able of Conten
Cybernetic Formulation of Some Functions of Management —
Types of Simulation and Optimization Approaches
Within The System Dynamics Method
Elzbieta Kasperska
Institute of Mathematics
Silesian University of Technology
Kaszubska 23, Gliwice 44-100, Poland
: elakaspe@polsl.gliwice.pl
Abstract
The purpose of this paper is to present the cybernetic formulation of some functions
Coyle, We
recent years. The author welcomes any discussion on t
erholm and others, but some constitute the author’s own ideas, developed in
Keywords: System Dynamics Method, Cybernetic formulation of management, Opti-
mization and simulation within System Dynamics Method.
1 Introduction
The problem of classification of the types of simulation approaches for supporting planning
and organizing in industry with continuous process, was first undertaken by the author in [11].
In this classification, the classic works of famous investigators within the System Dynamics
method were contained {2-6,8-10]. But some types of the approaches constituted the author’
prognosis of future work in this field. Now, ten year later, the author can say that the prognosis
has come true, mainly in the area of optimization approaches. The works of prof. Coyle and
the author’s own ideas have developed the simulation during optimization and optimization
during simulation [5,7, 12,13, 15].
In this paper a new classification of the simulation and optimization approaches within
the System Dynamics method is proposed. The background for such classification is the
cybernetic formulation of the function of management: PLANNING and ORGANIZING.
2 The author’s old classification of the types of simulation
investigation for supporting planning and organizing
in industry
In [11] the criteria for such classification were:
the character of modelled and simulated changes in investigated objects,
the purpose of simulation investigation, which determines the way in which the simu-
lation was used by people (planner, organizer),
the role of people, as the modelled element of real and regulatory sphere of management.
The author has used the methodological divisions of research area into the following
spheres: real and control (regulation) and: object and subject. Their natural interaction is
presented in Figure 1.
CONTROL SPHERE - STRUCTURE and PROCESSES
4 (The Subject of PLANNING and ORGANIZING) —k
/
Change Information ~ a
of structure Y fo |
| lof real |
“Shallow” control of real sphere Change
“Deep” | ‘ ___ of structure
control ‘ F . 4 i
of real Decisions _/ ~ }
sphere — _ |
\ REAL SPHERE - STRUCTURE and PROCESSES
(The Object of PLANNING and ORGANIZING)
Figure 1. The interactions between real and control spheres
The author proposed the names of 19 directions of the investigation:
40
20
3
4°
5°
6°
7
go
Situation prognosis of: what
subject is modelled as ”explic
if?” type in the subject sphere of ORGANIZING (the
ys
Situation prognosis of: ” what if?” type in the subject sphere of PLANNING (the subject
is modelled as ” explicit”).
Situation prognosis of: what if?” type in the object sphere of ORGANIZING (the
object is modelled as ” explicit”).
Situation prognosis of: *what if?” type in the object sphere of PLANNING (the object
is modelled as ” explicit”).
Designing the structure of ” verification of dec:
ORGANIZING (the subject is modelled as
ion rules” type in the subject sphere of
explicit” ).
Designing the structure of ” verification of decision rules” type in the subject sphere of
PLANNING (the subject is modelled as ” explicit”).
Designing the structure of ” verification of decision rules” type in the object sphere of
ORGANIZING (the object is modelled as ” explicit”).
Designing the structure of ” verification of decision rules” type in the object sphere of
PLANNING (the object is modelled as ” explicit”).
9° Similar to 1° but the subject is modelled ”implicit”.
10° Similar to 2° but the subject is modelled ”implicit”.
11° Similar to 3° but the object is modelled ”implicit”.
12° Similar to 4° but the object is modelled ”implic
13° Similar to 5° but the subject is modelled ”implicit”.
14° Similar to 6° but the subject is modelled ” implicit”.
15° Similar to 7° but the object is modelled ”implic
16° Similar to 8° but the object is modelled ”implicit”.
17° Descriptive-explanative approaches in the ” diffusive” sphere of real and regulation
ic System Dynamics method.
18° Descriptive-explanative approaches in the ”diffusive” sphere: real and regulation (with
* deeper” modelling in the regulation sphere) ~ a modification of classic System Dyna-
mics method.
19° Descriptive-explanative approaches in the “diffusive” sphere: real and regulation (with
”deeper” modelling in the real sphere) — a modification of classic System Dynamics
method.
On the Table 1 author presents in syntetic form characteriscic of types of simulation
investigation within System Dynamics method.
Nowadays, this classification can be supported by stricte optimization approaches
which are contained in the direction: ” verification of the decision rules”. These approaches
were developed by the author in the last few years. Some of them have been derived from
the ideas of prof. Coyle; others are the author’s own ideas (see [5-7, 12,13, 15]). The idea of
optimization approaches will be extended after the presentation of the cybernetic formula-
tion of some functions of management, and against this background, the proposal for a new
classification of types simulation and optimization approaches within the System Dynamics
method.
3 The cybernetic formulation of source functions of
management — types of simulation and optimization
approaches within the System Dynamics model
In Figure 2 and 3 the idea of a cybernetic view of some functions of management: PLANNING
and ORGANIZING, are presented. We observe the feedback loops, typical for the System Dy-
namics method. Presently, it is the author’s proposal to interpret such loops as the types of
simulation investigations for supporting the functions of management. For instance, the inve-
stigation: "what if?” in a classic loop: decisions + actions — results of actions + perception
of results — perception of differences — planning tasks — decisions, support the analysis and
simulation of the situation prognosis (see: the ”old” classification, direction 1° and 9°).
This investigations, however, offers more possibilities, for instance: taking into consideration
’ or “disturbance of decisions” are the extension of the what if?”
the ” disturbance of actions
investigation in the described loop.
Criteria Decision rules
of estimation of building PLAN
Estimation C Set of. Criteria of
of planning | / 1 policy choosing
/ alternative ra allermatives JL policies
Pa < » Planning /
/ i ) alternatives a
A AH ‘i vA Disturbance
: Designnin x / of decisi
ac of the Seaictaké Choice ofpolicies ~ : yf OE decisions
mtenntits Of regulation —_ -~ in real sphere 7
x sphere ~~ :
\ - 4 J .
“ aa PLANNING
a ,
PLAN TASKS DECISIONS \
“Sy PERCEPTION 7 ; Disturbance J
. % * “ of actions > \
| Whatif? op DIFFERENCES ACTIONS L)
| o~ \e ‘What if? / ~~
Loy REALIZATION SK /o™ id Designning
~ _~ OF PLAN " ’ RESULTS the structure
ee OF ACTIONS of real sphere
DETERMINANTS /
OF PLAN + \ a
- quantity INTERNAL ‘PERCEPTION EVALUATION
DETERMINANTS OF RESULTS OF RESULTS
EXTERNAL
DETERMINANTS
Figure 2. Feedback loops as types of simulation investigations for supporting ” PLANNING” in companies
CHOICE OF CRITERIA
ENABLING SOLUTIONS
We » DETERMINANTS
/ OF DECISION \_
4
ser OF *) .
\ )
SOLUTIONS \/ Designning DECISIONS
the structure
\ of regulation \
\ sphere . s
\ a What if? ACTIONS
% ORGANIZATIONING ~*~
___*_ CHOICE ~-~~~~~~* SOLUTION ,. LY
OF SOLUTION (in real sphere) \_ :
y x \ RESULTS
oo Designning : Sy OF ACTIONS
Designning of the structure NN J
the structure \ of real sphere N\ /
of regulation ESTIMATION _ \ x
*\ sphere OF SOLUTIONS (\ \ PERCEPTION
LC) oe a \ OF RESULTS
’ — Be PROGNOSIS
“CHOICE VALUE OF - OF RESULTS
OF CRITERION ~* THE CRITERION * OF ACTION
i OF ESTIMATION
PRIORITIES
OF CRITERIA
Figure 3. Feedback loops as types of simulation investigations for supporting ” ORGANIZING” in companies
Another example is presented by ” designing the structure of real sphere”, running in the
loop which contains ” choice of policies in real sphere”. This choice requires the: set of policy
alternatives”, “criteria of choosing policies”. In the classic System Dynamics model such
choice tokes place outside the model (we can name this direction as ”suboptimization” ).
The opposite possibility is to guide the choice “by the model”, i.e. by the objective function
with "the subjective sphere modelled” (man). This is the optimization in Coyle’s and the
author’s understanding.
The author raised this subject in [12, 13,15]. Now, the author wants to present the clas-
sification of the types of investigation within the System Dynamics method, against the
background of the above mentioned cybernetic formulation of the functions of management.
The traditional directions of investigation within the System Dynamics method represent
two types of approaches:
A) The descriptive-explanatory: the simulation model is used as a tool of the replica-
tion rules of the functioning of the system (we known the input and the output, such
as the reaction of the system).
B) The ’ what if?”: the simulation model is used as a tool of the examination of the re:
tion of the system (with known structure and rules of functioning) when we determine
the inputs of the model.
Types A) and B) satisfy, to a different degree, the needs of those who manage (plan or
organize). But some needs require a different kind of simulation; such as in type C):
C) normative: the simulation model is used as a tool of choosing the kind and intensity
of inputs to obtain the required reaction.
The scope of the normative type includes the wide range of optimization approaches
(for instance: simulation during optimization and optimization during simulation).
It is interesting to analyze the role of man in types A), B) and C). In the case of A)
human activities consist in analyzing the feedback loops, which form the structure of the
system. Generally these feedback loops determine, the dynamic behaviour of the system.
Such activity requires a certain scope of preparation from the human factor, who should
interpret the facts, know the convention of the description of the system, etc. In other words,
the expected benefits require a great deal of work.
In the case of B) the activities of man involve analyzing the times series of the observed
variables of the models, which represent the effects of different inputs. Such activities occur
outside the model. This is the so called post simulative studies”. The interpretation of
the outputs requires a lot of knowledge about the system, its rules of functioning.
In the case of C) the activities of a man one limited to the formulation: the criteria
of assessing the behavior of the system, the alternatives of policies rules of the scopes of
parameters. Such activities require some preparation on the part of man, but they render
great benefits (they consider the decision needs human).
Coming back to Figure 2 and 3, it may be noticed that the direction of the investigation
” designing the structure of real sphere” , require ” evaluation of results”, which leads to ” choice
of policies in real sphere”. Thi contained in type C), but two different consequences
are possible. The ”evaluation” can take place “outside the model”, or ”inside the model”.
In the first case, this is the suboptimization study” (conducted by most of modellers of
the System Dynamics), the second case is ”optimization” in Coyle’s sense (in the strict
’simulation during optimization”). New possibilities were presented in the author’s
investigation in (12,13, 15].
The so called: ”constrained and unconstrained optimization of the dynamics balance of
production” requires "optimization during simulation”. The main idea of such a” balan-
ce” was ”solving the system of balance equation during simulation”. The author has investi-
gated so the called ”pseudosolution” of differences (Ma = b, at the condition x; > 0). The
system of the equations was created from the balance of the value of three properties of flow:
s balance ("rate of flow”), in Forrester cost balance and personal balanc
The author proposes to name this model of ”optimal balance of production”: as
DYNBALANCE(1-3) model, because only three items are considered.
The opposite proposal is presented by DYNBALANCE(3-1) model, in which the author
has considered three raw materials and one product. The article on the DYNBALANCE(3-1)
model is in preparation. If possible, it will be presented in Palermo.
At the end of the paper author present Table 2 with some chosen examples of models
within System Dynamics (in context of author classification of models). The author welcomes
any discussion on this subject.
4 Conclusion
The author realizes that she has only have ”touched” the problem, signalled in the topic of
this article. The problem is wide and has many aspects. The proposal for the classification of
the types of investigation within the System Dynamics method is one of may other possible
formulations of the problem. The background for the idea of classification was the cybernetic
formulation of some functions of management. The characteristic feedback structure has its
connections with the System Dynamics method, and because of this it may be conceived as
”compatible” with the main idea of the System Dynamics method.
References
[1] COSMIC and COSMOS user manuals, The COSMIC Holding Co., Shrivenham, 1994.
[2] R. G. Coyle, Management System Dynamics, John Wiley & Sons, New York, 1977.
[3] R. G. Coyle, System Dynamics — The state of the art, Dynamica, 5 (1978), pp. 3-23.
[4] R. G. Coyle, E. P. Wolsterholm, Modelling discrete events in System Dynamics model.
A case study, Dynamica, 6 (1980), pp. 21-27.
[5] R. G. Coyle, System Dynamics modelling. A practical approach, Chapman & Hall, Lon-
don, 1996.
[6] R. G. Coyle, The practice of System Dynamics: milestones, lessons and ideas from
30 years experience, System Dynamics Review, 14 (1998), pp. 343-365.
[7] R. G. Coyle, Simulation by repeated optimization, Journal of the Operational Research
Society, 50 (1999), pp. 429-438.
[8] J. W. Forrester, Industrial Dynamics, MIT Press, Massachusetts, 1961.
[9] J. W. Forrester, Principles of Systems, Cambridge Press, Massachusetts, 1972.
{10] J. W. Forrester, Collected papers of Jay W. Forrester, Cambridge Press, Massachusetts,
1975.
{1
{1
{1
i
1] E. Kasperska, Methods of simulation of the investigation into supporting planning and
organization in industry with continuous processes, Ph.D. thesis, Polish Academy of
Science, Warsaw, 1990 (in Polish).
2] E. Kasperska, D. Slota, Mathematical Method of Management in the Concept of System
Dynamics, Silesian Technical University, Gliwice, 2000 (in Polish).
3] E. Kasperska, E. Mateja-Losa, D. Stota, Some etension of System Dynamics method
theoretical aspects, in: Proc. 16th IMACS World Congress, ed. M. Deville, R. Owens,
IMACS, Lausanne 2000, 718-10, 1-6.
4] E. Kasperska, E. Mateja-Losa, D. Stota, Some extension of System Dynamics method
practical aspects, in: Proc. 16th IMACS World Congress, ed. M. Deville, R. Owens,
IMACS, Lausanne 2000, 718-11, 1-6.
E. Kasperska, E. Mateja-Losa, D. Slota, Some Dynamics Balance of Production via
Optimization and Simulation within System Dynamics Method, in: Proc. 19th Int. Conf.
of the System Dynamics Society, ed. J. H. Hines, V. G. Diker, R. 5. Langer, J. I. Rowe,
Atlanta 2001, 1-18.
J. Legras, Praktyczne metody analizy matematycznej, WNT, Warszawa 1974 (translation
from French: Methodes et Technique De l’Analyse Numerique, Dunod, Paris 1971).
R. Lukaszewicz, Management System Dynamics, PWN, Warsaw, 1975 (in Polish).
R. Lukaszewicz, The direct form of structure models within System Dynamics, Dynamica,
2 (1976), pp. 36-43.
Professional DYNAMO 4.0 for WINDOWS. Reference manual, Pugh-Roberts Assi
tes, Cambridge, 1994.
Table 1: Synt
System Dynamics models)
is of author classifiction of the types of simulation investigation (within
Main type Modelling the spheres The kind of modelled
*implicite”).
of the information and pre-
paring and decisions making
proces); structure of infor-
mations and decisions is not
changing during the experi-
ments.
of study of management and changes the man
Situation prognosis | Subjective sphere of PLAN- | Subject is modelled ”explici-
of "what if?” type | NING and ORGANIZING | te” which means: clear, direc-
(the subject is mo- | (the processes of perceiving, | tly, distinctly, like the ”me-
delled ”explicite” or | transfering and transforming | dium” of modelled world (le-
vels and rates of labours or
s); when subject is mo-
delled ”implicite” if means:
guessingly, supposlly.
clear!
Table 1:
System Dynamics models) (continuation)
is of author classifiction of the types of simulation investigation (within
Main type
of study
Modelling the spheres
of management and changes
The kind of modelled
the man
Situation prognosis of
”what if?” type (the ob-
ject is modelled ”expli-
Objective sphere of PLAN-
NING and ORGANIZING
(the real economic proce:
production, ordering, finan-
cing, investitions, etc.); struc-
ture of processes is not chan-
ging during the experiments
with the model.
Object is modelled ”explici-
te” (levels and rates of: ma-
terials, products, money, equ-
ipement, etc.); in case of
plicite the real world proces-
ses are in such high aggrega-
tion the we only ”guess” the
flow of information or the de-
ion making proces, has its
*material” base.
cite” or ”implicite”).
Designing the struc-
ture of ation
i ” type
(the is mo-
delled or
*implicite”).
In case of basely known stu-
dy, the options of structure of
decision policies are ” outside”
the model; so called ”subop-
timization” of model structu-
re is derived by heurictic w:
method
*trials and errors”;
structure is changing during
the series of the experiments.
The regulating sphere (or
*plane”) is created by ob-
jective function with models
managers preferencies to cho-
ose the examine options; the
objective function is ” inside”
the model which means di-
rect optimization of structure
("explicite” case).
Designing the structure
of
sion rules” type (the ob-
ject is modelled ”expli-
cite” or ”implicite”).
‘ification of deci-
The structure of real processes
(for example: balance of pro-
duction, balance of raw mate-
rials) is optimized during the
simulation experiments; the
way of optimizing is heuristic
or embedding in model simu-
lation.
See remarks in previous type.
Descriptive explana
tive approaches (class
System Dynamics).
The simulation model is used
as a tool of the replication ru-
les of functioning of the sys-
tem; the diffusive” sphere of
real and regulation is in dif-
ferent (mainly large) kind of
aggregation.
This
ted methodologically which
type of ” what if?” , because we
put to trial the structure of
model by different inputs — in
order to select the one, which
has desired behaviour (which
explains the real world aspect
em).
‘ase of study is connec-
oO
Descriptive — explanati-
ve approaches with ” de-
epe” modelling in real
or regulation sphere.
Clas
rates
ic System Dynamics ope-
very high aggregation of
in some casses the
proces
including of much details in
model is required.
For example: very compliac-
ted discontinuouse decision
making proce:
evants in real or regulation
sphere (with random charac-
ter of some variables).
‘s or discrete
Table 2: Some chosen examples of models within System Dynamics (in context of author
classification of models)
Main type
Author and name
Description of subject
Some remarks
of study of model and object of modelling and conclussions
‘iptive 1961 J. W. Forre- | Structure of — flow The study with the mo-
explanative ster — A custo- | material, raw material, | del allows to choose the
approaches mer ~ producer orders, people, money | value of parameters and
(c employment. s} (models of decisions | the structure of model
tem Dynamics | tem”. which regulate the | (by experimentals type
model). intense of flows); this | ’trials and errors
is “diffusive: sphere of
real and regulation.
Descriptive 1971 J. W. For- | Structure of flows: po- | The explanation of in-
explanative rester World | pulation, natural reso- | fluences of sectors of
approaches model”. urces, investitions, po- | model to each other-
(classic Sys- lutions, investittions in | helps to study ”structu-
tem Dynamics agriculture; high aggre- | ral sensitivi of mo-
model).
gated model of flows
and theirs connections;
It contain many mul-
tipliers (tables) which
models local relation-
del; it also help investi-
gate the influence of va-
lue of some parameters
on way the world will
develop.
ships of object (real
world).
>What if?” | 1996 R. G. Coy- | Structure of flows: | The experiments of ty-
experiments le — *Domestuic | osders, raw material pe “what if?” preceded
and normative | Manufactu- production; models of | the optimization; they
study (opti- | rmg Company ms which regulate | helps choose the ranges
mization of | (DMC)”. of mention kinds.
structure). medium aggre- | options of given policies
gation of polisy of real
sphere of management;
the model developed
the objective function
by formulating the
equations to penalize
failure to meet the
target factor.
to study.
10
Tr
le 2: Some chosen examples of models within System Dynamics (in context of author
classification of models) (continuation)
Main type Author and Description of subject Some remarks
of study name of model | and object of modelling and conclussions
Normative 2001 E. Kasper- | Structure of three | Two kinds of optimiza-
study with | ska, E. Mateja- | dimensional” balance | tion were performed
*deeper” mao- | Losa, D. Slota. of production of three
delling od real
and regulation
sphere.
products from one raw
material; the objective
function involves three
with three
weighting factors; these
criteria
elements measures the
discrepancies between
the actual and target
levels of ’mass balan
of production,
balance” of production,
“labour
production; the deeper
modelling of regula-
sphere depend
on creating objective
the
model” (not “outside”
balance” of
tion
function inside
the model. like in many
suboptimiza-
tion experiments on the
field).
heurictic
a) optimization em-
bedding in simu-
lation on System
Dynamics models;
b) simulation
bedding in opti-
mization (in
Coyle’s sense);
em-
the optimization expe-
riments help to choose
the optimal structure
of production of three
items; the point of de-
eper modelling of real
sphere is that three dif-
ferent items from one
raw material is model-
led, which has better c
nections with real eco-
nomic world.
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