The Structured Systems Approach for the Design of Optimisation
and Simulation Models
Heiner Miller-Merbach
Universitat Kaiserslautern
D-6750 Kaiserslautern, Germany
Abstract: The structured systems approach integrates the design of computerised
models and information systems with comprehensive relational data bases. It can be
applied to any kind of optimisation and simulation models including system
dynamics. In addition, the structured systems approach supports the model design
process and its documentation; it stimulates the interdisciplinary and
interpersonal participation in the model design process.
1. Changed Architecture of Computerised Models and Information Systeas
The architecture of computerised (optimisation and simulation) models and
information systems has changed in the past and will keep changing in the future.
So did and will do planning and modelling procedures.
In the past, computerised models and information systems were more or less
isolated, single-purpose representations of sections of reality; each model and
each information system had its own individual data base. Planning and modelling
as activities were considered as an art, and very little attention was paid to its
systematisation.
In the future, models and information systems will have to be considered in a
broader and more comprehensive way. This will be accompanied by a methodological
support of the planning and modelling procedures.
The centre of future models and information systems will be comprehensive
relational data bases. All the models and information systems will take access to
central data bases, and the planning and modelling procedures will be carried out
in a systematic grammar, again based upon the relational data base terminology.
The methodology based upon the grammar of relational data bases shall be called
"structured systems approach".
Conclusion of section 1: The future architecture of (optimisation and
simulation) models and information systems is characterised by
comprehensive data bases in the centre, to which any programme (and query)
refers. The data bases will be relational, and the relational grammar will
be constituent for planning and modelling procedures.
2. Relational Data Bases and the Structured Systems Approach
Relational data Lases were initiated by Codd (1970), succeeded by numerous
contributions since. Many others have contributed to this characteristic of
thought, such as Wedekind (1974) with his “object type approach" and Chen (1976)
with his “entity relationship approach". The structured systems approach follows
the same principles, but is less closely linked to computer applications and
closer to model design in general (Miller-Merbach 1981, 1983).
The structured systems approach is an extension of many traditional forms of the
systems approach (for its variety see e.g. Bahm 1981). It is common use in the
systems approach to understand the world (and its many mini worlds) as a system
(or as a hierarchy of systems and sub-systems, respectively) consisting of single
elements. The elements have certain properties, and each system has additional
Properties which are not properties of their sub-systems. This leads to the
traditional, 2,500 years old insight that "the whole is more than the sum of its
parts". This has been expressed in different wording by the ancient Greeks, such
as Heraklitus (ca. 550 - 480 B.C.), Plato (427 - 347 B.C.) and in particular by
Aristotle (384 - 322 B.C.), also by the chinese philosophy of Lao-Tse. They are,
indeed, the ancient founders of the systems approach (Muller-Merbach 1988).
Examples for thinking in systems:
@ A word is more than the sum of its letters. A sentence is more than the sum of
its words. A chapter is more than the sum of its sentences. A book is more than
the sum of its chapters. An author is more than the sum of his books.
@ A bicycle is more than the sum of its frame and its wheels. A wheel is more
than the sum of the tire, the spoxes, the hub etc., a spoke is more than the sum
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of its crystals. A crystal is more than the sum of its atoms.
The structured systems approach is based upon this thinking and makes usage of it
for design purposes. It works with a notation of six terms: with elements and
element sets, with relationships and relationship sets, and with attributes and
attribute values.
The element sets and the relationship sets are the "coat hangers" for information,
i.e. for the attributes. For each single element (of an element set) and for each
single relationship (of a relationship set) data, i.e. attribute values, can be
assigned to the attributes.
This "grammar" is quite general and in many aspects applicable to model and
information system design; in particular, it refers immediately to the notation of
mathematical models (Miuller-Merbach 1981, 1983): A single index specifies a
certain element of an element set; an index tuple specifies a certain relationship
of a relationship set; any constant or variable is represented by an attribute.
Take, for instance, a standard constraint of linear programming:
Yy 4 SUM; ajjxy = by Fi
In this equation, the index i may indicate a single resource of the element set
RESOURCE, while the index j indicates a single product of the element set PRODUCT.
The constant. by may then represents the attribute "capacity" of resource i while
the variable yy represents the attribute “idle capacity". Similarly, the variable
xX. represents the attribute "quantity" of product j. The index tuple ij indicates
a Single relationship pair of resource i and product j; the constant aij
represents the attribute "production coefficient" between resource i and product
i.
In the structured systems approach, the process of designing such mathematical
models goes via a set graph as follows:
capacity b; prod. coefficient aij quantity x
idle capacity y, 7
Such a set graph is a comprehensive documentation of the information required for
a particular model. The element sets are drawn as circles, the relationship sets
as ellipses. The corresponding attributes can (in case of not too many sets and
attributes) physically be assigned to the sets.
Set graphs do not only support the documentation, they also serve the purpose of
communication between the modeller and the problem owner. They can use the set
graph to find consensus about the relevant sets and their relevant attributes.
Set graphs can be designed for single purposes and the corresponding models. In
general, such single-purpose graphs would be merged with the data base of the
institution, e.g. an enterprise. The totality of single set graphs required within
any institution constitutes the full data base structure for the institution's
comprehensive information system.
Comprehensive information systems come into existence by the continuous extension
of its central data base through repeated application of the structured systems
approach to all the models of the institution. Any programme or query or
(optimisation and simulation) model will eventually refer to the data base. Should
any element set, relationship set or attribute not as yet be available, the data
base would have to be extended accordingly.
Conclusion of section 2: The structured systems approach would organise the
information required in an institution as attributes assigned to element sets
and relationship sets. The integration of al] the sets and their attributes
required would eventually bring about the data base of a comprehensive
information system.
3. The Structured Systems Approach for System Dynamics Models
The structured systems approach (or any other relational data base terminology)
serves the same purpose for any kind of model, be it an optimisation or a
simulation model, including system dynamic models. This is even independent of the
fact whether a comprehensive data base is being designed or whether the
information structure supports the individual model only.
Considered be the world model by Meadows at al. (1972). They decided to model the
world with respect to five element sets: POPULATION, natural RESOURCES, INDUSTRY,
AGRICULTURE, and POLLUTION. All of these sets accommodate at least one element
each, and it is up to the model designer to differentiate between different kinds
of population, of resources, of industry etc.
The element sets are presented in the following graph (circles). They are
connected by relationship sets (ellipses). A particular property of system
dynamics models is the relationship between any particular state of today and the
corresponding state of tomorrow. This can be represented by relationship sets
which connect an element set with itself.
This graph represents the element sets and the relationship sets and is now ready
for the attributes to be assigned to the sets. The attributes can be constants,
state variables, rate variables, or any other kind of variables.
The structured systems approach helps to organise the modelling process in that
the different levels of design decisions can be separated: What are the relevant
element sets? Which are the relevant relationship sets between the element sets?
What are the relevant attributes of the element and relationship sets? Many
individuals can participate in this process without any specific competence in
mathematics and computer sciences.
Conclusion of section 3: The structured systems approach can be applied to
‘system dynamics modelling in the same way as to optimisation and other
simulation models.
4. The Modelling Process
Models and information systems are the results of design processes. These
processes require many decisions. Models are not just photographs of reality;
instead, they are constructions carried out by conscious human minds.
The process of modelling (at least if the model serves a relevant purpose) is
necessarily at the same time interdisciplinary, interpersonal and exploratory. It
should be interdisciplinary in order to cover more aspects than just that of one
discipline, be it physics, chemistry, electrical engineering, economics, or
sociology etc. It should be interpersonal, i.e. represent different persons
views, since its results should be acceptable for groups of people and not just
for a single individual. It should be exploratory in that the modelling process
itself will open the eyes and provide additional insight into the problem area
under study.
Therefore, the model design process itself requires a procedural structure that
covers more than just the mathematical model as the outcome. Instead, the
modelling process requires a documentation that follows the top down process of
design decisions. For this purpose, a five level organisation is being suggested
(see Milller-Merbach 1983):
@ Level I - unstructured verbality: At least - but not only - in the beginning of
the modelling process, much unstructured communication will take place. Different
ideas and views will be expressed, and dissenting expectations will eventually
have to be brought to consensus and/or compromise.
@ Level IJ - set design: The relevant element sets and the relationship sets are
being defined and connected to each other in a set graph.
@ Level IJI - attribute design: The relevant attributes are being defined and
assigned to the corresponding element and relationship sets.
@ Level IV - function design: The functional dependencies between the attributes
are being defined and transformed into mathematical equalities and inequalities.
@ Level ¥ - data management: The attribute values (data) have to be assigned to
the single elements and relationships (of the corresponding sets). Some of the
a
data may be available from data bases while others have to be collected somewhere.
Even if there is some internal top down structure from level 1 to level V, the
design process need not precisely follow the sequence of the levels. Instead, all
the five levels can be accomplished in some parallelity. The levels should be
unterstood as simultaneous components rather than as consecutive phases
(Miller-Merbach 1982).
The level structure guides the design process, serves as top down documentation
and supports the interdisciplinary and interpersonal communication:
@ It guides the design process in that it helps to control the questions
regarding the relevant personal views, the relevant sets, the relevant attributes
etc.
@ It serves the purpose of documentation in that each level brings about its
specific documents.
e@ It helps to communicate. in that (i) the unstructured verbality will eventually
be mapped in terms of sets, attributes, functions etc. and in that (ii) these
records will increase the systematic order of communication.
Thus, the structured systems approach may help to stimulate the participation in
the design of optimisation and simulation models - as well as of comprehensive
information systems (see also Geoffrion 1987). This includes experts of methodolgy
as well as, in particular, experts in the relevant substance matters.
With the ongoing systematization of modelling processes, the design of models and
information systems will more and more become a common skill and will not remain
the prerogative of mathematicians and computer scientists etc.
Conclusion of section
mathematical models and information systems, but also improve the documentation
of models and intensify the communicative design process.
The structured systems approach will not only integrate
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