choosing level
variables according to this criterion, the the flows which fill or empty the levels, finally
all variables, parameters and constants which influence flows.
Introducing the principles of System Dynamics and some practical notions about SD
modelling, with a few relatively simple examples, takes relatively litte time, about 9 to
10 hours. The next step consists in having the students develop a practical model
and use the resulting simulator to analyze and get to know better the system under
study.
We have always felt that leaming SD must imply the creation, development and use
of some real model, if only to teach students how to obtain and explain results,
whether interesting and curious and even counterintuitive, or on the contrary banal,
expected and with no new informational content (the latter being a result by itself).
The question then arises, as to what type of system should students analyze. Should
we impose or at least propose certain problems, certain areas of analysis, such as
logistics, production problems, company management, directly connected to their
main subjects of study ? Or is it possible to give total freedom of choice, with the only
restriction that the proposed problem (system) shows complex time behavior, a
complexity certainly due to feedback loops within the system ?
These questions are linked to two seemingly contradictory aspects we mentioned
above, namely the ‘youthful imagination” of most students and “down to earth”
attitude required from them. Which of these aspects should be favored ? Can they be
combined ?
3 - Developing Imagination
Since SD can be applied to practically every domain involving either nature or man,
or both, we feel that giving students a freedom of choice is one way of letting them
develop their imagination. It is also a good way to let them realize - through some
hard to accept and bear, but healthy failures - the limits of wild topics, wildly
imaginative suggestions, unrealistic ideas.
As examples of such “wild” topics analyzed by students using SD, let us mention :
- succesful development of a music group (a topic often proposed by students,
which shows a frequent interest in music),
- competition between two ant colonies,
- management of a football club, or of a pizzeria,
-happiness within a couple.
4- Obtaining and showing practical results
Whatever the subject, we have always insisted on the practical and quantitative
aspect of SD, hence on the need to develop a realistic simulator which could show
useful results and lead to a better understanding of the dynamics of the system being
analyzed.
Rather than developing at length the aspects of practicality upon which we insist
mostly when working with students, we shall discuss the main difficulties or
shortcomings students encounter when dealing with SD as applied to whatever
problem they chose to study. Obviously, creating an interface using the
corresponding possibilities of the available softwares, does not generate problems (it
tends, in fact, to become one of the easiest aspects of modelling, and we have to
insist that the content is more important than the showcase). On the other hand, we
insist again and again on the notion of feedback loops, a notion students should
keep in mind from start to the end of the course (and hopefully all their life !) and in
particular when presenting and explaining results.
5 - Loops
But all loops are not of equal interest, and we try to develop in students the capacity
to realize that, and to be able to show these differences.
1 - “hardware” loops are evident, unavoidable and not modifiable. For
example, the “population - death” loop
a
Population death
is automatically taken into account by everyone, even if totally ignorant of SD,
of modelling, of simulation, of abstract thinking. Such loops must not, and
generally are not omitted by students, but they generate litte new information
as to the behavior of the system.
2 - “policy” loops which involve policy and decision variables, whose effect can
be short term or relatively long term, but which are in both cases well known
and recognized, their individual dynamics corresponding to expected behavior.
The analysis of such loops is useful because the corresponding effects are
generally a mix of many loop behavior types, and a loop by loop
decomposition helps understand what was possibly expected, hoped for or
forecast through intuition, but was too complex to be rationally and simply
analyzed and explained. These are the feedback loops one can expect
students to show, to analyze and to explain.
Here is an example of such a long term loop whose existence and effects are
quite evident. It comes from a study? which was done on freight transport, and
Patrice SALINI (INRETS, France), Mich KARSKY (KBS, France) (2002), « SIMTRANS (Freight Transportation
Simulation Model)’, System Dynamics Intemational Conference, July 2002, Palermo
the possible effects (or lack of effects) of emission permit policies. The
following causal diagram drawn after the model was developed, simulated and
analyzed showed a multitude of “policy” type feedback loops. Here is an
example of a long term loop whose existence and effects are to be expected
and are not surprising. This loop brings no surprising information, but
forgetting to take it into account could lead to trouble in the long term.
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and noms
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+ xation:
A long-term « evident » feedback loop
3 - Most eften, when modelling some real complex problem, one finds loops
often involving quite a few variables, with long term and sometimes
counterintuitive effects, but whose existence is ill perceived, or ignored or
forgotten. To show and analyze these loops one by one, showing also how
they can combine effects, has proven to be very effective in the process of
convincing users, experts and clients, that their problem is in effect a complex
one and that long term consequences of decisions can be forecast and can be
taken into account It is rare for students to succeed in finding and analyzing
such loops, if only because this requires experience (the presence of experts
for the field) and time.
Taken from the same freight transport model, here are two long term loops
which may contradict each other, and must therefore be analyzed carefully.
pe spat other offers
+ by +
OP
i:
demand + spay
Ls : el
supplyidetend ratio rs i
Freight-km offeredg. ? average unit price
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wverage Unit Congestion -
. Investment Load ¢ \B
fuel consumptioit ‘. a Unit margin
+ * Infrastructures 9
‘Total authorized ‘2
+ *. weight
Unit Cost
Unit Consumption rel,
co2 rig 4
emission regulations
‘and nom fed urate:
wt”
Warming effect ages Negociable 2
‘palcg, Emission Permits labor unit cost
halen
A slow stabilizing and favorable loop
emoet
Sector Growth “icin other supply sources
+ -
a7
* demand ply
r : ; .
supply/demand rio :
—_iahtimoffored £ average mit price
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" ° Capacity A
eS ehh A Maxspeed Deve ait Margin
/ AN aN Unit Load opin, i
feel Investment vege # 7 %
‘ + J Unit
con: mpcion, a : Infrastructures oo
e 5 Total authorized 4 :
+ weight
C02 Uae cg crrtion ad Cost
emission regulations’
non: fuel unit cost
4 id
Warming effectiy, — Negociable
policy + Emission Permits labor unit cost
4
+ taxation:
A slow acting loop whose effect would
contradict that of the previous loop
For both types of “policy” loops, whether evident or not, whether short or long term,
we insist in our teaching on the necessity to bring them out by redrawhg a causal
diagram at the end of the study, after having become well versed in the system being
analyzed. This “a posteriori” causal diagram should be an important part of the whole
exercise, it shows how well the student has mastered the problem and, not less
important, how he/she can pass this understanding to others.
To conclude this chapter, let us make a resume of the steps we find important when
teaching System Dynamics, and the main difficulties students seem to have when
leaming this discipline :
- the basic concepts, which give a quasi-philosophical view of our approach to
systems :
1 - feedback loops, a universal concept - though often overlooked -,
responsible for most of the complexity of dynamic behaviors of systems.
At ECP, students have no problem with the concept and effects of loops, but they still
have difficulties transposing their knowledge onto “soft” systems, so as to recognize
in the latter at first sight the presence or absence of such loops. Unfortunately,
students less versed in feedback theory (business schools, some economists, etc.)
have even more difficulties with the concept.
2 - complementary and mutually interacting notions of state which
characterizes a system, and of force which causes change.
Questioning and analysing the reasons for some behavior, whether normal or
unexpected, is not in the habit of most students in their early twenties. Although the
softwares available allow easy causal analyses, we must constantly remind students
to use these cause searching tools, rather than developing a paralyzed type of
attitude when faced with a seemingly unusual model behavior (we repeatedly have to
remind them that such unusual behavior is most likely due to an error in the model,
rather than the fault of the computer, of the real system being analyzed...or even of
the tutor !)
- But SD is a pragmatic, quantitative approach to complex systems, hence practical
tools are needed, and exist, to model and simulate. The successive steps, both
theoretical and practical, in the analysis of dynamic systems, the possible
consequences and conclusions that can develop from such studies, can be
summarized in the diagram on the next page.
Most students at ECP have no problem with the use of the available softwares, with
mathematical, logical or graphical functions. Rather, they tend to use too much
mathematics, with three or four line long equations, but this youthful defect is easily
overcome.
REALITY
Orderly
Representation
of Knowledge
Y PERCEPTION
CAUSAL ANALYSIS
UNDER\STANDING Formalizing
and
Y quan tify ing
MODELING
(Déferentiation of Dynamic variables)
Correction
y
SIMULATION
(Time Be havior)
UNEXPECTED FORECASTING
RESULTS
THE MODELLING AND SIMULATION PROCESS
- Because of the variety of systems around us, and the applicability of SD to most of
them, we feel it worthwhile to let students use their imagination, however wild it
seems to be - as long as it remains realistic and practical -,in their choice of the
system they want to analyze using SD. We must add that we have been seldom
disapointed with the subjects which were chosen, modeled and simulated.
Here again, we have observed, that students have difficulties in differentiating
between problems which can be tackled by means of SD (because of the presence of
feedback loops) and those where no loops exist or are effective.
- It is extremely important to leam how to show and explain results as clearly as
possible. Most softwares used for SD analyses have interface possibilities which help
in this final task, and we require that the final presentation use these facilities. This
poses no problem, whether at ECP or elsewhere, and it is in fact the prefered and
easiest part of the project.
In addition, we ask - and shall develop this aspect of the final phase of the project -
that students analyze the problem and explain possible short or long term
developments with the help of a causal diagram drawn after the model has been
developed and used. Students who succeed in this final task, really benefit fully from
our course and will have understood in depth, and hopefully for a very long time, the
System Dynamics approach.
4 - Some examples of students projects
Types of projects proposed by our students:
Management/Finance
@ Management of a supermarket
@ Management of an investment company in office real estate
@ Management of a soccer stadium
Model of companies
@ Ski ressort
@ Restaurant managing
@ Manufacturing plant
Organisation
@ Management of a French university
@ Management of a small town
@ Management of a soccer team
Miscellaneous
@ The development of an Ant’s Nest
@ Evolution of a butterfly specie
@ Happiness of a couple
@ Development of a music band
Example 1: Cohabitation between two Ant’s Nests
Definition of the problem
«Some information about Ant'’s Nests
oO 1 queen per nest
0 two sortofants :
0 soldiers
oO workers
o Population of a nest: from 100 000 to 1 million
o Ants are agressive
0 Two nest can’t exist on the same territory
Modelling through Stella®
General behavior of the system
Food stodk ;
AN2 >
Food
Teserve
2 Food stock ‘
ANI :
Food is brought by workers while soldiers try to eliminate the whole population of the
other nest (workers, soldiers and queen).
The food stocks of both nests can deplete the total food reserve.
A queen lays eggs which become nympheas which in turn become soldiers or
workers depending on the rate of stress of the nest: the higher the stress due, for
example, to some danger, the more soldiers are created at the expense of workers,
thus diminishing the input to the food stock of the nest.
Results
1-A single nest stabilises its population around 150 000.
2 - When two similar nests coexist, the stress becomes important, the number of
soldiers strongly increases at the expense of workers, insufficient food is brought to
each nest and borth of them disappear.
Evolution of nest 1
a 1: reine 1 2: jeunes ouvriér... 3: vieilles ouvrid... 4: soldates 1 §: total fourmis 1
a1
ARM
i i Fae tae
100.00 150.00 200.00
Page 1 Days 17:03 mer 12 fév 2003
XJ a aF ? Populations
ALO
tT)
3 - It is not surprising to find that a nest disappears sooner if itis weaker than its
competitor ( scenario parameter : strengh; <strenghij)
4- A counter-intuitive result: nest 1 has a birth rate 50 times less than that of nest 2,
hence a much lower population. When competing with each other, and contrary to
expectations, itis nest 2, the bigest one, which suffers and disappears. This is
because the stress rate of nest 1 increases much faster than that of nest 2
(population of nest 1 seems too small to appear dangerous to nest 2, hence the
coresponding danger is overlooked). Soldiers of nest 1 attack and kill the population
(soldiers and workers) of nest 2. When the latter begin to realize the danger, itis too
late.
Let us add that this example was very well presented, both in written and oral form,
the variables and results were well documented.
Example 2 : Management of a soccer stadium
Definition of the problem
0 Management model ofa soccer stadium.
o Simulation over five championship seasons (95 weeks).
0 Ifmoney is gained, it can be invested into the extension of the stadium.
oO Supporters satisfaction depends on the results of the team, and
influences the number of subscribers.
Model Structure
Filling of the stadium.
Supporters
satisfaction
Subscribers Stadium.
finances
National
i ell A
tating ce Oe Non subscribers
KU”
a Sponsors
the team
Results
1- A Weak team causes the financial balance of the stadium to progressively
deteriorate.
On the contrary, and not surprinsingly, good results lead to an improvement of the
financial balance of the stadium, which can be offset by a tendency to overinvest
Among other results, this work allowed students to confront their mental model and
the corresponding model of a system, with reality.
5- Conclusion
This topic interests students whose attendance to the course has more than doubled
from year to next They seem to be particularly attracted by :
- the novelty of approach to systems, an approach they were not used to in
their previous training,
- the freedom to apply a scientific and quantitative method to problems
considered as “non-scientific”,
- the freedom we give them in the choice of the subject, thus developing their
imaginative approach to topics of very different kinds,
- the use of new software (ithink, stella, vensim) which require rigorous
thinking and modeling.
We believe it essential that young engineers and future managers develop their
sense of system approach in order for them to improve their ability to make as righta
decision as possible, realizing that feedback loops exist not only in machines but all
over the soft systems that surround them.Beyond the year to year requirements of
teaching System Dynamics, there is also within ECP a desire and an ambition to
develop a center of competency in this subject, with seminars, conferences, and
master and doctoral projects and theses.
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