Enlarging the Paradigm: Historical View From 1973 until 1983
Hermann Kralimann
‘Technische Universitat Berlin
338
Enlarging the Paradigm: Historical view from 1973 until 1983
Summary
This paper will provide an overview of the past ten years
describing the activities of enlarging the paradigm of
System Dynamics (SD). The first chapter tries to explain
why this has been done. Chapter two is concerned with the
optimization of SD models. The global optimization of system
Dynamics models is realized by its integration into a higher
level feedback loop structure. The use of optimal variables
in SD models is handled by linear programming models.
In chapter three the integration of SD and Input-Output
models has been realized to describe complex macroeconomic
systems. Chapter four describes System Dynamics models as
decision support systems based on model and methods base
systems. The last chapter is concerned with a new developed
approach - an integration of the methods ABRAHAM/ISAC and
Petri nets-which is able to build models of System Dynamics
type on a proved theoretical basis.
I. Why enlarging the paradigm
This question has simply to be seen with respect to the
fundamental objective to find the best possible solution in
the process of modelling complex parts of the real world.
Fig. 1 shows the underlying structure of the process of
finding the adequate methods concerning the characteristics
of the problem, the objective system and the available methods.
Characteristics of problems are
- number of variables (heterogenous components; hard and
soft variables)
+ relationship of variables (feedback nature; nonlinear)
- problem dynamics, bad structured systems etc.
339
‘The objective system of a project is defined e.g. to
describe or to explain real phenomena, to forecast their
behaviour and/or to provide optimal decision. With respect
to the characteristics of the methods a single or a number
of methods integrated will be used which is or are most
congruent to the characteristics of the specific problem
and the objective system.
aracteristics
of the objective
system
Characteristic
of the problem
to be analysed
Selection of
methods
Characteristic
of the available
methods
Fig. 1: Selection of Methods
Evidently the above explanations don't offer a scientific
justification for enlarging the paradigm but a very
pragmatic one. The following projects realized in business
or administration try to prove the last statement.
II. Optimization of System Dynamics models
1, Global Optimization
The global optimization of System Dynamics models is realized
by the feedback structure described in Fig. 2:
es System ees) objektive
Fost. Dynamics == function
Model
s(t)
Optimization
Algorithm
Fig. 2: System Dynamics model in a feedback loop structure
The control system is identical with the corresponding System
Dynamics model, whereby its output variables (state vector z
(s,t)) are compared with the objective function of getting
the deviations of the desired and actual values. The controller
- the optimization algorithm - tries by modifying the control
vector s(t) (the input variable of the system dynamics model)
to minimize these deviations in order to fit the objective
function (see Fig. 2).
The objective can be defined as to determine an optimal control
vector s(t), such that the state vector, z(s,t) follows a
feasible and user defined path as closely as possible, which
is described in the objective function. The problem is to
minimize the deviation of each state strajectory, z (3,t),
k=1,2, m from user defined state trajectory, r(t), k=1,2,...m
nm
Min U(s,t) = z 7 a (st) ~ ry (t) /
=1
To allow for a variation in acceptable values we introduce
upper and lower boundary x(t), ty 't) of the target interval
for state variable 2 at sampling time t and add weighting
341
factors w(t), wi(t) for the deviation from the upper and
lower boundary.
To normalize all state variables values and to emphasize
or deemphasize state variables the objective function U(s,t)
can be defined as follows
Min U(s,t) = S W(t) /2y (SE) “Ep CE) /g (ED /2y (srt) Ey (ED /
kc
The Fig. 3 shows simplified behaviour of the global optimi-
zation procedure.
The optimization algorithm acting as controller is in most
of the cases the so-called razor search-method developed
by Bandler und Macdonald. The algorithm a modified pattern
search method, belonging to the direct search and climbing
procedures for optimizing multidimensional problems.
The pattern search-method has here the main tast in this
problem of directing the output variables z, (s/t) of the
model into the user defined solution space described in the
objective function U(s,t). To do so, the modeller must vary
the parameters of the control vector s(t) by exploratory
moves.
Experience with pattern search-method indicates that the
procedure is very efficient in reaching an optimum also in
circumstances where the feasible region for the control
vector has fairly narrow valleys in it. Classical methods
(such as steepest descent-, generalized Newton-Raphson-,
Fletcher-Powell method etc.) slow down or even fail to get
an optimum in such cases.
An important modification of the pattern search procedure
is the so-called razor search method. This routine overcomes
the difficulties of discontinuous partial derivatives with
respect to the control variables. Otherwise efficient search
342
Initialize
3(t) methods fail to converge, particularly when the objective
function's hyperspace includes narrow curved valleys in the
vicinity of the path of discontinuous partial derivatives.
oo
Generate z(s,t)
The razor search routine normally overcomes these difficul-
ties by a search strategy that begins with a version of
Search Algorithr pattern search and then applies this until it fails.
determines new
Run Simulation
Then, the procedure automatically selects a random point in
values of s(t) the immediate neighbourhood. The random point is selected
based on previous goxthat:
trials 5, (t) = sO(t)+ pRin) + €
Evaluate Objective
Function U(s,t) where s,(t) is the new value of the ith control variable,
sQ(t) is the old value of the ith control variable, p is a
scale factor, R(n) produces random numbers between -1, and +1, and
€ represents the current value of the exploratory increment.
When the pattern search fails again the same valley (or
boundary) is assumend to be responsible, and an attempt is
are
finished made to establish a new pattern in the direction of the
ceiierls minimum. The process is automatically repeated until any of
se E
several possible terminating criteria are satisfied.
The razor search presented in this paper has two further
essential characteristics
yes
1) The exploratory increments depend on the total progress
made between the previous two base points. Therefore,
Best they automatically increase or decrease in accordance
s(t) with previous successes or failures, respectively.
2
When a pattern move plus exploratory moves fail, the
pattern is not immediately discarded. Instead, the same
Fig.3 Simplified flow diagram of global optimization procedure is repeated closer to the base point. If this
effort also proves unsuccessful, the procedure is attemp-
ted in the opposite direction.
The razor search-method has been successfully applied to
microwave optimization.
343 BAG
1.1 Global Optimization applied to Business applications
1.1.1 Optimal Control of a Chemical Process
- "Polycondensation" plant (Krallmann, 1976)
At the production of the synthetic fibre the polycondensation
is a very important process. Polycondensation means the
amalgation of simple molecules of same or different kind to
new and larger chain of molecules. During this process by-
Products as e.g. water and alcohol are separated. The output
of the polycondensation plant will be spun to thread with
high speed. As the essential assumption and condition for
the spinning process exists, that the output viscosity has
to be constant or is limited by an upper and lower boundary.
The threads will get brittle below the lower boundary and
are difficult to spin outside the upper boundary. Time
variant behaviour of the input material and the unsteady
input viscosity are the disturbances of this condition. By
varying the control variables temperature and pressure these
disturbing variables can be eliminated. The following chap-
ters describe a heuristic procedure combined with a computer-
based model to control the output viscosity in defined
boundaries.
The System Dynamics model applied to this optimization problem
describes the chemical process inside the main condensor of
a "TPA"-plant. The adjustments to the pressure and temperature
Should be computed at each point of time t, for a throughput
changes from 900 kilogram per hour (kg/h) down to 600 kilo-
gram per hour (kg/h). The primary condition is that the
viscosity SVE at the entry of the main condensor remains
constant (SVE = 390 SV-units) while viscosity of the output
SVA1 should remain between defined limits.
The equations written in DYNAMO language, describe the struc-
ture of the problem. The System Dynamics model has to be
extented by the three external FORTRAN subroutines LAST,
BER and BER1, which are linked to the model during the
running time.
345
The system dynamics model of the polycondensation plant
has been integrated as a control system into the feedback
loop. The control vector s(t) - i.e. the input variable to
the model - consists of the two components temperature T
and pressure V. The viscosity SVA1 is the state vector
2(S,t) controlled by the optimization algorithm.
The optimization algorithm, the razor search-procedure, is
responsible for varying the parameters of the control
vector A (pressure) and B (temperature) so that the state
variable SVA1 follows a user defined objective function.
The control variables, pressure and temperature, may only
be modified within fixed boundaries. The current limits for
the pressure are 1.0¢ V < 4.0 (Torr). The lower boundary of
the temperature is given at 290° C and the upper is 300° c.
The tolerance zone for the viscosity SVA1 is LIM1 <SvAl =
LIM2. At each point of time t,, the optimization algorithm
razor search tries to vary the parameters A and B of the
control variables, pressure and temperature, within the
defined boundaries so that the state variable SVA1 follows
the desired value SVA1 as closely as possible within the
desired limits.
The optimization algorithm razor search succeeds in control-
ling the viscosity SVA1 with the help of continuous and
simultaneous modifications of the control variables, pressure
and temperature, so that SVA1 will always stay within the
Gefined boundaries. Figure 4 shows the changes in pressure
and temperature needed to stabilize viscosity SVA1 within
the defined range.
In fact all chemical processes have inherent time lags.
Considering these time lags any parameter changes imposed
on the control vector s(t) will result in delayed actions
of the state variables z,(s,t). Because of these inherent
characteristics, the razor search procedure has to be modi-
fied by an additional logical step and different program
changes. To take care of the impact of the parameter changes
346
SVAIEs Veo) Tate De?
600.00 650.00
1175 2150
292.50 295-00
670-00 730.00
on s(t), the system dynamics model has to be simulated
ahead by a definite time interval which corresponds to the
longest delay constant of the model. If the parameters of
s(t) result in an improvement of 2,(s,t) at the final point
of time of the “advance simulation" the procedure is reem-
ployed at time print t,+1 to find a new set of parameter
combinations for s(t), and the “advance simulation" is
repeated.
1.1.2 Optimal Control of Investment Strategies in the
Tanker Market (Krallmann a. Nestaas 1979a)
a
A
viscosity
(svat)
Another example of optimizing a complex system should only
40.9
an
te be presented in a summarized way. The essential difference
es between the above described study consists in the use of
on the evolution strategy method as optimization routine instead
of the explained razor search procedure.
40.9 pee The main objective of this study consists in making a contri-
ae bution to overcome the crisis on the tanker-market. The
™~ erisis is caused by a surplus of tanker-tonnage and a tanker-
! fleet too big.
al : . a7 The conditions of this market are described by three essen-
“es tial factors:
lot 1) The group of demanders at tanker-tonnage consists mainly
: in seven large oil companies!) while the group of suppliers
J consists in about five hundred shipowners.
10000 2) The demand at tanker-tonnage is relative inflexible because
of being determined by the total economic demand at oil.
The small number of parameters of action the oil companies
have to influence their demand at tanker-tonnage can be
described as stock changes and as a limited possibility,
old, the structure changes of purchase, which causes changes
in the route of transportation.
1) Exxon, Royal Dutch/Shell, British Petroleum Co.,
Fig.4 Plotted results of the Polycondensation plant model Texaco Inc., Mobil Oil Corp., Standard Oil Co. of
( Oboe, California
Caused by increasing specialization the suppliers (the
shipowners) have become more and more dependent of the
tanker-market. Their parameters of action are reduced to
changes in tanker-capacities, changes in speed and in
time of loading and unloading.
3) The industry of shipbuilding is the third main factor.
The shipyards have adapted to the demand of the ship-
owners e.g. in the way that those are able to build large
ships in a short time. With corresponding docks these
shipyards are directly dependent of the tankermarket.
This set of problems described in a rough way is presented
in detailled model based on System Dynamics and problem
oriented FORTRAN algorithms.
The main parts of model are the demand sector, the supply
sector, the capital sector, the sector of the tanker-market,
and the sector of ship construction. The demand sector
describes the world demand and supply situation of crude
oil and the behaviour of the demanders at the market. The
sector of the tanker-market analyses the technical spezi-"
fications and the development as well of the tanker-fleet as
of the combined ships. The important factors concerning the
route of transportation, the pipelines and canals (e.g. Suez
Canal) are integrated. The capital sector deals with profits,
costs and the strategies of investments of tanker-shipowners.
The data used in the model are based on statistics and ex-
plorations (forecasts) of INTERTANKO (1976), OECD (1973),
EXXON (1977) , UNITED NATIONS "Yearbook of International
frade Statistics" (1975) , Shipping Statistics and Econo-
mics (1977) , Institute for Shipping Research, Bergen etc.
Bag
The objective of this study consists in supporting decisions
to overcome the crisis at tanker-market with approximate
optimal investment strategies under the assumption of a
reasonable freight rate. The principle of a feedback loop
can be used tosolve the optimization of such a complicated
model of the tanker-market. In this procedure the System
Dynamics model corresponds to the control system, the opti-
mization procedure “Evolution strategy" is identical to
controller. In the objective function the deviations of the
desired and actual values are computed. The objective is to
control the state vector z(s,t) “freight rate" (output vari-
able of the System Dynamics model) in defined boundaries by
varying the parameters of the control vector s(t) (input
variables of the system dynamics model) which are limited
between upper and lower boundaries. In this case the control
vector is identical with the different investment strategies
of the tanker-shipowners. In the model the tanker fleet is
classified into nine categories as a function of size e.g.
the control vector has nine parameters. Modifying the ele-
ment s(t) of the control vector means that the investment
is performed in the ith category and with the corresponding
volume.
The evolution strategy, with multiple elements, is an ite-
rative direct search method for optimization problems with
nondiscrete parameters. It determines minimum of a nonlinear
function of an arbitrary but definite number of variables.
Derivatives of the object-function would not be used.
Conditions in form of unequalities could be taken into
consideration. The user has to specify initial values for
the variables and the increment.
Under the control of the optimization algorithm the model
produces results with the following main characteristics
(see Fig. 5):
eunenasis
1) in periods with high freightrates the parameters of
the control vector are chosen so that tankers below
300000 tdw. (ton dead weight) are ordered with
priority;
2) an opposite situation occurs in periods with low
freight rates.
The following facts have to be done to improve the model to
get a powerful tool of supporting investment decisions of
tanker-shipowners:
- investigation and improvement of the data base,
~ investigation and improvement of. the model structure.
amet 1.1.3 Optimal introduction of innovative products into a
competetive market (Krallmann 19808)
After several years of work of research and development a
known German enterprise has introduced into the market a
product for the disgerminating of water on the technologi-
cally new basis of the anodic oxidation. The competetive _
snus.) : advantage based on the innovative character as well as the
high technical reliability of the product and coincidently
missing negative accompanying symptoms as other classical
procedures (taste changing by chloric tablets etc.) have
given a justified argument for good market expectations.
However, within the first year the expected market succes
could not be realized. As a consequence, the enterprise
initiated an investigation of the problem for analysing the
small turn-over. For this purpose a project team of the
sveace|
responsible managers and external consultants was establi-
shed.
It was intended to fulfill the following tasks successively
by the project study:
Fig.5: Demand,Supply,freight rate and ordered tanker-tonnage
351
- Analysis of the essential variables as well as of the
relevant structure of the existing problem (e.g. analy-
sing the bottlenecks in the marketing process of the
relevant product).
- Definition and analysis of different marketing strategies
for increasing the turn-over.
- Documentation of the consequences of different market
strategies on the profitability of the product.
In first discussions with brainstorming character first of
all an analysis of the problem was performed. On this
occasion a qualitative model was constructed based on
description techniques which documented particularly the
following matters of facts:
~ detailed structure of the main objective variables
(customers' potential)
~ influence factors on the main objective variables and
their characteristics
- detailed structure of the sales flows etc.
Important conclusions of this first phase of the project
study consisted in:
- the importance of system variables which had so far been
neglected (i.e. trade cycle, three devided trade struc-
ture), and
~ the great importance of observed facts as e.g. delivery
delays.
The System Dynamics approach had been applied to formulate
a formalized quantitative model based on the qualitative
one. In the process of the model development the different
modeling strategies were quantitatively confirmed by a
market research institute. The single phases of the model
building process occurred in an interative feedback process
between the external consultants and the responsible people
of the company in order to enhance on the one hand the
353
quality of the model and to strengthen on the other hand the
acceptance and the confidence of the model users (see Keen
1980 , p. 36). The model system to be developed was classi-
fied into five functional submodels with the intention to
reuse it for sequence products with the same distribution
structure (producer - trade - final user). The standardiza~
tion of these modula subsystems (e.g. subsystem 4 ~ execu
tion of trade orders) was done from the point of view of
larger modifications and modular extension. "he result is
represented in fig. 6 as a basic structure of the model.
The decision to represent the introduction process of an
innovative product line in a computer supported manner was
the basis for the development of a future model base system
(see in detail chapter IV.).
In the subsystem 1 “investiga:ion of real purchase intentions"
all the belaviour attitudes and relations are summarized
which are ¢eterminant for the monthly numer of resolute
buyers. Excgenous variables to this subsystem are represented
~ the reccmmended standard pzice for the product
- expenses of the enterprise for quality 1aprovements as
well as
- the pronction activities aijusted to the client and to
the consignees of the mailing action (physicians and
pharmacists) «
An endogenous variable to this. suzsystem within the system
boundary zs the
= average delivery time -
generated in the subsystem 4, vhich influences in a negative
manner the aunber of firmly de':erminec buyers with increasing
tendency.
In the subsystem 2 "supplier structure" the trade's opinion
with regard to the product is modeled. As an endogenous
variable the customers' demand of the subsystem 1 (jump
promotion) has a positive influence on the dealer (trade);
354
customer price expenditures for product wholesaler
promotion quality improvement and
retailer
promotion
~*~ 2.
investigation’
of real jump promotion
purchase
intentions
supplier
structure
il 4
nbengsons delivery acceptance
time of
purchase supplier
acceptance
of
supplier
4.
order
performance
3.
inventory
and
order system
deliveries
orders orders
deliveries deliveries
5.
company
production
sector
Fig. 61 Structure of the model
355
as an exogenous variable the promotion activities of the
producer have a positive influence on the trade.
In the subsystem 3 "inventory and order system" the stock-
keeping policies and the order attitude of the dealers due
to the new product are shown. The acceptance of the product
to take it into their assortment will strongly be influenced
by subsystem 2 "supplier structure", For filling up the
relevant stock, further informations concerning the supply
on the producer's part (subsystem 5) become necessary.
In the subsystem 4 "order performance" the detailed strate-
gies of supply of the orders of firmly decided buyers are
simulated. The endogenous input into the subsystem are on
the one hand the real monthly buying intentions (subsystem 1),
on the other hand the acceptance of the trade, measured in
the readiness to reorder the product for the customer (sub-
system 2). Further input variables are necessary from. sub-
systems 3 and 5. Subsystem 5 describes the production sector
of the company with the administration of the ordering
process.
With the grown spectrum of use it had become necessary to
extend the model by evalution systems in order to enable a
comparison of alternative strategies, also with a view to
the product rentability (profit. and loss account). For this
purpose the enterprise's cost accounting system was inte-
grated into the existent model as a independent subsystem.
As a result of the modular construction this was connected
with a very little coupling effort.
The objective of optimizing the marketing strategies is to
offer optimal control over sales and return of investment
of the product, which are the variables of the state vector z
(s, t). The variables of control vector are defined by price,
marketing budget and degree of product distribution.
With this methodological extension the development of an
optimal, time variant marketing-mix strategy is performed
by the computer.
1.1.4 Some critical remarks
The above described three applications developed in and
with well known companies demonstrate the pragmatical use
of this approach.
But the general, very important question in this context
is what is the amount of improvement concerning the global
optimization of system dynamics models to the quantity and
quality of information as essential inputs of real decision
situations.
Without going into much detail of the discussion of this
question the most important criteria are the quality and
validity of the model e.g.
- the closeness of reality of the model, similarity of
model structure
- the quantity and quality of the data of the real system
and its environment.
The result of this investigation (- we are performed -) can
be made that the global optimization of system dynamics
models describing technical or management problems can be
recommended.
But the end user should always be conscious about the fact
that the optimization algorithm (s)takes the corresponding
model as a formal system and defines the optimal control-
variables due to objective criterias independent of the
congruence of the model and the real world. Without concer-
ning about the above mentioned critical points the global
optimization of dynamic models is only a scientific toy.
2. Partial Optimization
Following our statements we made in chapter I the partial
optimization can simply be described by the integration of
system dynamics and linear programming models. The attempt
to explain some conceptual aspects shall be described as
follows:
357
“The structure of rates, which determines the rules for
transforming decisions into actions, can be described by
four components: the desired value of the "policy state-
ment", the actual condition, the deviation of apparent and
desired condition and the corrective action. Rates are
decisions which initiate certain actions according to given
rules within specifically defined policies. A decision is
made in accordance with an objective function towards which
the system should move. Desired state often differs from
the apparent state of actual conditions.
As a result of this discrepancy, the rate will initiate an
action in order to eliminate the deviation.
The fact that the LP-program will establish an optimal value
for a rate implies special consequences for the system
aynamics philosophy. The iP program's secondary requirements
describe in detail problem stages (partial problems) and
compute the optimal value fo. this partial problem. The
delivery of the optimal value to the rate at any point of
time t, results in the action initiated by deviation being
optimal.
The outlined combination rate-LP program thus represents
optimal behaviour of the real system.
Two practical examples of the partial optimization are des-
cribed in the chapter (III.2) focussing on the integration
of system dynamics and econometric approaches.
III. Econometric Approaches and System Dynamics Models
1. Introduction
In this context most of our interest focusses on the integra-
tion of System Dynamics and Input-Output models. But as
already mentioned before the two comprehensive projects
which will be discussed in detail involve two essential
linear programming models as examples for the partial opti-
mization. The project "Model Chemical Industry" founded by
358
the German Government is concerned with the supply of raw
material for the chemical industry. Another project founded
by the German research foundation describes the planning
process of innovative investments of the machine’ building
industry.
2. Two practical Applications of the Integration of System
Dynamics, Linear Programming and Input-Output-Models.
2.1 Model Chemical Industry
2.1.1 Introduction
For the investigation of problems concerning the supply of
raw material the Germain government has promoted a model
project!) which shall support the decision maker in finding
the best R & D strategies in the chemical industry with
respect to a modified supply of raw material. The model will
simulate the next 25 years (see Fig. 7).
Two essential questions should be answered by the model:
- Which technological and economic processes of adaption
are necessary to react efficiently on an assumed price
development at the raw material market and/or on a
modified supply of raw material?
- Which importance do process and product innovations have,
developed in the course of an investment program in
order to overcome critical raw material shortages and/or
in order to realize the saving of raw material?
1) Model Chemische Technik/Vorstudie vom Institut fiir
Angewandte Wirtschaftsforschung (IAW), Tiibingen,
vom Industrieseminar der Universitat Mannheim (ISM) und
vom Institut fiir Systemtechnik und Innovationsforschung
der Fraunhofer-Gesellschaft (ISI), Karlsruhe, im Auftrag
des Bundesministeriums ftir Forschung und Technologie,
Juni 1976.
359
~supply of raw material
quantity + price
-total economic develop-
quantities deve-
lopment of the
chemical industry)
capital,price, and|
forecasted
demand
{
H
H
H
T
H
i 4
1 | optimal structure | supply of raw
1 1 of processes cost | material tech-
H | of production H nologies
{
H H H
H H i demand of demand of
{ H H basic and basic and
i H i raw mate raw mate-
H H 1 rials out rials of
H H i of chem. chemical
H H ‘ industry industry
{ H
{ be Lin. Optimization- 4
{ Limit of Model
{ investments
ment
-technologies of chemical
industry
7
{| total economic development
H |
i i
System-Dynamics- i Input-Output-
Model H Model
i
aynamic behavior | initial ! | production-
(accumulation of H use
of the develppment of + economic
different branches impacts
chemical
industry.
evaluation of
technological
development
(chemical
industry)
R+tD
strategies
Fig. 7: Basic concept of the total model
360
The over-all problem causes the requirement to analyse the
technologies (production structures) and their development
of this sector of economy and to present it in a model
(Kornprobst and Pfeiffer, 1976).
Because of changing costs of production it is necessary to
integrate the market behavior for the corresponding pro-
ducts into the simulation model. Important macro-economic
variables, as demand of sectors for primary inputs, price
relationship etc. had to be taken into consideration based
on the total economic constellation and the development of
the Federal Republic of Germany (RFG). Concerning the com-
plexity of these questions the requirements at the methods
of the total model are:
- description of the total economy and consistent embedding
of the sector chemical industry (input output model),
- dynamic description of the cause-effect relationships of
product demand and investment behavior of the sector
chemical industry (System Dynamics),
- description of the technological development of production
process inside the sector chemical industry (linear
optimization model).
Because a comparable study had never been realized it was
necessary to test the effectivity of such a project at a
destined production sector of the chemical industry, the
organic basic materials, synthetic materials and synthetic
fibres and threads.
2.1.2 Submodels
2.1.2.1 The Input/Output Model
The I/O model describes the total economic activity which
includes as well all economic sectors of the FRG as des-
cribed some parts of the chemical industry in all details.
The principle of this disaggregation corresponding to the
361
relevant raw material was based on macroeconomic tables of
the Deutsches Institut fiir Wirtschaftsforschung (DIW), which
used the institutional principles for sector building thus
having the firm as the basic statistical unit. The quanti-
fication of intersectoral activities was made with the help
of experts, official statistics, statements of unions, and
own calculations.
The basic component of input-output analysis is the design
of the input-output table according to which empirical data
are collected. An input-output table assigns the collected
data to individual production sectors. The table, therefore,
offers an insight into the economic production structure
which cannot be had by any other statistical tools. Input-
output tables describe flows of goods and services between
individual sectors of economy.
Reading a table by rows it can be determinined how much a
certain individual sector delivers to other sectors. In
this way, some elements of the first row indicate how much
the first production sector delivers to itself and to other
sectors. Other elements of the first row indicate deliveries
to final demand sectors i.e. private households, goverment,
investment (capital expenditures and inventories), and export
sector. The deliveries to the production and final demand
sector depict, by definition, the total production of the
first sector and also by definition total demand for the
products of the first sector. The columns of the table give
the demand by each sector for deliveries or services of
other sectors which by definition is put equal to the trans-~
fers it receives from other sectors. Reading the table by
columns reveals the transfers which the individual sector
xeceives from other sectors (inputs). Included in the so-
called primary inputs are imports which among others include
foreign raw material deliveries. The remaining primary inputs
show the amount of capital depreciation, the renumeration of
labour and capital.
362
One problem in this model is to generate the I/O table
(56 x 56) for future points of time. Some data can be got by
the scenarios, which deliver possible alternatives of the
economic growth and the simulation of raw material. From the
SD model, the I/O model will get future data of the gross
production and the demand of the chemical industry.
The LP programm delivers informations about the demand of
basic and raw materials of the chemical industry. With the
application of a mathematical procedure called MODOP the rest
of data is computed. The quality of this projection method
was determined with statistical data by performing an ex-post
simulation from 1958 to 1972 and comparing the actual with
computed data.
2.1.2.2 The Linear Optimization mMode1!)
The main task of the LP model is to compute the technological
development of the chemical industry as a function of changes
in price and shortages in raw materials (Burger et al 1976).
By determining a demand function with reference to the deve-
lopment of the particular branch and its long-termed ten-
dencies, future quantities and prices of products of the
chemical industry can be found out. This estimated demand,
besides the investment plan, the demand for raw materials and
preproducts of other branches delivered from the 1/0’ model
as well as the prices of raw materials and changed technolo-
gies from other scenarios, serve as a guide line for calcu-
lating the process structure with the minimum cost.
The basic structure of the LP model is shown in fig. 8.
The production of the final products occurs from different
raw materials, basic materials and preproducts. The total
flexibility of this branch of production is shown by the
fact that as well the final products can be produced by
1) This is the first practical example to the chapter II.2
partial optimization
363
raw materials R,
production processes T
of preproducts
preproducts V,
final products
e.g.
|—=——— Optimization
> «Vv
Ty" "sn
Fig.8: Basic Structure of the LP model
(Source: Modell Chemische Technik (1976),p. 5-2).
364
mineral oil,coal,
natural gas
. naphtha, fuel oil,
xaw beizol
ethylene,benzene
« products of polyme-
risation, synthetic
fibre
different processes of different preproducts as these pre-
products can be manufactured by different processes of
different basic materials. Each possible way of production
causes different costs of production. Under the assumption
to produce with minimal costs as main criteria, the LP-
model computes the optimal technological development of
production processes of the chemical industry.
2.1.2.3 The System Dynamics Model
In the SD model particular attention is given to the process
of capital formation which involves capacity employment and
depreciation. On this basis, fixed costs can be calculated,
which - together with the variable production costs calcu~
lated in the LP model - are used to form a supply function.
The System Dynamics model consists of the essential sectors:
- the capital and capacity sector,
- the market sector.
With a time interval of four years the SD model calls the LP
and I/O model. Data for the formulation of the objective
function and for the description of the boundary conditions
are delivered to the linear programming model, which. for
its part gives information about the optimal structure of
production processes and about specific product costs. Fig. 9
and Fig. 10 describe two main relationships between the
SD~ and LP model.
The optimal capacity data of the preproduct production pro-
cesses represent the desired values for the main feedback
loop realized in the SD model. The first loop structure
describes how the optimal value of capacity computed in the
LP program is realized within the four years optimization
interval (see fig. 9). Another, very essential integration
of LP and SD model becomes obvious with the production of
preproducts (see fig. 10).
365
optimal
capacity
investments additional Optinteation:
interval
capacity
reinvestments
tual (caused by depreciation)
capacity in the optimization
interval
Fig.9: Causal structure of the invetments of the preproducts
(Source :Modell Chemische Technik (1976),p. 4-6)
cost of raw
, ea materials
Senge forecasted
production processes ecast
and production capacities
NN sales rate
cost of market“price
products ——————,
production
plants
Fig.10: Causal relationship between the demand with the optimiza~
tion program
(Source:Modell Chemische Technik (1976), p- 4-9)
366
This model overlapping feedback describes that an increase
of raw material or other production cost leads to structural
changes of the technology mix. Thereby the costs of prepro-
ducts are changed which are concerned by the modifications
of processes.
In the SD model the capital building process is formulated sales and capacity
in the same sense as. the production processes are selected (in thousand ton)
in the LP model: The capital is invested and depreciated
gradually or capacities respectively are reduced of eliminate
computed capacyty-
with time. The capital formation process ~ once started - products of
influences the production costs with its typical time lags polymerisation
then again has an effect on demand and production.
/
y
In this case for every considered production method an extra
capital and capacity vector is formed, which is subdivided
into age-groups and others. A further subdivision is formed
with respect to the time.
actual sale -
products of polymerisation
2,000
The construction of capacity and capital vectors facilitates
finding out the correct production costs, even if capital:
computed sale -
products of polymerisation
is fully or partially depreciated, because the lifespan and
the period of depreciation of plant can vary.
2.1.3 The Total Model
The total model was simulated in an ex-post projection from 1958 1962 1966 1970 1972
1958 to 1972 and the results were compared with the reality.
These results can be considered as satisfactory with respect Figs12! Sales and dapaci of products of polymerisation
tO non sufficient data base (see fig. 11). Fig. 7 shows a (SourcetModell Chemische Technik (1976), p. 4=25)
survey of the interdependent relations of the total model.
The simultaneous model-method-linkage represents a new area
in the methodical and model technical sense. The arising
difficulties require essential consequences in the future
work in the area of model coupling. The definition of inter-
faces is a basic prerequisit of an integration of different
model types. Such a definition includes not only the number
367 368
and the type of variables but also the dimension and the
scale factor of the concerned size. Disregard of these re-
strictions leads to difficulties when the SD- and LP-model
are brought together with the I/O model regarding the valu-
ation of quantity streams.
The valuation at cost prices in the LP model (SD model) must
be made consistent with the valuation at ex-works-prices
in the 1/0 model.
Because of the different model concepts of System Dynamics
(dynamic) and the Linear Programming (static), difficulties
can arise in the timing of the coupling. The optimal capacity
fixed in the LP model should be realized in a four years
optimization interval by the SD model (that means that the
coupling is executed in a time interval of 4 years). This
model coupling as a function of time is a problem in the
sense that for example for profitability of the Chemical
Technique could change within one projected interval of two
optimization moments. This includes the risk of the optimal
operation structure of the LP model becoming invalid. The
following coupling concept shows an alternative to this
time dependent coupling and also a solution to the problem:
the control of the call of the LP model is carried out with
regard to defined boundaries that means, if the profitability
changes in a way to disturb the lower and upper conditions,
there is a new call of optimization. This concept burdens
the central processing time, but enables additional infor-
mations.
2.1.4 Summary
At this moment, the total model with its already relative
complex submodels (Input/Output-, Linear Optimization- and
System Dynamics Model) represents the first step in solving
the problems of a technology assessment with respect to
overcome critical raw material shortages and to realize the
saving of raw materials.
Such a model-method-integration is an instrument making plain
how to deal with complex and comprehensive socio-economic
phenomena in an easier way. After further experiences with
the practical model application and after methodical improve-
ments, an instrument should be created which will fulfill also
the requirements of practice. It is hope that further expe-
xiences with the practical model applications and the metho-
dical improvements would create an instrument which would
fulfill also the requirements of practice.
2.2. Model for planning innovative investments of the machine
building industry
2.2.1, The problematic nature and the process of development
of the innovative investment planning in the machine
building industry
This study deals with investment planning in providing of new
equipment to small and medium size companies in the machine
building industry, whereby an exemplary investigation of the
application of the NC-technology was performed and the analysis
of more complex automation (a computer based job planning
system and a flexible system of production manufacturing)
has been started.
The automation of limited quantity production of machine
building industry is characterized today by a conversion
process towards growing computer based applications both in
material processing and transport as well as in the planning
phases construction, operations scheduling and manufacturing
control. If from the technical standpoint individual pro-
cesses and elements of the manufacturing process are to be
automated the task of the investment planning consists in
conducting a critical report of the efficiency.
The problematic nature of such an investment decision can be
outlined as follows:
370
~ the introduction of certain production equipment is linked
to complicated and expensive technical/organizational
processes of adaption;
~ the production equipment determines in long range the
potential manufacturing program of a company?
~ the production equipment of the above mentioned industry
requires a considerable amount of capital;
= the question of financing of such investment projects has
great importance for the company;
~ in planning of automation processes of limited quantity
production for firms of machine building industry, the
consequences of different strategies must be investigated
concerning the objects of investments regarding the
financial, personal, organizational and social effects.
Because of the interactions between company and its environ~
ment next beside to the internal aspects, macro-economic
components are never-the-less important determinants of
innovative investment planning.
the description of strongly differing aggregated variables,
for example the representation of the global demand on the
one hand and the detailed analysis of the coordination of
capacity on the other hand, cannot be realized by a comprehen
sive macro-economic model.
Such a differentiating level of aggregation requests a hier-
archical-structured model system with an interdisciplinary
concept, which places the essential - the necessity of a best
possible possible solution of the problem with appropriate
techniques - into the foreground (Krallmann 1979b). On the
basis of these conclusions, the macro-economic area is re-
presented by an Input-Output model. A linear programming
model and a System Dynamics model describe a representative
firm of the machine tool building industry to outline the
operational and internal consequence of an innovative invest-
ment in the manufacturing area (see fig. 12). The three
level-model-method linkage on the one hand contributes to
the improvement of the transparence of the total system, and
371
on the other hand it succeeds in meeting the requirements
of the validation - even if only to a small extent.
2.2.2. Linear Programming Mode1!)
Principal item of this model linkage is a coupled system
Dynamics and Linear optimization model (SD-LP model). The
SD-LP model optimizes and simulates the investment activities
of a representative firm of the’ machine tool building industry.
The LP model fits-at the computed sales development by the
I/o-model ~ the investment and financial planning as optimal
final value, while the SD model simulates the company internal
processes and the consequences of this adaption in detail over
time.
In the optimization model the principle of “rolling planning"
is applied. The planning period comprises thereby respectively
24 months, that is, every 24 months, the LP-model is called
to establish new data. But the LP-model surveys 72 months and
delivers only the actual value for the first two years to the
SD-model, so that a data overlapping period of 48 months exists.
The planning horizon of the complete model is defined with
8 - 10 years. The financial restrictions appear as significant
secondary conditions: investments borrowing and withdrawals
are variables to be determined in each period from "t" to the
planning horizon "t + Q" in compliance with
- the financial balance between installments, pay-offs, and
cash balances during production and sale of the given output
- a capital dependent limit of credit
- a production capacity in the areas of drilling, lathe
tooling, and milling which is sufficient for the given
output.
The final amount of capital due to the planning horizon con-
sists of
1) This is the second example to the chapter 11.2 partial
optimization
312
Input-Output-Model
total economic determination of Consequences
aspects
of alternative developments
of ultimate demand on turn-
over rate
gross production data (turnover)
of machine tool industry
Linear Programming Model
company’s
aspects
medium term investment
production and financial
planning
‘desired data of actual production
investment and financial tool equipment in t
planning
financial situation
of company in t
System Dynamics Model
company’s
internal Production sector
aspects financial sector
Fig.12: Structure of the three step Model linkage
313
- the capital on the horizon at liquidation prices,
- cash balance on the horizon,
- the withdrawals (in the planning period)
computed including the interest at the horizon,
subtracting the not yet payed credit debts is to be
maximized.
The remaining system of restrictions, which consists of
capacity and equipment equations for the limitation of the
present alternative attainable production equipment guaran-
tees that sufficient installation capacity is available (in
each planning period), in order to produce the demanded
output.
2.2.3. The System Dynamics Model
The System Dynamics model transfers the delivered objective
variables of the LP-model in respect of time to short-term
dispositions and calculates the resulting consequenses in the
area of finance and production over the time. The System
Dynamics concept is used as a method for the representation
of the structure and the parameters. The variables for orga~
nizational levels in the workshop and the job planning
system form the basis of the model.
2.2.4. Input-Output Model
The expected sales in the machine tool building industry are
considered as an essential decision criteria regarding this
investment planning process. In order to show the process of
implementation of the NC-technique in this sector, the SD/LP
model is enlarged by an Input-Output model (I/O-model). It
4s an open static I/O-model, which has been expanded by a
dynamic model of the demand for investment goods. On the
entire model concept the I/O-system has the task to show the
effects of alternatively given developments of the final
demand for products of any sectors (for example airplane)
314
manufacturing, the manufacture of motor vehicles and ship
building) upon internal demand for investment goods in the
machine tool building industry. This formulation of the
problem has the advantage, in comparison to an isolated
observation of the development of sales in a single sector as
the basis of investment planning, that micro-economic foun-
dations of decision are taken from a macro-economic background.
Alternative developments for the components of the final
demand are supplied by the user so that the diffusion of the
NC-technology in the machine tool building industry which
results from that can be determined.
2.2.5, The Presentation of the Results of the Model Integration
In order to demonstrate the way in which the model integra
tion operates the data of a representative firm of a machine
tool building industry with a size of 400 employees with a
25 million turn-over per year were used. Fig. 13 shows the
resulting development of the absolute number of NC machines
of the representative firm.
The graph illustrates the consequences of the differing deve-
lopment (optimistic, pessimistic) of the final demand to the
introduction of the NC-technique in that company. The simula-
tion period is six years. When the market development is
favorable, eleven NC-machines are installed after six years,
when it is unfavorable, only eight NC-machines are installed.
The development of investments at the standard prognosis at
the end of the Planning horizon computes nine NC-machines.
A realistic interpretation of these results shows that, when
demand decreases furthermore at a limited extent only replace-
ment investments are carried out. The time difference of 3
years (see fig. 13) between the introduction of the eight
NC-machines into the firm with an optimistic versus pessimistic
demand prognosis documents the influence of different market
developments due to the realization of the technical progress
in the production process of machine tool building industry.
315
Number of
NC-Machine
1 2 3 4 5 6 Years
2
opt.
10
Standard
: pess.
—---} wl
6
4
12 24 36 48 60 72 Months
Fig. 13: Development of the NC-Technique in special company
different Market behaviors
376
The positive results of the discussions of the realized three
level integrated model system motivated for an analysis and
evaluation of more complex automated production equipment as
in this case investigations of computer based systems of job
planning and flexible production systems (Krallmann 1979¢ )
had been performed. Both projects, which are carried out in
close cooperation with two companies led to major changes in
model structure and to the application of a dynamic program-
ming model.
In order to present such measures of automation in combination
with one another, the instrument of linear programming is no
longer sufficient because of the appearing essential non-linear
impacts. Especially the instrument of dynamic programming
proves itself to be very promising. An intensification of the
interactions is aimed at the model of dynamic programming and
the Input-Output model. The essential point consists in the
realization of a bilaterial transfer of data between both
submodels.
The transfer of data describes on the one hand a sales fore-
cast into the model of dynamic programming and on the other
hand a forecast of investment planning and investment demand
into the Input-Output-model.
377
3. Some Critical Remarks
Input-Output analysis is a mechanism for decipting a complete
economic structure. Transferring the values of the Input-Output
table on to the auxiliaries of a System Dynamics model, as
e.g. the so-called input coefficients of the Input-Output table
are assigned. The input coefficients,
Rig
ayy = sil
a3 x;
are calculated for the production sector. They show what quan-
tity of product i sector j is used to produce one unit of
output j. The input coefficients, and therefore the correspon-
ding auxiliaries, can be interpreted as technical variables
or quantitative market variables which characterize the pro-
duction structure of the economy. The advantage of combining
System Dynamics with Input-Qutput analysis is that the degree
of reality is now incorporated in the system Dynamics model.
System Dynamics, Input-Output method and Linear programming
are well approved tools and successfully applied to different
problems. But using these approaches in an integrated system
there are somecritical facts which may not be kept secret
as e.g.
- the handling of the total model complexity
- high requirements are set to end users in handling these
different methods
- high data processing requirements are very evident.
The expenditures of these facts and of others in comparison
to the benefits must decide about the application of such
an integrated system.
IV. System Dynamics Models as Decision Support Systems
1, Introduction
This chapter describes the further development of the project
“Introduction of innovative Products into a competitive
Market" (see in this context the chapter I. 1.1.3 which
describes the problem in some detail) towards a model base
system.
The management of the company we worked together wanted to get
support in the decision making process of introducing inno-
vative but similar products into a competitive market. These
different products for sterile (pure) water processing
- are based on the same idea of performance but different
attributes (or properties)
- are of high quality
- use the same logistic
- operate in different markets.
Based on the two already developed System Dynamics models for
two different products (see Krallmann 1980b ), the idea was
born to create a model base system. In the first step this
model base system should contain
- a number of submodels (modules) describing different
sectors of different real systems
- a number of optimization routines (razor search, evolution
strategies and other heuristic search algorithms)
- a planning language beside general statements which can
handle the modules and algorithm routines with user
friendly commands and which takes care of the execution
process on different computers.
The second stage is to design an interface between the model
base system and a data base system to get access to company's
internal (e.g. cost accounting system) and external data.
This step is now in the phase of design.
319
The planning language now under development can be characte~
rized by interactive, flexible, transparent and user friendly.
Further on the surface of this language is easy to use,
reliable, reasonably self-explanatory, and responsive - just
like a staff assistance. This points out an important conclu-
sion: management wants to become directly involved in the
model building process so that they may understand it and so
that the model has credibility.
Another major additional change had to be performed at the
DYNAMO-Compiler and its produced FORTRAN-Code.
Special software has been developed to present the results
from the simulation models being investigated and data of
the cost accounting system in integrated figures (in any
desired arrangement of rows, columns, and headings). Report
formats may be called from storage or specified as needed.
The main advantage of such a decision support system (model
base system + planning language + report generator + data
base system)consists in the fact that the manager can formu-
late and simulate very easily his own problems based on
system Dynamics in this specific field at this time.
The requirements at decision support systems caused by growing
problem complexity and organizational structure demand in the
process of man machine communication the support of human
inhabilities as
= human memory through data base systems
- simultaneous consideration (analysis) of complex facts
(problems) through model base systems.
These tools can give an important support to human capabili-
ties as creativity and association of ideas.
380
2. Components of the DSS
2.1. Command and planning languages
The conversational language between decision maker and machine
should comprise linguistic elements and integration rules
which follow the expert languages of the decider in mnemonic
technical respect. The user surface of this language “must
be flexible, easy to use, reliable, reasonably self-explana-
tory, and responsive - just like a staff assistant" (Keen
1980 , P. 41). If possible, the command language should be
nonprocedural for supporting a thematic classification of the
model structure in respect of the model building (see Keen
and Wagner 1979 , p. 119).
For a future orientated DSS a user friendly control system
(also called method monitor) for the realization of complex
program systems will be evident. The final user can integrate
methods to parameterless procedures which can be established
by a simple command language. The procedures are registered
in a relevant file and are called with their names. Such ©
a structured control ensures for the user an excellent combi-
nation of the methods without establishing a program.
Beside the process of model building and of program realiza-
tion the phases of alternative finding and evaluation are to
be realized computer supported. The procedures which always
repeat in situations as alternative evaluation can be simu-
lated by special simple commands. A “what-if" command allows
after input of the strategy which shall be analyzed the auto-
matic output of the results of selected objective variables
in relation to the defined standard run. For supporting the
alternative finding in the case of a planning with defined
objective variables, the generating of a "goal-seeking" or
"“what-to-do-achieve" command is recommended which describes
the planning measures to be performed in order to achieve a
certain objective (see Wagner 1980° , p. 210). The evident
381
demand of the interactive equipment of the command and plan-
ning language (of the DSS) can at every time be argued as
follows:
- direct use of the DSS by the decision maker
- considerable enhancement of efficiency by immediate
reaction in group conferences and
- positive influence on the creativity and intuition of the
decision maker (see Vazsonyi 1978 , p. 76; Keen and Wagner
1979 , p. 119).
An extremely comfortable handling of the unformatted data in-
put up to normalized output routines, e.g. for tables and hi-
stograms, is a necessary request for the use of the system by
the decision maker. He is an expert in the scope of application
and disposes only of basic knowledges of the methods, he needs,
however, explanation and decision supports for the efficient
operating because of his limited know-how of EDP.
In this special project for the handling of the modular System
Dynamic model and the methods of heuristic optimization in
the process of global optimization we developed a userfriendly
interface part. The interface part is very reliable, easy to
learn, self-descriptive and flexible in task handling. A
communication part realized in this manner enables end users
with different know-how (EDP training etc.) and different
professional career to use the computer aided DSS, by having
realized first steps of the interface part with a view to
individual adaptability (see Fig. 14).
2.2. Data base system
Under the point of view of an extension of the possibilities
of application of data for many different applications as well
as for many different users the storage must be transmitted
from the so far usual orientation on a special application to
a general data orientation. The increasing data application
on higher decision levels in the case of problem solutions
382
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MODEL (FURTHER ON CALLED ZUPARMS), WHICH YOU CAN USE IN
YOUR OBJECTIVE FUNCTION.
EXAMPLE: OBJ.FUNCT.=WEIGHT1 * ZUPARM1 + WEIGHT2 * ZUPARM2
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383
which go across functional and organizational limits recom-
mends the development of a data architecture plan for pro-
cessing the concentrated information requirements of the
enterprise. The development in the data management can be
characterized by an
- increasing storage with direct access in the case of
decreasing costs and increasing capacity
- data structuring with the capability to describe more
complex data concatenation.
Thus the data base system becomes a necessary condition for
a strategic DSS. The transition from data files over data file
administration systems up to data bases considers the impor-
tance of the data as a basic auxiliary for decision functions.
Data bases have been created for the following reasons:
- The flexibility of the different applications resp. data
applications should be supported and not prevented.
- The redundant storage of similar data should possibly be
prevented.
~ The security of the data should be given by a consistent
data base.
- User programs should become independent of the physical
data organization.
In this special project we use the company's data base system
to get access to the data of the cost accounting system.
2.3 Model/Methods base system
As a second essential component of a strategic DSS, apart from
the data base system a methods/model base system is required
with the function to support the decision maker (model builder)
in the phase of modeling, i.e. of representing the real problem
to be solved in quantitative termini by farreaching standardi-
zed, often required, procedure appropriate program units (see
Hauer 1979, p. 262).
384
A methods/model base system is composed of
- a file of preproduced and documented program elements
(methods base system); these can be derived from existent
method base packages of the producers or can be supplied
by the final user himself
- a file of preproduced and documented model modules
- a method monitor (control system) with a data administra-
tion, a formula interpreter, a data base connection and
procedures for integrating user own programs as well as
- software components for the user friendly support (i.e.
choice of methods, interpretation and representation of
methods, results of methods etc. (see Gernert 1979,
p. 94 ££).
In this special project the developed model system was classi-
fied into five functional submodels with the intention to
reuse it for sequence products with the same distribution
structure (producer - trade - final user). The standardization
of these subsystems (e.g. subsystem 4 - execution of order by
trade) was effected under the points of view of larger modi-
fication tendency and modular extension. The result is re~
presented in fig. 6 as a basic structure of the model (see
in this context the chapter I. 1.1.3 which describes the sub-
models in some detail).
3. The integrated concept
The DSS for the time being in the process of investigation and
development are characterized by the integration concept with
the essential functions data manipulation and model building
which have been so far represented in the scope of data and
model base systems (see Wagner 1980 , p. 200). The realiza~
tion of an efficient strategic DSS needs the integration of
the functions “data handling" and "modeling" in the case of
mutual direct involvement of the end user. Out of this fact
three critical interfaces result which have to be got ander
385
control by the software of a DSS (see Bonczek, Holsapple and
Whinston 1980, p. 345) on the one hand by the transfers
between the system components data base and methods/model
base with regard to the user, one the other hand
by the system internal interactions of data bases and methods/
model base (see fig. 15).
In this special project the decision support system for the
“Introduction of innovative Products into a competetive
Market" is based on four essential components (see Fig. 16):
- the model base system with the System Dynamics modules
established by the usér in the simulation language DYNAMO
- the monitoring system with the essential part - EDT proce-
dure "SHOOT". The data file processor EDT is a user orien-
ted dialog text editor which modifies the FORTRAN code of
the SD model generated by the DYNAMO III/F-compiler. The
modifidied FORTRAN subroutine can then be linked with
other modules and can be integrated into the global opti-
mization process
~ the method base system for the optimization routines and
the modules for representing different objective functions
- the interface part.
386
END_USER
/Decision maker/
data
base
system
interface
part
method
model
base
system
system-
Dynamics montitoring
loptimizations+ system
routines
hardware
configuration
Fig. 15: Decision Support Systems
387
Model Base Data Base
system system
i iil MODEL
s(t)
e.g. SD Model
e(t)
Method
Method Base
System
c(t): control vector
s(t): state vector
d(t): desired vector
Fig.16: Total system Configuration
388
a(t)
The interface part serves the absolute priority of the reali-~
zation of a user friendly, computer supported planning system
(see also chapter IV.2.1.). The integration of the end user,
the reduction of his acceptance problem by a user friendly
interface part, which is on the one hand extremely robust and
on the other hand easy to learn, were the central points of
this software development. The easiness of use and the minimal
EDP specific know-how are demonstrated by the computer suppor-
ted dialog in the interface part (see fig. 14).
In principle, only the following informations are required of
the end user:
- Number, name and restrictions of the control variables
- Number and names of the state variables
- Specification and parameters of the objective function
- Declarations regarding the simulation/optimization
variants
- Choice of the optimization algorithm and the relevant
parameters (documented in a self-explanatory manner).
389
4, Some cr
cal remarks
For judging the presented DSS the criteria by Sprague and
Watson 1975 , p. 35 f£., shall be taken:
- Collection of modular models for support in different
functional fields and on different management levels;
- Modular model elements which are transferable single or
in any combination;
~ Mechanisms for direct automatic data supply of models out
of the data base;
- Common end user language for data handling and for model
building resp. execution.
Critically seen, it must be said that with the DSS for the
sales' planning of innovative products only proportional parts
of the criteria of Sprague and Watson could be realized, but
the basic conception as well as principle ideas could be
performed.
Some experierces and understandings of these first phases of
development implementation process can be summarized as
follows:
- The application spectrum and the extension of the DSS
should grow in a stepwise manner with the degree of ma-
turity and comprehension of technology resp. of personal,
i.e. only modules should be added which are applicable in
technical, organizational and economical respect;
- development of the DSS and the implementation into an
existent EDP system of the enterprise should be directly
supported and realized in cooperation with the end user
himself.
If the demand of the DSS is defined in the improvement of the
efficiency of the strategic decision procésses and in the
connection of the qualifications of men and machines, there
is still a far road to success.
390
V. System Dynamics Models based on the integrated
approaches of ABRAHAM/ISAC and PETRI nets
1. Introduction
This chapter is quite different in comparison to the previous
ones.
The previous chapters describe well-experienced approaches,
implemented in well-known companies. In this chapter an inte-
grated concept will be presented which is only applied to
academic examples (Godbersen 1983). But this approach based
on ABRAHAM/ISAC and PETRI nets is in my opinion very interes-
ting because the analysis of structure and dynamic behavior
of models can be performed by the mathematical calculus of the
Petri nets. By doing this the validation process of model
building can be supported and the attributes of the object
system can be established.
2. Description of the selected approaches
2.1 ABRAHAM/ISAC (Lundeberg et al. 1979)
ABRAHAM stands for ABbReviating Activities HAndling Methods.
ISAC (Information Systems Work and Analysis of Changes) is a
research group at the department of Administrative Information
Processing at the Royal Institute of Technology and the Uni-
versity of Stockholm, Sweden. Since 1971 research has been
performed in the ISAC group around a new approach to infor-
mation systems development with special emphasis on analysis
and design of information systems (Lundeberg et al. 1979).
This concept had been simplified from methodological point of
view to get an interface to the Petri net theory. There are
two kinds of elements:
Activities and information units (channels) /material units.
These elements can be connected by arrows describing relations
between the activities and the information units (see fig. 17).
391
An essential characteristic feature is the possibility to
redefine and to abstract gradually the activities and infor-
mation units. On this way a problem area can be described
on different abstraction levels of refinement (see fig. 18).
All different levels can clearly be summarized by activity
and information trees.
2.2 Summary of Petri net theory
Avhuge amount of literature is available describing the theory
of nets and further developments and improvements. Petri
describes the objectives of net theory:
"The theory of nets is a form of general systems theory,
developed as a tool for the system analyst for representing
and investigating real or planned information and communi-
cation systems in any required degree of detail. On the other
hand, net theory constitutes an axiomatic approach towards
establishing a conceptual frame for the description of the
phenomena of information flow. This approach is similar in
spirit, and to some extent influenced by the axiomatization
of relativistic spartio-temporal structure which Reichenbach
et al, undertook fifty years ago Petri 1973 , p. 137.. Later
on Petri introduced a General Net Theory (GNT). "General Net
Theory is a strong generalization of the theory of transition
nets. It was developed for the purpose of overcoming certain
practical and conceptual difficulties on all levels in the
computer field.” (Petri 1976 ).
The main features of the theory are:
A (formal) principle for system composition and decomposition
which works consistently on all levels of system description
and system specification.
A (formal) method for introducing and emitting detail in
system descriptions, accompanied by a graphical language
which facilitates communication about complex structures.
symbol
interpretation
PETRI_NET:
denotation
activity TRANSITION
- action
- process
- information processing
- data processing
- program execution
~ event structure
Ay
information unit (channel) PLACE
material unit
- message representating component
- carrier of messages
- carrier of material
- communication medium
> state structure
4)
access paths
describe the interrelationships between
the activities and the information
units
compound activity
describes an activity of the (n - 1)th
level on the n-th level (n 2 2)
compound information unit
describes an information unit of the
(n - 1)th level on the n-th level (n 2 2)
Fig. 17: Description of ABRAHAM
393
Level (1) Level (2)
(overview Leys) (ist refinement of level(1))
(1st abstraction of level (2))
Fig.18: Example of an ABRAHAM reqirement
394
A (formal) method for stepping through a series of conceptual
levels and for defining higher-level concepts in a rigorous
way on the basis of lower-level concepts.
Precision of modelling in the presence of "fuzziness" (e.g.
non-transitivity of concurrency and of other similarity rela~
tions arising naturally in technical contexts).
General net theory encloses:
Formal definition of nets; basic interpretation and derived
interpretations; dualities in nets; net mappings; the category
of nets; net topology; net completion; synchronic structure of
systems; enlogic structure of systems; fact logic in non-
sequential processes and distributed systems; system properties
"safe", "live", "conflict-free"; types of system components;
information flow graphs.
Some remarks shall follow to get in mind the fundamentals of
net theory. The purpose of net theory is not mainly descrip-
tive but rather to supply us with descriptive, deductive and
conceptual devices:
- descriptive devices for demonstrating the structure of
systems and of processes supported by a system, in terms of
axiomatically introduced co;.cepts;
- deductive devices for solving application problems such as:
synchronization problems, concurrency problems, problems
involving mutual exclusion, conflict, arbitration, sequen-
tialization, safety, problems of deadlock-avoidance
and of endlessloop avoidance, problems in asynchronous
switching logic, and last but not least, problems arising
in an area, not generally known of us yet, called formal
pragmatics, in which we are concerned with questions of the
form ‘What, precisely, do we do?, as opposed to formal
semantics in which we are concerned with questions of the
form 'What, precisely, does it mean';
395
conceptual devices producing precise concepts on many
levels or for promoting the communication between the
computer expert and other people; I see this as being a
main point of General Net Theory. We can communicate
between ourselves very well, but it is difficult to explain
computers to 'innocent' people. As a conceptual device, net
theory should promote this communivation and provide means
for introducing new concepts, in a precise, but, never-
theless, easily visualizeable way, hence the importance
of graph-theoretical methods, and of the idea of the ‘token
game' played by many independent actors.
Net theory is not primarily a mathematical device, rather it
is accompanied by a simple graphical means of expression con-
sisting, at the basic level, of four symbols only (see fig.19).
re
Fig. 19: Basic net structure
Thus, in this notation, we have the following four types of
symbols:
8: 0 state elements (also called places if they can
contain more than just one token);
S contains symbols denoting ‘supply stocks', and items in
these supply stocks are represented by tokens or markers
(dots) on the state elements.
T , transition elements, representing, for example,
—— processes; elementary events, of which processes
are built; alterations in the holdings of conditions;
transportations; transformations and so on.
y
flow relation, no longer denoting a transition
itself but only the relation between a state and
a transition; F might be read 'from ... to ....!
e + tokens, countable items, resources of any kind.
Thus, a net is defined to be a triple (S,T,F) where
S T = @ (state elements and transition elements
are disjoint sets),
S UT = field (F) (there are neither unconnected
state elements nor transition elements)
F #9 (nets cannot be empty)
F $xTUTxS (the flow relation holds only
between state elements and transition elements
or vice-versa)
A marked net is a net with a distribution of tokens over the
places.
The Petri net-(PN)-theory can be used to formulate a general
concept of model building because of
397
- PN support a reasonable graphical presentation
- two kinds of elements (state and transition elements)
- PN can model sequential and concurrent processes
~ PN have a mathematical theory to analyse the static
and dynamic behavior
3. ‘The Integrated Concept
3.1. Basic ideas of the new approach
To realize the integrated concept we have to close the con-
ceptual gap between the two different methods which
- the change from informal descriptions to formal models
without an explosion of the amount of representation
{realized by attributes provided for the node and
system relations)
- the change of anonymous 'token' to structured individuals
(realized by a message address)
- the inclusion of dynamic aspects and the performance of
operations on objects
~ the conceptual inclusion of the "time use"
- additional "transition rules"
- the consideration of different forms of system relations.
The inclusion of dynamic aspects is realized by the flow
of messages along the flow relations (arrows). Operations on
messages can only be performed in the transition elements.
fo include conceptually the time into the model the transition
elements are provided with the time use.
To describe the dynamic of a system we introduce the "OR"
relation additionally to the "AND" relation.
The processing of messages is done by the normal system rela~
tions 'INPUT' and ‘OUTPUT'. The additional relation is e.g.
"copy' to read the message without clearing.
398
All these additional changes and basic principles of both
methods are implemented on a computer (Godbersen 1983). The
next chapter shows a very simple example to demonstrate the
new approach to be applied on a System Dynamics problem.
3.2 Academic demonstration example 'Retail Sector’
The integrated modified approach ‘function nets' described in the pre-
vious sector is now applied to a very simple system dynamics
example explained in Pugh 1976, p. 9-17 .
The model will be a retail sector. The customer, who is exo-
genous to the model, places orders upon the retail sector for
an aggregate product. These customer orders reside in a “pool”
of unfilled orders until they are filled from inventory. The
xetail sector in turn orders to replace the items sold and
to correct the inventory to the desired level, which is
several weeks of average sales. These orders from the retail
sector are filled after a fixed delay (Pugh 1976, p. 9).
The basic structure of the model is shown in fig. 20.
The model behavior will be demonstrated,e.g. how will the
actual inventory react to ten percent increase of requisitions
received at retail as a function of the different delay.
In the model building process the variables ‘unfilled orders’
and ‘actual inventory' are accumulated in the transitions
‘unfilled orders' and'actual inventory’ (see fig. 20),
Roquisttons Untilled
received ‘onders
ac metal at retail
SL1}—o.
‘axigments sent}
‘from retail
Distributor | | Purchae onder Inventory actual,
sent at retail
Fig: 20: Basic structure of the model 'Retail Sector’
399
The following operational function net is the result of
the specifications of delay times, initial conditions and
the policies (see fig. 21).
6) 1 7 SS ontiniea
requisitions orders at
received at | retail
retail
Shipment sent
from retail
Inventory
actual at
\ retail
Purchase order
sent
Fig. 21: Retail Sector
The accumulation of ‘unfilled orders’ and ‘actual inventory'
is realized by the INTEGRATE transition in I5 and I6. 15 gets
the new orders from I1. The shipments sent from retail reduce
the level of actual inventory.
400
The order entry (requisitions received) is constant at RRI=
1000 (units/per week) until the fifth week, with a switch
: 1 it will make a change to 1100 units. The purchase
orders sent are smoothed over time in.I2. 13 describes the
policy for purchase order sent. Since in this simple model
the distributor will be represented by a fixed third order
delay of the retail order rate realized in 14. The distribu-
tor's delivery time is two weeks but can be changed in the
following reruns. 18 sends to all integration and Delay
transitions a start signal each time interval of DT so that
all computations are performed in constant time steps. A
performed analysis of validation shows that the net is with-
out any conflicts, overall ‘alive’ and ‘immortal', That means
there have been made no serious structural errors in the
model building process. The last fig. 22 represents the Petri
net of our discussed retail sector.
of
Fig. 22: Petri net of the retail sector
401
4, Some critical remarks
The methodological requirements in developing System Dynamics
models with the explained approach ‘function nets' are a lot
higher than normal. But the experiences over time can help
to reduce this problem. The available software tools due to
all criteria of the end user have to be improved.
The approach ‘function nets! allows the structural analysis
of the dynamic behavior well known already of the Petri net
theory. That means in the process of validation of complex
models we have now an approach which has a ematical theory
for the analysis of static and dynamic behavior. This fact is
an, enormous progress in the area of model validation to have
a tool delivering exact informations about structural errors
in t model building process.
402
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