System Dynamics and Decision Support in Complex Systems
Miroljub Kljajize, Andrej Skraba, Igor Bernik
University of Maribor
Faculty of Organizational Sciences
Kidriéeva cesta 55a
SI-4000 Kranj, Slovenia
Phone: (+386) (0)64 374-275
Fax: (+386) (0)64 374-299
E-mail: miroljub.kljajic @ fov.uni-mb.si
In the proposed paper, the relationship between system dynamics and systems
thinking as well as the dilemma about hard and soft methodology are discussed from
the general point of view. It shows that the main problem in the modelling of complex
systems derives from the complexity of the systems themselves and not from the
shortcomings of the particular methodology. The role of the subject in the modelling
of a complex system is discussed. The article continues with the general simulation
model of the business system described by Forester's system dynamics. The
methodology is sufficiently abstract to allow a qualitative and quantitative analysis of
system functioning through feedback loops. The multiple criteria function used for the
evaluation of different scenarios was defined with the aid of a decision group using
the group support system. The methodology was successfully tested on real cases.
Introduction
Complex systems are usually understood by intuition as a phenomenon consisting of a
large number of elements organized in a multi level hierarchical structure where
elements themselves could represent systems. The named complex is used just to point
out the fact that the problem treated here can't be expressed only in hard (quantitative)
relations but that most relevant values are qualitative. A description of the system
depends on the specific goal and point of view of the researcher. Although this problem
has been considered in the literature to date, there is no unique opinion on the influence
of the observer in the process of modelling. The whole issue of System Dynamic
Review Vol. 10 Numbers 2-3, were devoted to the problem of the methodology of
complex system modelling. The diversity of the relevant method (Checkland and
Haynes, 1994; Flood, 1994) known by different names, for example: system approach,
system thinking or system dynamics, Soft Systems Methodology etc. motivated us to
discuss this topic from a general point of view in order to highlight some similarities
and differences among them. The present article is a general approach to the method of
modelling the complex system from an epistemological and semantic point of view.
The article continues with the general simulation model of the business system
described by Forester's system dynamics. The multiple criteria function used at the
evaluation of different scenarios was defined with the aid of a decision group using the
group support system. The methodology was successfully tested on real cases.
The Epistemological Problem of Modelling
A system represents a whole consisting of parts and was the axiom for system
philosophers. However, the general system theory (GST) and cybernetics, clearly
pointed out the relevance of the order and structure of elements within a whole for its
behavior. In cybernetics there is no ontological problem. On the manifestation level,
the system is described as it appears, instead of as it is. By definition, we anticipate
that the system consists of elements and is greater than its parts. An element is the
smallest part of the whole necessary for system description, which can't or won't be
divided further. The essence of the elements is very important from the
epistemological point of view. From the general point of view system is defined by
set:
S=(E,R) (1)
where e,€ E,i=1,2,..n represents the set of elements and Rc Ex E the relation
between elements. Construction of concrete systems requires some procedure
K(e,)€E, knowledge, to identify the elements of the systems and theory
T(e,,e;) © R to find the relationship between the elements. In other words, modeling
represents the activity to describe our experiences by using one of the existing
languages in the framework of a certain theory. In this way, our experiences also
become accessible to others: they may be proven, confirmed, rejected, broadened or
generalized. This paradigm can be stated (Kljaji¢, 1998) with a triplet (O,S,M).
O represents the real object, original, independent from the observer, while S$
represents the researcher (subject) or an observer with his knowledge, and M the
model of the object. Their relations in the process of analysing are shown in Figure 1.
(8)
@)-——)
Figure 1: Subjects in the modelling process.
From Figure 1, a "naive realist" supposes that: 1. An external world exists
independently of the observer, 2. This world isn't directly observable and 3. For its
representation, we set up simplified models. The relation between the observer S and
the object O - is of essential significance in the cognitive method. The observer is a
man, with all his cognitive qualities, while the object of research is the manifested
world, which exists by itself, regardless of how we can describe it. In this case, the
object and the system have the same meaning. The third article of the triplet M is the
consecutive one and represents a model or a picture of the analysed system O .The
OS relation in Figure 1, indicates the reflection of human experiences to concrete
reality. This cognitive consciousness represents our mental model. The relationship
M«<S represents the problem of knowledge presentation, respectively the
translation of the mental model into the actual model. The O<M_ relation
represents the phase of model validation or proof of correspondence between theory
and practice, which render possible the generalization of experiences into rules and
laws. The S—O-M relationship is nothing else but an active relation of the
subject in the phase of the object's cognition. The M—+O-S relation is nothing
more than the process of learning and generalization. A theory is an intellectual
construction enabling us to give a more generalized form about the phenomena of the
research to the directly obtained results from the experiment. In the cognitive process,
the value standpoints of subject S, are far more important to us in relation to the
object of research in the modelling process. This can be stated in the following
equations:
S,A(0AM)=0 (2)
S,A(OAM)#40 (3).
In the second part of the equation (1) and (2) ON M <1 are always fulfilled. In the
case of OM M =1, the model and original are identical. The expression (2) is valid for
formal and natural sciences, where S, =@ (empty set). This means that it's impossible
to find any link between the axiom and the hypothesis linked to model M and value
standpoints of the subject. That is of course not valid for the scientific hypothesis in the
process of modelling, which is always the product of the intellect and historically
conditioned by the progress of science: these hypotheses are always rejectable
(Poper, 1973). In the case of organizational sciences and humanities in equation (3) the
value standpoints of the researcher and the object of the research are always S, #©@.
Some qualities are always added to the description of the observer in question which
are not provable. The conditions expressed by (2) and (3) have a key meaning in the
choice of research methodology and for the scientific value of the statement. The first
expression renders possible the setting up of the principle testable hypothesis by means
of active experiments of the subject, while the second can't and is not allowed to prove
the hypothesis through experiment, but by observation and generalization dependant on
the qualities of the observer. In this light it is not difficult to find an answer to the
dilemma in Richmond (1994), Lane (1994) and Forrester (1994) of what is broader,
system dynamics or systems thinking or when to use hard or soft methodology? The
answer lies in the problem itself, which needs to be solved and in what one understood
with system dynamics or system thinking methodology.
Several methods have been developed for mathematical modelling of real systems.
Each of them was motivated by the problem itself and the researcher in that field.
System dynamics (SD), compartment model, block diagram and so on are most popular
among them. In Cobelli et al. (1986) their similarities and differences were discussed.
Practically both representations lead to the same equations. There are some symbolic
differences in the graphic presentation of elements and their relationships. The system
structure in SD consists of level elements representing state variables of the rate
elements, representing the flow and the auxiliary elements connected in the flow
diagram. The diagram is sufficiently abstract to allow a qualitative and quantitative
analysis of the system functioning through feedback loops. As soon as one becomes
satisfied with the “picture” of the model, he will proceed by writing equations of the
simulation model. In our opinion, SD suggested by Forrester (1961) has some semantic
advantage for users less experienced with formal methods. In a practice closely related
to the SD methodology, some authors use a causal loop diagram or influence diagram
(Eden, 1994). In this case, the influence loop diagram precedes the SD flow diagram
because the former is more abstract while the second is more convenient for computer
programming. This can be explained by expression (1). Let denote elements
e,€ E, i=1,2,..n with the node representing the state and connection Rc EX E the
branch and we will get a graph, which represents the picture of the system. This graph
is equivalent to a causal diagram and represents a qualitative model of the problem to
be solved. If we replace the node with a rectangle and branches with rate input and rate
output, we will obtain a flow diagram of SD. The difference between the branches and
rate is just in the degree of abstraction; the rate expresses the quantitative relationship
measured in units while the branches express the direction of influence between the
elements. To illustrate this difference, arriving from a level of abstraction, we will
consider the well-known Malthusian law of population growth. Figure 2 shows an
influence diagram, which represents a “picture” of a population model, while Figure 3
represents a flow diagram in SD methods, leading directly to a difference equation (4).
+
SN i
+ ORE TS
- .
Birth rate Death rate
Figure 2: Influence loop diagram of population model
a) b)
Population
Births Deaths
Birth_rate Death_rate
Figure 3: Different graphical presentation of population model:
a) SD flow diagram and b) block diagram.
p(k +1) = p(k) + At(np(k) — mp(k)),k =0,1,2..N (4)
where n and m represent the birth rate and death rate respectively. n and m are time
dependent coefficients. For n>m exp. growth and for n<m exp. decrease and only for
n=m does the system reach equilibrium. If we limit At > dt equation (4) becomes the
differential equation p =(n(t)—m(t)) p(t) with a symbolic solution shown in Figure
3b). Here, symbol D™ represent integration block, which is equivalent to the level
element in SD.
Decision Support Oriented Enterprise Simulation Model
In light of equation 2 and 3, three groups of the system can be identified: formal,
natural and human. The formal system consists of abstract objects, where relations
among them are based on a set of axioms. Natural systems consist of real objects
where relations among them are founded by evolution. Knowledge about it, in
principle, is accessible by experiment up to the Heisenberg's Principle of Uncertainty.
Human systems or organization consist of different interactions between people and
nature in order to realize certain purposes. Prior knowledge about system behaviour is
limited and experiments are not allowed. Intuition is the main component of creation.
The model of these objects represents a description of real objects in terms of an
abstract system. How good and useful these descriptions are is the problem of model
validation. From equation (3), the observed system is complex and its model contents
subjective to assumptions of the observer. Such systems are open, dynamic and goal
oriented (Ackoff, 1994).
From the decision point of view, the organizational system is defined as S =(P,D),
if mapping exists P:XxU—Y and D:XxXY-U such that, it is satisfied
G:XxYxU >VeER and E:X XY xV ~U, where X and Y represent the input
and output of the system, P process, D decision process, G objective function and E
evaluation strategy.
Figure 4: Universal model of goal oriented system
Note that G represents the objective of alternative, while E represents the subjective
evaluation of decision. Consequently, decision in enterprise is not primarily
concerned only with feedback dynamics (selecting of proper parameters of rate
elements) but on rate elements matched with possible input into the system and
prescribed criteria (Kljaji¢ et al., 1998). As it is shown in Mesarovié and Takahara
(1989) that according to Arrow's Impossibility Theorem, it is not possible to find a
democratic solution of social choice which will satisfy some socially acceptable
conditions imposed on the decision problem. Arrow's axioms (1 to 5) are logically
incompatible (Rapoport, 1986). The fifth axiom, which states the absence of a dictator
(even in implicit form) is relevant in using GDSS.
The general simulation model of the business system has been described by
Forrester's system dynamics. The system structure consists of level elements and
parameters defining the rate and the auxiliary elements connected in the flow
diagram. The diagram is sufficiently abstract to allow a qualitative analysis of the
system functioning through feedback loops. As soon as someone becomes satisfied
with the picture of the model, it will proceed to the definition of the simulation
model. The state equation of the simulated system is described by the non-linear
differential equation:
yk +1) = f(v(k), (k),a(k)); k = 0,1,2,..N (5),
where y€Y represents state variables such as inventory of material/products, cash,
income, liabilities, backlog, etc., s;¢ S represents the external input to the system
(exogen scenario) and a,€A represents the control vector (endogen scenario).
Decision strategy was defined as: for scenario s, (state of nature) and_ its
probability p, < P, find alternative a,, which will solve the problem and satisfy the
performance function, which reflects managers preferences. The results of the
simulation are collected in a decision matrix, which represents the payoff of the
strategy.
There are many different forms of the utility function. In actual case we considered
two criteria: Expected value criteria defined by equation:
max EV(a,)= )C,p; (6),
where C, represents the values of the i-th scenario at j-th strategy, and linear
weighted sum of multiple criteria:
max J(a,) = Sw,J,(a,) (7),
rat
where w, represent the weight of the r-th objective, which reflects the decision
maker's preference of business politics. The individual objective J, =q(y,s,a) is a
function of the system state, state of nature and chosen alternative in achieving the
goal. Satty's AHP method (Satty, 1990) was used to determine the relative importance
of objectives w, and pairwise comparison of alternatives a, for the r-th objective.
The business simulation core consists of three parts: the basic model, modelled with
the SD technique that represents the business process, program the scenario
formulation, program for the analysis of simulation results and selection of solutions,
and program for normative analysis. The simulation scenarios are made of two
subsets: a subset of input that anticipate the impact of the environment (exogenous
scenarios) or the state of nature, and a subset of management decisions that represent
(endogenous scenarios). They give the answer to the basic question with regard to the
problem situation for which the answer is being sought. In literature, it is known as
the what if, then, so what analysis. The generation of scenarios of the simulation
system that respond to the what if, is based on the variation of parameters of the basic
scenario at the extrapolation of past behaviour and expert evaluation of development
targets with the Brainstorming method. Variants of business scenarios are evaluated
with the linearly weighted sum of the multi-criteria decision function. The complete
simulation system for decision support consists of commercially available packages,
for example: Powersim, ProModel, Group Systems, Expert Choice and Ventana
Group Systems. The principal scheme of the system is shown in Figure 5.
Business
System
Simulator
Business
Database
Simulation Scenario
Results Rank
KX 7
ES
Scenarios
Figure 5: Decision support system structure
Results
Case 1: The objective of the study on the academic enterprises simulation model was
to find the relevance of weighting factors of the multi-objective decision problem with
GDSS in order to evaluate exogenous and endogenous scenarios.
Participants involved in the group decision experiment were last year graduate
students. Three groups of students participated in the experimental sessions. Each
group consisted of 15 randomly selected students. Subjects were recruited from a
university level Decision Process Course. Students in the course were assigned to the
groups at the beginning of the semester to cooperate in the sessions by the end of the
semester after completing the course. The experiment started with a brief introduction
to the business simulator application. Working with a simulator was simple and user-
friendly. The user interface is based on classical Windows GUI, which allows
participants to enter parameter values with sliders, input boxes and radio buttons.
Participants can make variations of parameters in a permitted area and observe the
behavior of the system. All of the user definable parameters were explained and tested
in the course of the experiment. Basic scenarios were presented and the simulator
response was verbally analyzed. To get better insight into the problem, an electronic
brainstorming session was held as the starting point for the session. The next step was
geared to the goal of scenario evaluation. Participants determined the parameters
values of the business simulator as each individual saw possible business politics in
order to get the sense of the model responses to different simulation scenarios. The
session of criteria determination was open for debate among participants so that a
common view could be established.
After experimenting on the simulator, the group determined important criterions.
Gained ideas were categorized and ranked by the selected voting method. The
experiment was continued on the simulator where predefined scenarios were
presented. Basic simulation scenarios take into consideration the parameters of
average price, material costs, desired inventory level and payment delay. The
parameter of average price, for example, was used for simulating different market
demands. There were five simulation runs executed for five simulation scenarios. All
of the scenarios were also stated verbally. Actual scenarios were observed and
compared with the aid of the simulator. The business simulation model was observed
for 120 simulation days. Participants observed the dynamics of the different
parameters in the simulator. This option was used for the analysis of different
simulation scenarios. The graphs represent the course of time series of a chosen
variable. Participants voted regarding the importance of scenario evaluation criterions
in order to get the group evaluation of simulation scenarios. The evaluation was
continued by using the linear multicriteria weighting function. Overall, criteria have
been defined as the linearly weighted sum defined by equation (7). Decision groups
have to determine the values of the weights w,; i=/, 2, 3, 4 respectively. The results
of separate criteria weighting by groups and the average value is shown in Figure 6.
There is no significant difference between average and group estimation of weights.
The average weighting value of the evaluation criteria revealed the next order: Profit /
Sum Value of the Company Ratio, Profit, Inventory Value, Sum Value of the
Company.
0.35
03
3 025 mGrmup1
3
Fon mG wup 2
2
G20up 3
$ ons [| [ass
4 DAvermge
= oa ||
0,05 ||
o
Pf /Sum Pott Sum Vale ofthe Inventory Vale
Vahe ofthe Com pany
Com pany rat
Criterions
Figure 6: Group criteria weighting
The value of each objective for 5 scenarios has been analyzed according to the
principle of the analytical hierarchy processes AHP, which ranked the scenarios in the
following order: Jz, Js, Ja, Ji, J3 that would in the real case determine the business
strategy for the evaluation period.
On the basis of the criteria weights, rank of the scenarios was determined. As a result
of the decision making process, the best scenario i.e. the best parameter combination
was selected using the group evaluation of criterions. The presented approach
enhances decision processes by effectively exploring the methodology of system
dynamics and group support systems allowing experimentation on business
simulation models for the purpose of solving multiple criteria group decision
problems.
Case 2: The described methodology was tested in a medium sized factory of concrete
goods for reengineering assessment. Due to a raised demand for the article and better
quality requirements of the products, the firm’s management considered investigating
a new production line. There are three suppliers besides the existing technologies
considered for decision-making. Suppliers denoted as alternatives aj=a),a2,a3,a4 and
their cost in many unit is: c= 0, 371, 392, 532 respectively. a; represent current
technology.
Estimation of the state of nature s; for the next 8 years and its probability are: s; - no
change in market demands (15%); sz - medium increase of demands (40%); s3 - high
increase of demands (35%) and sy - medium decrease of demands (10%). The
probability of the state of nature has been estimated by the application of the
brainstorming method conducted in the meeting room and using GSS. Several
requirements for the new technology were imposed: Quality of products, Net profit,
Risk of company ruin, Market demands and Flexibility of technology.
With discrete event simulation models, we analyzed alternatives from a technological
point of view for different conditions relevant for operative planning. A cost benefit
analysis of alternatives was obtained with a continuous simulation model by using the
system dynamic method. For each alternative, four scenarios representing the state of
nature were prepared and simulated. The expected values of payoff for alternatives for
an 8-year period were computed according to equation (2). Cj is a function of: cost of
investment, productions cost and market demands for i” alternative and ia state of
nature. The results of evaluation are shown in Figure 7.
Expected values 1999-2006
1400
i at
600 = 2)
ee Lf rae
Years
Figure 7: Expected value criteria in MU for the four alternatives as a function of time
The average expected value by alternatives for 8 years are shown in bar graphs in
Figure 8. Because of the well-known shortcoming of the expected value criteria
(subjective probability, uncertainty of expected value, etc.), users like to additionally
examine the linear weighted sum of the criteria. Satty's Analytical Hierarchy Process -
AHP Method was used for this purpose. In our case, there are three levels of
hierarchy. On the first level, the goal L itself is placed. At the second level there are
five criteria: Net profit, Quality of products, Risk of company ruin, Satisfying market
demand and Flexibility of technology. The last level offers alternatives for ranking. It
is necessary to choose the best alternative through the five criteria so as to achieve the
overall goal. User gained information for their decision from the simulation of
alternatives and discussions in the meeting room as well as from provider properties.
Here, the full advantage of visual interactive simulation connected with the group
decision support system in reengineering process was achieved. For example, the
comparison of alternatives under the criteria Risk of company ruin was estimated
using data from Figure 8. For this reason the preference of alternative ay through the
Risk Criteria is less desirable. The decision horizon of 8-year use was defined by
means of simulation methods. The results of multi criteria evaluation are also shown
in Figure 8.
Average EV(a) Multicriteria
1999-2006 evaluation J(a)
600 os00 =
8 040 =
500
0400
2
aa 0350
Bat]! | 0300
5
so LR m2)! | o250
Oa3
naal| | 2200 4
200
050 4
tm 0,100 4
050
fT 0000
a b
Figure 8: Bar Graph results of Expected Value and the AHP Method of four
alternative evaluations.
The right graph shows the value of obtained alternatives: as a sum of products of
weighted objectives with the value of alternatives. The alternative a3 has the highest
score according to the chosen preference. It is obvious that the a3 alternative is most
preferable in both criteria. Of course, such coincidence is incidental and a result of
direct analyses. In the case where two different criteria gave different results, the
simulation method together with GDSS is an excellent tool for group judgment about
alternatives through simulation in different conditions.
Conclusion
In this paper, the relationship between system dynamics and systems thinking as well
as the dilemma about hard and soft methodology are discussed from the general point
of view. It is shown that the main problem in the modelling of complex systems
derives from the complexity of the systems themselves and not from the shortcomings
of the particular methodology. The role of the subject in the modelling of a complex
system is discussed. The article continues with the Enterprise Simulation Model
described with Forester's system dynamics for business behaviour and event oriented
model for technology process. The methodology is sufficiently abstract to allow a
qualitative and quantitative analysis of the system functioning through feedback
loops. The multiple criteria function used at the evaluation of different scenarios was
defined with the aid of a decision group using the group support system. The
methodology was successfully tested for the reengineering process in a medium size
factory.
Acknowledgement
This research has been supported by the Ministry of Science and Technology of the
Republic of Slovenia, Grant No. PP-0586/99.
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