294THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY, CHINA
SIMPLIFICATION BY PLANNING: THE THIRD WAY
Raimo Keloharju
Helsinki School of Economics :
Runeberginkatu 14-16, Helsinki 10 Finland
ABSTRACT
This paper puts forward the idea that essential parts can be removed: from a SD
model without harm if the model is revised successively during the simulation,
The revision requires an optimization package, called DYSMOD (Oynamic Simulation
Model Optimizer and Developer). A multi-stage production model, developed by
J.M.Lyneis, is used for demonstrating that the idea works in practice.
Conceptual background
Classical system dynamics can be described as being based on a concept of pre-un-
derstanding. The process starts by considering a reference mode over time concer-
ning the real world behaviour of interest. A feedback model is conceptualized from
the reference mode to explain the observed behaviour. This creates a dynamic
hypothesis. The computer is then used as a fast calculating machine to check if
the model can reproduce the reference behaviour and hence substantiate the hypot-
hesis.
Revisions to model parameters are made manually until the model can achieve
this objective. When it does so, the model is considered validated and appropriate
for use in designing other system behaviour modes by making further parameter
and structural changes. This process is shown as an iterative procedure in Fig.1.
MANUAL CHANGES TO
| SIMULATION MODEL
ACTUAL. NEW PARAMETER
BEHAVIOUR VALUES AND STRUCTURES
DESIRED SIMULATION
BEHAVIOUR,
Fig.l. The process of model design in classical SD
THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA 295
The concept of dynamic optimization in SD is based on a belief that the manual
procedure of system design given in Fig.l can be automated (Keloharju, 1983). It
is done by interfacing a heuristic optimization algorithm with a system dynamics
simulation prograinme. The optimization algorithm used is the extended Search
Decisicn Rute algorithm (SDR) and the systern dynamics software used is the Dyna-
mic Systern Modelling Analysis Programme (OYSMAP). The combined programme is
known as C'YSMOD (Dynamic Simulation Medel Optimizer and Developer). The pro-
cess of model design that uses it is shown in Fig.2.
SDR ALGORITHM
(OPTIMIZATION)
VALUE OF NEW PARAVETER
Om CT YE FUNCTION : VALUES AND STRUCTURES
DESIRED VALUE
OF O8JECTIVE = S IMULAT ICN
FUNCTION
Fig.2. The process of mode! design in optimized SD
Fig.2 shows how the combination of optimization and simulation seeks a solution
iteratively in optimized system dynamics. Before starting, it is necessary to take
two steps. Firstly, an objective function must be defined within the simulation
model which summarizes the overali model behaviour. Secondly, a number of para-
meters within the model must be chosen as candidates for sptimization together
with a range of feasible numerical values for each.
Each iteration starts with a simulation run which calculates ‘the value of the
objective function chosen within the initial conditions set for the simulation para-
meters. The SDR algorithm then treats these parameters as varia‘ optimization
and optimizes them heuristically. In other words, the algorithm s them one
at a time using the objective function as a measure of per The output
from the optimizer comprises a new set of parameter values.
Subsequent iterations repeat this cycle by using the modified parameters. The algo-
rithm compares the value of the objective function at the end of the simulation
run to the corresponding value from the best run received. Although the objective
function may fluctuate from one iteration to another, the best solution is always
kept stored in the computer memory. This guarantees that optimization never ma-
kes the initial situation worse.
The modeller must decide on the number of iterations which are appropriate for
achieving some desired value of the abjective function. The number chosen is,
however, not too important as the whole procedure can be subsequently continued
until the value of the objective function stabilizes.
Additional pseudo-parameters can be introduced into the simulation model for the
purpese of aptirnization. This is a powerful use of optimization since it creates 4
means of carrying out structural rather than straight parameter optimization.
296 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
The optimizer revises the modelling culture in SD. If the optimizer knows which
way to go during the search for better ‘riodels, the initial model need not be of
high quality. Pre-understanding is not necessary since the modeller can learn from
the computerized modelling process. In this way, he acquires post-understanding.
System dynamicists have traditionally thought that the role of models is to repre-
sent complex sociotechnical systems. The opposite viewpoint is to accept models as
thinking aids only. Two quotations fram Forrester indicate that a search for balance
between the opposite roles might be the next in line:
"All systems that change through time can be represented by using only
levels and rates. The two kinds of variables are necessary but at the
same time sufficient. for representing any system" (Forrester, 1971)
"The proper balance between size and simplicity suggested simplification
(in the National Model)" (Forrester, 1986)
Several methodological choices are available to solve problems of model simplifica-
tion. Keloharju and Luostarinen have developed a ‘black box’ approach, based on
extended use of the optimizer (Keloharju and Luostarinen, 1983). In this methodolo-
gy, the computer simplifies a model structure by partitioning it in parameter spa-
ce. The work is done by algorithms which calculate model sensitivity to various
parameters. The procedure is fully automatic and has several steps. Wang-and Yan
have recently introduced a mathematical method which enables the partitioning of
SD models for simplification (Wang and Yan, 1986).
So far, it has been assumed that a model has redundancy that should be removed.
Suppose, however, that the reverse is true: a model is so simple that it is defi-
cient. This paper will show that even such a model works well if it is revised from
time to time. This is the third way of simplifying and it requires the explicit use
of planning. A well known model by Lyneis (Lyneis, 1980) serves as a demonstration
case in experiments that will be reported below.
The Lyneis model
Lyneis has a simple two-stage production model in his book ‘Corporate Planning
and Policy Design’. Fig.3 gives the influence diagram of the model, Appendix A
lists it. The present author has added six pseudo parameters (41,A2,B1,..,84) and
an objective function (OBJF.
The objective function accumulates production fluctuations (GOAL), raw-material
inventory (GOAL2) and the error term of finished inventory (GOAL3). The sum of
these weighted (WG1,WG2,WG3) components is minimized.
Any influence diagram can be presented in open form. Fig.4 shows the lyneis
model after the required transformation. Connections between the information flows
and the physical flow were cut off in the sources of information. The objective
function has been added to the figure.
THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA 297
Fig.3. The influence diagram of the Lyneis model
am2 om Ls
Pia FIG
PR. POO. PAR. PI PR IP. Pc. Ft
Pic PL POO v oR Fic Fl wip ~
APR APR ado ai
om
Fig.4. The Lyneis model after rearrangements
298 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
The model has three parts: objective function, physical flow and model structure.
The physical flow flows-from parts order rate (POR) to sales (SR) through: interme-
diate stages. It is the horizontal flow in Fig.4. The objective function and its
components are above the physical flow, the information network is below it.
fet us look at the part of the information network which defines Production Or-
der Rate, POR. Suppose that parameters Bl and B2. are given the value. of zero.
The reduced model is an oversimplified version: of the original model, which has
now lost certain essential parts.
Double-dynamic optimization
An acceptable model must be created in parameter space before the ‘real time’
simulation begins. The optimizer does this work of dynamic optimization by repea-
ted simulation. The cycle that starts at time 0 in Fig.5 is the same as in Fig.2.
The time horizon of the model equals the length of the cycle.
Fig.5 Double-dynamic optimization illustrated
Fig.5 is needed to understand the difference between dynamic and doubie-dynamic
optimization. In double-dynamic optimization, the model is reviséd. at least once
during the simulation and that is shown by point N on the time axis. The length
of the cycle is now called ‘planning horizon’, The distance between two successive
cycles, like O-N, is called ‘action time’.
Solution interval OT is.a technical parameter which separates two groups of suc-
cessive calculations from each other at times J’ and *K’. It creates the dynamics
of a discrete model that should approximate the behavior of the corresponding
continuous model. When DT is made too long, even a stable model may explode
(Forrester, 1968).
The planning horizon gives the modeller the possibility to distinguish between two
successive models which were developed by the computer. The action time is the
distance between them. It is conceptually similar to DT and should be seen as a
technical parameter. As the action time links models instead of variables of the
madel in time, it also has to react to unexpected changes of importance. DYS-
MOD has the capacity to do that but it will not be discussed here.
THE 1987 INTERNATIONAL. CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA 299
Fig.6 summarizes eight experiments that were performed to find out the useful-
ness of oversimplified models. ©
Run Description Total cost Relative Relative
cost length of
i action time
i simulation 21.9E12 100%
2 dynamic optimization 75.1E11 34.2%
Double-dynamic optimization,
Complete model
Planning horizon Action time
3 480 240 68.2E11 31.1% 10%
4 240 120 65,2E11 29.8% Yo
5 120 60 62.5611 28.5% 2.5%
Double-dynamic optimization,
Reduced model
Planning horizon Action time
6 480 240 30.1612 137.1% 10%
7 240 120 85.2E11 38.9% 5%
8 120 60 9EAL 29.1% 2.5%
Fig.6. The cost comparison of eight experiments
Run 1 in Fig.6 relates to the original L_yneis model. The total cost, generated by
objective function OBJF, is taken as 100% as it gives a yardstick for cost compa-
risons to follow.
The model was optimized in run 2 by taking the pseudo-parameters A1,42,B1,..,B4
into optimization. Their ranges were defined from 0 to 3. As a compromise bet-
ween convergence of the solution and computing time, the number of iterations was
chosen as 150 in runs 2 to 8.
411 pseudo-parameters were used for optimization in runs 3-5. In runs 6-8, Al
and A2 were optimization parameters and B1,..,B4 had the value of zero. In this
way, the complete model was changed to a reduced Version without feedback loops.
To simplify the experiment, the length of planning horizon was always twice the
action time.
Fig.6 shows that
(a) it was possible to improve the simulation model (run 1) by dynamic optimizati-
on. This bears out what we have learnt from experience namely that a simulation
model can always be improved by the optimizer.
(b) double-dynamic optimization (runs 3-5) gave better results than dynamic optimi-
zation (run 2) when the relative length of action time varied from 2.5 to 10%
300 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
(c) the quality of double-dynamic optimization in the reduced models (runs 6-8)
improved very rapidly when the action time was shortened. The cost exceeded the
cost obtained from the simulation model when the action time was 10% of the
total runlength. In the last run, the cost was close to the cost generated from
the complete model with equal action time. This means that feedback information
from the correction terms (PIC,POC,WPIC,FIC) had only. marginal value!
System dynamicists: extend their models by redefining some model parameters as
new variables and, after that, by adding the necessary causal relationships. In runs
6-8, the ‘extended’ model was reduced, however, by allowing some model parame-
ters (A1,A2) to take charge of omitted variables (PIC,POC,WPIC,FIC).
Reduced models were based on two kinds .of trade-offs:
(a) Parameter Al in run 8 corresponds to Al,81 and B2 in run 5. Therefore there
is a trade-off between parameter aggregation and the frequency of model. revisi-
on.
(b) Either continuous local information or discontinuous global information can be
used, The earlier is obtained from the correction terms (via Bl,..,B4); the latter
relates to the values of Al and A2. Figures 7 and 8 show plottings from runs 1
and 8. The improvement looks impressive.
It is generally accepted that models should be as simple as possible. A double-dy-
namic model, however, can be oversimplified without harmful side-effects. Such a
model works well for a short time; after that, change it!
cee
a oe
22 8 bg g 8
- 8 $ 8 35
$3 8 8 3 is
Eb a8 &
e¢ 2 8 &
52 8 8 8 8
i
oe 8 BS
8 ge 8
eb eg e
222 8 8 &
“ ete
~ =. § §
coe 8 & ¢
Fig.7. Some plottings from run 1
THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA 301
PLOT INCR
s:2:3
$e¢2: 8
£8 ge 3
=
eee ss
gb ed?
28 2 § & &
z
“ e+e
rigs
cor 8 Be .
zor § ES
Fig.8. Some plottings from run 8
Conclusions
Conventional SD has two axioms, relating to the importance of mode! structure
and feedback. The oversimplified model violates them since feedback loops were
removed and model structure was deliberatly deficient. The control was trarsfer-
red to implicit feedforward paths via the objective functign. Here feedforward me-
ans the use of future information, derived from the past, to present needs.
a
A
A ct
1
PR wip
[ao Peng
acre =o. FIC i wPIC
i er
Fig.9. Feedback and feedforward illustrated
The relationship of feedback to feedforward is seen in Fig.9. The model structure
with its feedback loops is shown as an ‘organization chart’, drawn in a continuous
line. The dotted lines depit feedforward paths at the end of planning horizon.
302 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
A model which cannot be replaced has to be robust in order to safeguard against
uncertainties. Reduced models have a life-length which equals the action time
that was chosen. Therefore they need not be robust.
Figure 10 presents a framework which might be called systems cross’. It consists
of two concept pairs and can be used for classifying different modelling approac-
hes in SD.
CLOSED
FEEDBACK FEEDFORWARD
OPEN
Fig.10. The systems cross
Fig.11 shows all configurations which can be derived from the systems cross. Their
meanings will then be explained.
! -_ _—
(A) (B) (C) ((D)
oR 7 7
(E) (F) (G) (H)
(1) (3) (K) (L)
(m)
Fig.1l. The configurations of systems cross
Fig.11 includes models which can be interpreted as follows:
(A) Open models without feedback or feedforward. Linear programming models, for
example, belong to this group .
(8) Closed models without feedabck. Not feasible.
(C) Feedback models which are not closed. Not feasible.
(0) Feedforward models which are*neither open or closed. Not feasible.
(E) Closed feedback models. Purists’ are system dynamicists who do not accept
partially open models. Models of the purists belong to this group.
(F) Closed feedforward models without feedback, The objective function itself is
now the. model to be optimized. The idea was put forward by Taubert in his
THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA 303
(G) Open feedback models. Not feasible.
(H) Open feedforward models. All feedforward models are closed via implicit links
from the. objective function to optimization parameters. Not feasible.
(I) This is an extension of case (E), The model is solved by optimization.
(3) Open feedback models. Not feasible.
(K) Also this is an extension of case (E) as a non-purist also accepts exogeneous
real-life variables to his model.
(L.) A feedforward model which is both open and closed. Run 8 is an example of
case (L),
(M) This can be interpreted either as the extension of case (K) or (L). The model:
is now partially open; see run 5.
The systems cross is reduced to a simpler. form where ‘open models and ‘closed
models’ are replaced by ‘model structure’ :
STRUCTURE
FEEDBACK
FEEDFORWARD
Figure 12. The systems triangle
Figure 12 summarizes the evolution of the SD paradigm. The classical SD needs
two corner points of the triangle, i.e. feedback and structure. Reduced models
need the remaining corner point of feedforward. They are complementary approac-
hes and each may (or may not) work well.
Forrester has emphasized model acceptability instead of some statistical validation
criteria (Forrester, 1961). A model is then valid when the structure of the model
is meaningful, the model behaves as anticipated and it is accepted by the users.
If the model cannot be revised when in use, the validation procedure has to be
based on descriptive validation. The model to be validated then describes a situation
which is or was, not as it should be.
Since models are replaceable when needed, the validation procedure could be less
formal than before. it is mot any more a question of how man makes decisions
but how man and the computer should make them in symbiosis. This viewpoint
requires a great deal more maturity from decision makers than has been the case
in the past.
Reduced models from double-dynamic optimization are created by a black-box,
i.e. the optimizer. The idea may sound strange but it already has a real life
counterpart. OPT (Optimized Production Technology), which combines the concepts
of MRP and Japanese JIT-production, is based on similar principles (Goldratt and
Cox, 1984).
304 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
REFERENCES
Forrester, J.F. (1961), Industria} Dynamics. The M.1.T. Press and John Wiley, New
York, London ’
Forrester, J.W. (1968), Principles of Systems. The M.I.T. Press, Cambridge, Mass.
Forrester, J.W. (1971), World Dynamics. Wright-Allen Press, Cambridge, Mass.
Forrester, J.W. (1986), "Lessons from System Dynamics Modeling”. The paper pre-
sented in the 1986 International Conference of the System Dynamics Society in
Sevilla. October 1986, pp 1-16
Goldratt, E.M. and Cox, J. (1984), The Goal: Excellence in Manufacturing. Creative
Output (Netherlands) BV. Printed in the United States
Keloharju,R. (1983), Relativity Dynamics. Acta Academiae Oeconomicae Helsingien-
sis, Series A:40
Keloharju, R and Luostarinen, A. (1983), "Achieving Structura} Sensitivity by Auto-
Matic Simplification". Dynamica, Vol.9 Part 2, pp 60-65
Lyneis, J.M., (1980), Corporate Planning and Policy Design: A System Dynamics
Approach. The M.I.T. Press
Taubert, W.H. (1968), "A Search decision Rule for the Aggregate Scheduling Prob:
lem". Management Science, Vol.14 N.o 6, pp B343-B359
Wang,Q and Yan,G (1986), "Studying the Relationship Among the Whole, Parts and
Environment of a System Dynamics Mode]". The paper presented in the 1986 Inter-
national Conference of the System Dynamics Society in Sevilla. October 1986, pp
501-509
OAvagCcauanmas
19
JANUARY 53,1987 ##PRODUCTION MODEL BY LYNEISe#
¢ POR.KL=AL#APR.K+B18PIC.K+B24POC.K
POO.K=POO. J+DT# (POR. JK-PAR. JK)
POO=PSDT#CCOR ‘
PAR .KL=DELAYS(POR. JK + PSDT)
PSDT=60
PI.K=PI.J+DT# (PAR. JK-PR. JK)
PI=DDPI*CCOR
PIC.K=(PIG.K~PI.K)/TCPI
TCPI=60
PIG. K=DDPI#APR.K
DDPI=60
GOAL2.K=(PIG.K-PI.K)#(PIG.K-PI.K)
POC. K=(POOG.K-POO.K)/TCPI
POOG.K=PSDT#APR.K
APR. K=SMOOTH(PR. JK» TAPRPO)
TAPRPO=GO
Z#ACOR.K+RSG#F IC. K+B4#WIPC.K
PRX. J+DT# (PR. JK-PRX.J/DT)
GOALI .K=(PR.KL-PRX.K)#(PR.KL-PRX.K)
KeWIP.J+DT#(PR.JK-PC. JK)
s TCNIP#CCOR
PC..KL=DELAY3(PR.JK,TCWIP)
TCNI
FI.K=FI.J+DT# (PC. JK-SR. JK)
FI=DDFI®CCOR
SR.KL=COR.K
ACOR.K=SMOOTH(COR.K,TACOR)
TACOR=GO
FIG.K=DDFI#ACOR.K
DDFf=30
GOAL3.K=(FIG.K-FI.K)#(FIG.K-FI.K)
FIC.K=(FIG.K-FI.K)/TCFI
TCFI=60
WIPC.K=(WIPG.K-WIP.K)/TCFI
WIPG.K=TCHWIP#ACOR.K
COR.K=CCOR#(1+STEP(COSH, COST) +ACOS#SIN(G.28*TIME.K/PCOS) )
GRSrDoPaIPprapaszrere Hae
ACOS=0.2
PCOS=960
At=1
A2Z=1
Piet
B2=1
BQ=t
B4=1
OTE OBJECTIVE FUNCTION
OBJ .K=NG1#GOAL 1. K+NG2Z2*GOAL2.K+NG3#GUAL3.K
WG1=1.5E4
NGZ=1
NGSS1E3
OBJF .K=OBJF. J+DT#OBJ. JS
OBJF=0
DT=2
LENGTH=2460
PLTPER=46
PRTPER=2400
VOT FISF(0,24000)/PI=P(0, 48000) /COR=C, POR=+,PR=R(150,650)
PRINT GOAL1:GOALZ,GOAL9, OBJF
Rutt
F
ASZOMANAAAAAAATD.PHVPPNPHyPMeraazZ
oona2zra
APPENDIX A
