PEMODELAN SISTEM Dalam

KAJIAN LINGKUNGAN

diabstraksikan oleh: smno.psl.ppsub.sept2012

“Semua benda hidup dan mati yg terdapat secara alamiah di bumi,

Bermanfaat bagi manusia,Dapat dimanfaatkan oleh manusia,

untuk memenuhi kebutuhan hidupnya

Keberadaannya & ketersediaannya:

1. Sebaran geografisnya tdk merata2. Pemanfaatannya tgt teknologi

3. Kalau diolah menghasilkan produk dan limbah

A Comprehensive Model

Land use = is a way of managing a large part of the human environment in order to obtain benefits for human.

Land use development

The complex problems

The Comprehensive Model

Systems theory is an interdisciplinary theory about the nature of complex systems in nature, society, and science, and is a framework by which one can investigate and/or describe any group of objects that work

together to produce some result.

FIVE GEOMETRIES in Resources use system

Natural resources geometry

Human demand geometry

NATURAL RESOURCES USE GEOMETRY

Resources Degradation Geometry

Natural Resources Geometry

SISTEM sbg suatu pendekatan

1. Filosofis

2. Prosedural

3. Alat bantu analisis

Systems thinking is the process of predicting, on the basis of anything at all, how something influences another thing.

It has been defined as an approach to problem solving, by viewing "problems" as

parts of an overall system, rather than reacting to present outcomes or events and

potentially contributing to further development of the undesired issue or

problem.

FILOSOFI

“Sistem”: Gugusan elemen-elemen yg saling berinteraksi dan terorganisir peri-lakunya ke arah tujuan tertentu

“Tiga prasyarat aplikasinya”:

1. Tujuan dirumuskan dengan jelas2. Proses pengambilan keputusan sentralisasi logis3. Sekala waktu -------- jangka panjang

Science systems thinkers consider that:

A system is a dynamic and complex whole, interacting as a structured functional unit;

Energy, material and information flow among the different elements that compose the system; A system is a community situated within an environment;

energy, material and information flow from and to the surrounding environment via semi-permeable membranes or boundaries;

Systems are often composed of entities seeking equilibrium but can exhibit oscillating, chaotic, or exponential behavior.

PROSEDUR“Tahapan Pokok”:

1. Analisis Kelayakan2. Pemodelan Abstrak3. Disain Sistem4. Implementasi Sistem5. Operasi Sistem

Need Assesment

Tahapan Pokok: ---

Evaluasi

Outcomes

A conceptual framework is used in research to outline possible courses of action or to

present a preferred approach to a system analysis project.

The framework is built from a set of concepts linked to a planned or existing system of methods, behaviors, functions, relationships, and objects. A conceptual framework might, in computing terms, be

thought of as a relational model.

For example a conceptual framework of accounting "seeks to identify the nature, subject, purpose and broad content of

general-purpose financial reporting and the qualitative characteristics that financial

information should possess".

ALAT -BANTU

“Model Abstrak”: Perilaku esensialnya sama dengan dunia nyata

“digunakan dalam”:

1. Perancangan / Disain Sistem 2. Menganalisis SISTEM ……………strukturnya

INPUT …...…….. beragamSTRUKTUR …….. fixedOUTPUT ……….. Diamati perilakunya

3. Simulasi SISTEM

untuk sistem yang kompleks

SIMULASI SISTEM:

OPERASINYA

“Penggunaan Komputer ”:

Simulasi Komputer: Disain Sistem

Strategi Pengelolaan Sistem

MODEL SISTEM

PROGRAM KOMPUTER

programming

A model is a simplified abstract view of the complex reality.

A scientific model represents empirical objects, phenomena, and physical processes in a logical way. Attempts to formalize the principles of the empirical

sciences, use an interpretation to model reality, in the same way logicians axiomatize the principles of logic.

The aim of these attempts is to construct a formal system for which reality is the only interpretation. The world is an interpretation (or model) of these sciences,

only insofar as these sciences are true.

For the scientist, a model is also a way in which the human thought processes can be amplified.

Models that are rendered in software allow scientists to leverage computational power to simulate, visualize,

manipulate and gain intuition about the entity, phenomenon or process being represented.

SIMULASI SISTEM:

METODOLOGI

“Model dasar”: Model Matematik

Model lain diformulasikan menjadi model matematik

“tahapan”:

1. Identifikasi subsistem / komponen sistem 2. Peubah input ( U(t) ) ……….. Stimulus3. Peubah internal = peubah keadaan = peubah struktural, X(t)4. Peubah Output, Y(t)5. Formulasi hubungan teoritik antara U(t), X(t), dan Y(t)6. Menjelaskan peubah eksogen7. Interaksi antar komponen ………… DIAGRAM LINGKAR8. Verifikasi model …….. Uji ……. Revisi9. Aplikasi Model ……. Problem solving

A simulation is the implementation of a model over time. A simulation brings a model to life and shows how a particular object or

phenomenon will behave. It is useful for testing, analysis or training where real-world systems or concepts can be represented by a model

PEMODELAN SISTEM:

RUANG LINGKUP

“Pemodelan”: Serangkaian kegiatan pembuatan

model

MODEL: abstraksi dari suatu obyek atau situasi aktual

1. Hubungan Langsung 2. Hubungan tidak langsung

3. Keterkaitan Timbal-balik / Sebab-akibat / Fungsional

4. Peubah - peubah 5. Parameter

MODEL KONSEP

MATEMATIKA

Operasi Matematik:Formula, Tanda, Aksioma

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JENIS-JENIS MODEL

“MODEL SIMBOLIK” : Simbol-simbol Matematik

AngkaSimbol “Persamaan”Rumus Ketidak-samaan

Fungsi

“MODEL IKONIK” :

Model Fisik1. Peta-peta geografis

2. Foto, Gambar, Lukisan 3. Prototipe

“MODEL ANALOG” :

Model Diagramatik: 1. Hubungan-hubungan

2. …... 3. …..

A system is a set of interacting or interdependent entities, real or abstract, forming an integrated whole.

The concept of an 'integrated whole' can also be stated in terms of a system embodying a set of relationships which are differentiated from relationships of the set to other

elements, and from relationships between an element of the set and elements not a part of the relational regime.

SIFAT MODEL

PROBABILISTIK / STOKASTIK Teknik Peluang Memperhitungkan “uncertainty”

“DETERMINISTIK”:

Tidak memperhitungkan peluang kejadian

Systems Engineering is an interdisciplinary approach and means for enabling the realization and deployment of successful systems. It can be viewed as the application of

engineering techniques to the engineering of systems, as well as the application of a systems approach to engineering efforts.

Systems Engineering integrates other disciplines and specialty groups into a team effort, forming a structured development process that proceeds from concept to production to

operation and disposal. Systems Engineering considers both the business and the technical needs of all

customers, with the goal of providing a quality product that meets the user needs

FUNGSI MODEL

MODEL DESKRIPTIF

Deskripsi matematik dari kondisi dunia nyata

“MODEL ALOKATIF” :

Komparasi alternatif untuk mendapatkan “optimal solution”

Scientific modelling is the process of generating abstract, conceptual, graphical and/or mathematical models.

Science offers a growing collection of methods, techniques and theory about all kinds of specialized scientific modelling.

Also a way to read elements easily which have been broken down to the simplest form

TAHAPAN PEMODELAN

1. Seleksi Konsep

2. Konstruksi Model: a. Black Boxb. Structural Approach

3. Implementasi Komputer

4. Validasi (keabsahan representasi)

5. Sensitivitas

6. Stabilitas

7. Aplikasi Model

1. Asumsi Model2. Konsistensi Internal3. Data Input ----- hitung parameter4. Hubungan fungsional antar

peubah-peubah5. Uji Model vs kondisi aktual

Scientific modelling is the process of generating abstract, conceptual, graphical and/or mathematical models.

Science offers a growing collection of methods, techniques and theory about all kinds of specialized scientific modelling.

Also a way to read elements easily which have been broken down to the simplest form

PHASES OF SYSTEMS ANALYSIS

Recognition….

Definition and bounding of the PROBLEM

Identification of goals and objectives

Generation of solutions

MODELLING

Evaluation of potential courses of action

Implementation of results

Mengapa kita gunakan Analisis Sistem?

1. Kompleksitas obyek / fenomena /substansi penelitianMulti-atribute Multi fungsionalMulti dimensional Multi-variabel

Proses Abstraksi & Simplifikasi

2. Interaksi rumit yg melibatkan banyak hal Korelasional PathwaysRegresional Struktural

3. Interaksi dinamik: Time-dependent , andConstantly changing

4. Feed-back loopsNegative effects vs. Positive effects

PROSES PEMODELAN

INTRODUCTION

DEFINITION

HYPOTHESES

MODELLING

VALIDATION

INTEGRATION

SISTEM - MODEL - PROSES

Bounding - Word ModelAlternatives: Separate - Combination

Relevansi : Indikator - variabel - subsistem Proses : Linkages - ImpactsHubungan : Linear - Non-linear - interaksiDecision table:

Data : Plotting - outliers Analisis : Test - EstimationChoice :

Verifikasi: Subyektif - reasonable Uji Kritis: Eksperiment - Analisis/SimulasiSensitivity: Uncertainty - Resources -

- Interaksi

Communication

Conclusions

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Proses Pemodelan

SISTEM: ApproachSimulasi SistemAnalisis Sistem

Model vs. Pemodelan

Mathematical models: An exact science,

Its Practical Application:1. A high degree of intuition2. Practical experiences3. Imagination4. “Flair”5. Problem define & boundingModelling refers to the process of generating a model as a conceptual representation of

some phenomenon. Typically a model will refer only to some aspects of the phenomenon in question, and two models of the same phenomenon may be essentially different, that is in which the difference is more than just a

simple renaming. This may be due to differing requirements of the model's end users or to conceptual or aesthetic differences by the modellers and decisions made during the modelling

process. Aesthetic considerations that may influence the structure of a model might be the modeller's

preference for a reduced ontology, preferences regarding probabilistic models vis-a-vis deterministic ones, discrete vs continuous time etc. For this reason users of a model need to understand the

model's original purpose and the assumptions of its validity

DEFINITION & BOUNDING

IDENTIFIKASI dan PEMBATASAN Masalah penelitian

1. Alokasi sumberdaya penelitian2. Aktivitas penelitian yang relevan3. Kelancaran pencapaian tujuan

The whole systems vs. sets of sub-systems

Proses pembatasan masalah:1. Bersifat iteratif, tidak mungkin “sekali jadi”2. Make a start in the right direction3. Sustain initiative and momentum

System bounding: SPACE - TIME - SUB-SYSTEMS Sample vs. Population

COMPLEXITY AND MODELS

The real system sangat kompleks

Proses Pengujian Model Hipotetik

The hypothesesto be tested

Sub-systemsMODEL

Trade-off: complexity vs. simplicity

The process of evaluating a modelA model is evaluated first and foremost by its consistency to empirical data; any model

inconsistent with reproducible observations must be modified or rejected. However, a fit to empirical data alone is not sufficient for a model to be accepted as valid. Other factors

important in evaluating a model include: Ability to explain past observations

Ability to predict future observations Cost of use, especially in combination with other models

Refutability, enabling estimation of the degree of confidence in the model Simplicity, or even aesthetic appeal

WORD MODEL

Masalah penelitian dideskripsikan secara verbal, dengan meng-gunakan kata (istilah) yang relevan dan simple

Pengembangan Model simbolik

Hubungan-hubungan verbal dipresentasikan dengan simbol-simbol yang relevan

Simbolisasi kata-kata atau istilahSetiap simbol (simbol matematik) harus dapat diberi deskripsi penjelasan

maknanya secara jelas

A conceptual schema or conceptual data model is a map of concepts and their relationships.

This describes the semantics of an organization and represents a series of assertions about its nature.

Specifically, it describes the things of significance to an organization (entity classes), about which it is inclined to collect information, and characteristics of (attributes) and

associations between pairs of those things of significance (relationships).

GENERATION OF SOLUTION Alternatif “solusi” jawaban permasalahan , berapa banyak?

Pada awalnya diidentifikasi sebanyak mungkin alternatif jawaban yang mungkin

Penggabungan beberapa alternatif jawaban yang mungkin digabungkan

A conceptual schema or conceptual data model is a map of concepts and their relationships. This describes the semantics of an organization and represents a

series of assertions about its nature. Specifically, it describes the things of significance to an organization (entity classes), about which it is inclined to collect information, and characteristics of (attributes) and associations between pairs of

those things of significance (relationships).A conceptual schema or conceptual data model is a map of concepts and their

relationships. This describes the semantics of an organization and represents a series of assertions about its nature. Specifically, it describes the things of

significance to an organization (entity classes), about which it is inclined to collect information, and characteristics of (attributes) and associations between pairs of

those things of significance (relationships).

HYPOTHESES

Tiga macam hipotesis:

1. Hypotheses of relevance: mengidentifikasi & mendefinisikan faktor, variabel, parameter, atau komponen sistem yang relevan dg permasalahan

2. Hypotheses of processes: merangkaikan faktor-faktor atau komponen-komponen sistem yg relevan dengan proses / perilaku sistem dan mengidentifikasi dampaknya thd sistem

3. Hypotheses of relationship: hubungan antar faktor, dan representasi hubungan tersebut dengan formula-formula matematika yg relevan, linear, non linear, interaktif.

Penjelasan / justifikasi Hipotesis

Justifikasi secara teoritisJustifikasi berdasarkan hasil-hasil penelitian yang telah ada

A conceptual system is a system that is composed of non-physical objects, i.e. ideas or concepts. In this context a system is taken to mean "an interrelated, interworking set of objects".

A conceptual system is simply a . There are no limitations on this kind of model whatsoever except those of human imagination. If there is an experimentally verified correspondence between a

conceptual system and a physical system then that conceptual system models the physical system. "values, ideas, and beliefs that make up every persons view of the world": that is a model of the

world; a conceptual system that is a model of a physical system (the world). The person who has that model is a physical system.

MODEL CONSTRUCTIONKonstruksi Model

Proses seleksi / uji alternatif yang ada

Manipulasi matematis

Data dikumpulkan dan diperiksa dg seksama untuk menguji penyimpangannya terhadap hipotesis.

Grafik dibuat dan digambarkan untuk menganalisis hubungan yang ada dan bagaimana sifat / bentuk hubungan itu

Uji statistik dilakukan untuk mengetahui tingkat signifikasinya

Simulation is the imitation of some real thing, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics

or behaviours of a selected physical or abstract system.

Simulation is used in many contexts, including the modeling of natural systems or human systems in order to gain insight into their functioning.

Other contexts include simulation of technology for performance optimization, safety engineering, testing, training and education.

Simulation can be used to show the eventual real effects of alternative conditions and courses of action.

VERIFICATION & VALIDATION

VERIFIKASI MODEL1. Menguji apakah “general behavior of a MODEL” mampu mencerminkan “the real system”2. Apakah mekanisme atau proses yang di “model” sesuai dengan yang terjadi dalam sistem3. Verifikasi: subjective assessment of the success of the modelling4. Inkonsistensi antara perilaku model dengan real-system harus dapat diberikan penjelasannya

Proses Pemodelan

VALIDASI MODEL1. Sampai seberapa jauh output dari model sesuai dengan perilaku sistem yang sesungguhnya2. Uji prosedur pemodelan3. Uji statistik untuk mengetahui “adequacy of the model”4.

SENSITIVITY ANALYSIS

Perubahan input variabel dan perubahan parameter menghasilkan variasi kinerja model (diukur dari solusi model) ……… analisis sensitivitas

Validasi MODELModel validation is possibly the most important step in the model

building sequence. It is also one of the most overlooked.

Often the validation of a model seems to consist of nothing more than quoting the R2 statistic from the fit (which measures the fraction of the

total variability in the response that is accounted for by the model).

Variabel atau parameter yang sensitif bagi hasil model harus dicermati lebih lanjut untuk menelaah apakah proses-proses yg terjadi dalam sistem telah di

“model” dengan benar

PLANNING & INTEGRATION

PLANNINGIntegrasi berbagai macam aktivitas, formulasi masalah, hipotesis, pengumpulan data, penyusunan alternatif rencana dan implementasi rencana. Kegagalan integrasi ini berdampak pada hilangnya komunikasi :1. Antara data eksperimentasi dan model development2. Antara simulasi model dengan implementasi model3. Antara hasil prediksi model dengan implementasi model4. Antara management practices dengan pengembangan hipotesis yang baru5. Implementasi hasil uji coba dengan hipotesis yg baru

DEVELOPMENT of MODEL1. Kualitas data dan pemahaman terhadap fenomena sebab- akibat (proses yang di model) umumnya POOR2. Analisis sistem dan pengumpulan data harus dilengkapi dengan mekanisme umpan-balik3. Pelatihan dalam analisis sistem sangat diperlukan4. Model sistem hanya dapat diperbaiki dengan jalan mengatasi kelemahannya5. Tim analisis sistem seyogyanya interdisiplin

PEMODELAN KUANTITATIF : MATEMATIKA DAN STATISTIKA

MODEL STATISTIKA:FENOMENA STOKASTIK

MODEL MATEMATIKA:FENOMENA DETERMINISTIK

Deterministic Model Example

Diunduh dari: …………… http://www.vertex42.com/ExcelArticles/mc/MonteCarloSimulation.html

. An example of a deterministic model is a calculation to determine the return on a 5-year investment with an annual interest rate of 7%, compounded monthly.

The model is just the equation below:

The inputs are the initial investment (P = $1000), annual interest rate (r = 7% = 0.07), the compounding period (m = 12 months), and the number of years (Y = 5).

A parametric deterministic model maps a set of input variables to a set of output

variables.

Conceptual modelling framework

Diunduh dari: …………… http://2007.igem.org/wiki/index.php/Glasgow/Modeling

WHAT IS SYSTEM MODELLING ?

Recognition

Definitions

Problems

Evaluation

Identification

Feed-back

Solution

Modelling

Amenable

Worthwhile

Compromise

Bounding

Complexity

Simplification

Stopping rules

Generality

GenerationFamily

Selection

Objectives Hierarchy

PrioritiesGoals

Inter-relationship

Sensitivity & Assumptions Implementation

PHASES OF SYSTEM MODELLINGRecognition

Definition and bounding of the problems

Generation of solution

Identification of goals and objectives

MODELLING

Evaluation of potential courses of action

Implementation of results

Model evaluationA crucial part of the modelling process is the evaluation of whether or not a given

mathematical model describes a system accurately. This question can be difficult to answer as it involves several different types of evaluation.

Fit to empirical dataUsually the easiest part of model evaluation is checking whether a model fits

experimental measurements or other empirical data. In models with parameters, a common approach to test this fit is to split the data into two disjoint subsets: training

data and verification data. The training data are used to estimate the model parameters. An accurate model will closely match the verification data even though this data was

not used to set the model's parameters. This practice is referred to as cross-validation in statistics.

Defining a metric to measure distances between observed and predicted data is a useful tool of assessing model fit. In statistics, decision theory, and some economic models, a

loss function plays a similar role.

While it is rather straightforward to test the appropriateness of parameters, it can be more difficult to test the validity of the general mathematical form of a model.

In general, more mathematical tools have been developed to test the fit of statistical models than models involving Differential equations.

Tools from nonparametric statistics can sometimes be used to evaluate how well data fits a known distribution or to come up with a general model that makes only minimal

assumptions about the model's mathematical form.

Scope of the model

Assessing the scope of a model, that is, determining what situations the model is applicable to, can be less straightforward. If the model was

constructed based on a set of data, one must determine for which systems or situations the known data is a "typical" set of data.

The question of whether the model describes well the properties of the system between data points is called interpolation, and the same question for

events or data points outside the observed data is called extrapolation.

As an example of the typical limitations of the scope of a model, in evaluating Newtonian classical mechanics, we can note that Newton made his

measurements without advanced equipment, so he could not measure properties of particles travelling at speeds close to the speed of light.

Likewise, he did not measure the movements of molecules and other small particles, but macro particles only.

It is then not surprising that his model does not extrapolate well into these domains, even though his model is quite sufficient for ordinary life physics.

Philosophical considerations

Many types of modelling implicitly involve claims about causality. This is usually (but not always) true of models involving differential equations.

As the purpose of modelling is to increase our understanding of the world, the validity of a model rests not only on its fit to empirical observations, but also on its ability to extrapolate to situations or data beyond those originally

described in the model.

One can argue that a model is worthless unless it provides some insight which goes beyond what is already known from direct investigation of the

phenomenon being studied.

An example of such criticism is the argument that the mathematical models of Optimal foraging theory do not offer insight that goes beyond the common-

sense conclusions of evolution and other basic principles of ecology.

MODEL & MATEMATIK: Term

Variabel ParameterLikelihood

Konstante Tipe

Dependent

Independent

Regressor

Populasi

Sampel

Probability

Maximum

Analitik

Simulasi

Modelling and Simulation

One application of scientific modelling is the field of "Modelling and Simulation", generally referred to as "M&S".

M&S has a spectrum of applications which range from concept development and analysis, through experimentation, measurement and verification, to disposal analysis.

Projects and programs may use hundreds of different simulations, simulators and model analysis tools.

JENIS VARIABEL

Independent

Intervening(Mediating)

Dependent

Confounding

Moderator

Concomitant Control

EXTRANEOUS

INTRANEOUS

Variabel tergantung adalah variabel yang tercakup dalam hipotesis penelitian, keragamannya dipengaruhi oleh variabel lain

Variabel bebas adalah variabel yang yang tercakup dalam hipotesis penelitian dan berpengaruh atau mempengaruhi variabel

tergantung

Variabel antara (intervene variables) adalah variabel yang bersifat menjadi perantara dari hubungan variabel bebas ke variabel

tergantung.

Variabel Moderator adalah variabel yang bersifat memperkuat atau memperlemah pengaruh variabel bebas terhadap variabel

tergantung

Variabel pembaur (confounding variables) adalah suatu variabel yang tercakup dalam hipotesis penelitian, akan tetapi muncul dalam penelitian dan berpengaruh terhadap variabel tergantung dan pengaruh tersebut mencampuri atau berbaur

dengan variabel bebas

Variabel kendali (control variables) adalah variabel pembaur yang dapat dikendalikan pada saat riset design. Pengendalian dapat dilakukan dengan cara

eksklusi (mengeluarkan obyek yang tidak memenuhi kriteria) dan inklusi (menjadikan obyek yang memenuhi kriteria untuk diikutkan dalam sampel penelitian) atau dengan blocking, yaitu membagi obyek penelitian menjadi

kelompok-kelompok yang relatif homogen.

Variabel penyerta (concomitant variables) adalah suatu variabel pembaur (cofounding) yang tidak dapat dikendalikan saat riset design. Variabel ini tidak dapat dikendalikan, sehingga tetap menyertai (terikut) dalam proses penelitian, dengan konsekuensi harus diamati dan pengaruh baurnya harus dieliminir atau

dihilanggkan pada saat analisis data.

MODEL & MATEMATIK: Definition

Preliminary Goodall Mathematical

Formal Expression

Words

Physical

Mapping

Representational

Rules

Predicted values

Maynard-Smith

Comparison

Mathematical

Homomorph

Symbolic

SimplifiedData values

Model

Simulation

Model adalah rencana, representasi, atau deskripsi yang menjelaskan suatu objek, sistem, atau konsep, yang seringkali berupa penyederhanaan atau idealisasi.

Bentuknya dapat berupa model fisik (maket, bentuk prototipe), model citra (gambar rancangan, citra komputer), atau rumusan matematis.

MODEL & MATEMATIK: RelativesAdvantages Disadvantages

Precise

Abstract

Communication

Distortion

Opaqueness

Transfer Complexity

Replacement

Eykhoff (1974) defined a mathematical model as 'a representation of the essential aspects of an existing system (or a system to be constructed) which presents

knowledge of that system in usable form'.

Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a

variety of abstract structures

MODEL & MATEMATIK: Families

Types Basis

Dynamics

Compartment

Network

Choices

Stochastic

Multivariate

A mathematical model uses mathematical language to describe a system.

Mathematical models are used not only in the natural sciences and engineering disciplines (such

as physics, biology, earth science, meteorology, and engineering) but also in the social sciences (such as economics, psychology, sociology and

political science); physicists, engineers, computer scientists, and economists use mathematical

models most extensively.

The process of developing a mathematical model is termed 'mathematical modelling' (also modeling).

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BEBERAPA PENGERTIANMODEL DETERMINISTIK: Nilai-nilai yang diramal (diestimasi, diduga) dapat dihitung secara eksak.

MODEL STOKASTIK: Model-model yang diramal (diestimasi, diduga) tergantung pada distribusi peluang

POPULASI: Keseluruhan individu-individu (atau area, unit, lokasi dll.) yang diteliti untuk mendapatkan kesimpulan.

SAMPEL: sejumlah tertentu individu yang diambil dari POPULASI dan dianggap nilai-nilai yang dihitung dari sampel dapat mewakili populasi secara keseluruhan

VARIABEL DEPENDENT: Variabel yang diharapkan berubah nilainya disebabkan oleh adanya perubahan nilai dari variabel lain

VARIABEL INDEPENDENT: variabel yang dapat menyebabkan terjadinya perubahan VARIABEL DEPENDENT.

PARAMETER: Nilai-nilai karakteristik dari populasi

KONSTANTE, KOEFISIEAN: nilai-nilai karakteristik yang dihitung dari SAMPEL

BEBERAPA PENGERTIANMODEL FITTING: Proses pemilihan parameter (konstante dan/atau koefisien yang dapat

menghasilkan nilai-nilai ramalan paling mendekati nilai-nilai sesungguhnya

ANALYTICAL MODEL: Model yang formula-formulanya secara eksplisit diturunkan untuk mendapatkan nilai-nilai ramalan, contohnya: MODEL REGRESI

MODEL MULTIVARIATEEXPERIMENTAL DESIGNSTANDARD DISTRIBUTION, etc

SIMULATION MODEL: Model yang formula-formulanya diturunkan dengan serangkaian operasi arithmatik, misal:Solusi persamaan diferensialAplikasi matrixPenggunaan bilangan acak, dll.

A mathematical model usually describes a system by a set of variables and a set of equations that establish relationships between the variables.

The values of the variables can be practically anything; real or integer numbers, boolean values or strings, for example.

The variables represent some properties of the system, for example, measured system outputs often in the form of signals, timing data, counters, and event

occurrence (yes/no). The actual model is the set of functions that describe the relations between the

different variables.

DYNAMIC MODEL

MODELLING

Dynamics SIMULATION

Language

Equations

Computer

GeneralSpecial

DYNAMOCSMPCSSL

BASIC

FORMAL

ANALYSIS

DYNAMIC MODEL DIAGRAMS

RELATIONAL SYMBOLS

RATE EQUATIONS

LEVELS

PARAMETERINFORMATION FLOW

SINK

AUXILIARY VARIABLES MATERIAL FLOW

Data Flow Diagram (DFD) adalah suatu diagram yang menggunakan notasi-notasi untuk menggambarkan arus dari data sistem, yang penggunaannya

sangat membantu untuk memahami sistem secara logika, tersruktur dan jelas.

DFD merupakan alat bantu dalam menggambarkan atau menjelaskan sistem yang sedang berjalan logis.

48

DYNAMIC MODEL:

ORIGINS

Computers Equations

Other functions

Steps

Discriminant Function

Undestanding

Simulation

Abstraction

Hypothesis

Logistic

Exponentials

49

MATRIX MODEL

MATHEMATICS

Operations Matrices

Types

Eigen value

Elements

SquareRectangular

Diagonal Identity Vectors

Dominant

Eigen vector

Scalars

RowColumn

AdditionsSubstraction

MultiplicationInversion

50

MATRIX MODEL DEVELOPMENT

Interactions Groups

Development stages

Stochastic

Size Materials

cycles Markov Models

The term matrix model may refer to one of several concepts:In theoretical physics, a matrix model is a system (usually a quantum mechanical system)

with matrix-valued physical quantities. See, for example, Lax pair. The "old" matrix models are relevant for string theory in two spacetime dimensions. The

"new" matrix model is a synonym for Matrix theory. Matrix population models are used to model wildlife and human population dynamics. The Matrix Model of substance abuse treatment was a model developed by the Matrix

Institute in the 1980's to treat cocaine and methamphetamine addiction. A concept from Algebraic logic.

51

STOCHASTIC MODEL STOCHASTIC

Probabilities History

Stability

Other Models

Statistical method Dynamics

A statistical model is a set of mathematical equations which describe the behavior of an object of study in terms of random variables and their associated probability distributions. If the model has only one equation it is called a single-equation model, whereas if it has more

than one equation, it is known as a multiple-equation model.

In mathematical terms, a statistical model is frequently thought of as a pair (Y,P) where Y is the set of possible observations and P the set of possible probability distributions on Y. It is

assumed that there is a distinct element of P which generates the observed data. Statistical inference enables us to make statements about which element(s) of this set are

likely to be the true one.

52

STOCHASTIC MODEL Spatial patern

Distribution Example

Binomial

Pisson Poisson

Negative Binomial

Others

Negative Binomial

Fitting Test

In statistics, spatial analysis or spatial statistics includes any of the formal techniques which study entities using their topological, geometric, or

geographic properties. The phrase properly refers to a variety of techniques, many still in their early

development, using different analytic approaches and applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, to

chip fabrication engineering, with its use of 'place and route' algorithms to build complex wiring structures.

53

STOCHASTIC MODEL

ADDITIVE MODELS

Basic Model Example

Parameter

Error Estimates

Block

Treatments

Analysis

Effects

Orthogonal

Experimental Significance

Variance

54

STOCHASTIC MODEL REGRESSION

Model Example

Linear/ Non-linear functions

Error Decomposition

Assumptions

Equation

Reactions

Oxygen uptake

Experimental Empirical base

Theoritical base

In statistics, regression analysis includes any techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more

independent variables. More specifically, regression analysis helps us understand how the typical value of the

dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed.

55

Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables — that is, the average value of the dependent

variable when the independent variables are held fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the

estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent

variable around the regression function, which can be described by a probability distribution.

Regression analysis is widely used for prediction (including forecasting of time-series data). Use of regression analysis for prediction has

substantial overlap with the field of machine learning. Regression analysis is also used to understand which among the

independent variables are related to the dependent variable, and to explore the forms of these relationships.

In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables.

56

Underlying assumptions

Classical assumptions for regression analysis include:The sample must be representative of the population for the inference prediction. The error is assumed to be a random variable with a mean of zero conditional on

the explanatory variables. The variables are error-free. If this is not so, modeling may be done using errors-

in-variables model techniques.

The predictors must be linearly independent, i.e. it must not be possible to express any predictor as a linear combination of the others. See Multicollinearity.

The errors are uncorrelated, that is, the variance-covariance matrix of the errors is diagonal and each non-zero element is the variance of the error.

The variance of the error is constant across observations (homoscedasticity). If not, weighted least squares or other methods might be used.

These are sufficient (but not all necessary) conditions for the least-squares estimator to possess desirable properties, in particular, these assumptions imply

that the parameter estimates will be unbiased, consistent, and efficient in the class of linear unbiased estimators. Many of these assumptions may be relaxed in

more advanced treatments.

57

STOCHASTIC MODEL MARKOV

Example Assumptions

Transition probabilities

Analysis Disadvantage

Raised mire

Advantages

Analysis

What is a Markov Model?

Markov models are some of the most powerful tools available to engineers and scientists for analyzing complex systems.

This analysis yields results for both the time dependent evolution of the system and the steady state of the system.

58

MULTIVARIATE MODELS

METHODS

Variable Classification

Independent

Dependent Descriptive Predictive

VARIATE

Principal Component

Analysis

Cluster Analysis

Reciprocal averaging

Canonical Analysis

Discriminant Analysis

59

MULTIVARIATE MODEL PRINCIPLE COMPONENT ANALYSIS

Example Correlation

Organism

Environment Eigenvalues

Regions

Objectives

Requirement

Eigenvectors

Principal Component Analysis (PCA) involves a mathematical procedure that transforms a number of possibly correlated variables into a smaller number of

uncorrelated variables called principal components. The first principal component accounts for as much of the variability in the data

as possible, and each succeeding component accounts for as much of the remaining variability as possible.

60

MULTIVARIATE MODEL CLUSTER ANALYSIS

Example Spanning tree

Rainfall regimes

Demography

Minimum

Settlement patern

Multivariate space

Similarity

Distance Single linkage

Cluster analysis or clustering is the assignment of a set of observations into subsets (called clusters) so that observations in the same cluster are similar in some sense. Clustering is a method of unsupervised learning, and a common technique for statistical data analysis used in many fields, including machine learning, data mining, pattern recognition, image analysis and bioinformatics.

Besides the term clustering, there are a number of terms with similar meanings, including automatic classification, numerical taxonomy, botryology

and typological analysis.

61

MULTIVARIATE MODEL CANONICAL CORRELATION

Example Correlation

Urban area

WatershedPartitioned

Irrigation regions Eigenvalues Eigenvectors

Canonical correlation analysis (CCA) is a way of measuring the linear relationship between two multidimensional variables.

It finds two bases, one for each variable, that are optimal with respect to correlations and, at the same time, it finds the corresponding correlations. In

other words, it finds the two bases in which the correlation matrix between the variables is diagonal and the correlations on the diagonal are maximized.

The dimensionality of these new bases is equal to or less than the smallest dimensionality of the two  variables.

62

MULTIVARIATE MODEL Discriminant Function

Example Discriminant

Vehicles

VillagesCalculation

Structures Test

Discriminant function analysis involves the predicting of a categorical dependent variable by one or more continuous or binary independent variables. It is

statistically the opposite of MANOVA. It is useful in determining whether a set of variables is effective in predicting

category membership.

It is also a useful follow-up procedure to a MANOVA instead of doing a series of one-way ANOVAs, for ascertaining how the groups differ on the composite of

dependent variables.

OPTIMIZATION MODEL

OPTIMIZATION

Meanings Indirect

Minimization

Simulation Objective function

Maximization

Linear

Experimentation

Constraints

Solution

Examples

Non-Linear

Dynamic

Optimum Transportation RoutesOptimum irrigation schemeOptimum Regional Spacing

OPTIMIZATION MODEL

Diunduh dari: ……………http://www.answers.com/topic/optimization-model-1

A model used to find the best possible choice out of a set of alternatives. It may use the mathematical expression of a problem to maximize or minimize some function. The alternatives are frequently restricted by constraints on the values of the variables.

A simple example might be finding the most efficient transport pattern to carry commodities from the point of supply to the markets, given the volumes of production

and demand, together with unit transport costs.

Read more: http://www.answers.com/topic/optimization-model-1#ixzz2JbXsisBX

Ten Keys to Success in Optimization Modeling

Richard E. RosenthalOperations Research Department

Naval Postgraduate School

INFORMS Atlanta, October 2003

Key #1: Communicate Early and Often

Mathematical formulation – kept up to dateVerbal description of formulation

Executive summary – in the right language

Mathematical Formulation

Index use

Given data (and units) in lower case

Decision Variables (and units) in UPPER CASE

Objectives and constraints

Verbal Description of Formulation

“Constraints ensure that one service facility is assigned responsibility for each product line p.”

You wonder why I mention this, but look at our applied literature.

Non-mathematical Executive Summary

Jerry Brown’s Five Essential Steps:• What is the problem?• Why is the problem important?• How will the problem be solved without you?• How will you solve the problem?• How will the problem be solved with your results, but

without you?

Key #2: Bound all Decisions

A trivial concept, too-often ignored

Remember all the formal “neighborhood” assumptions underlying your optimization method?

Bob Bixby tells of real customer MIP with only 51 variables and 40 constraints that could not be solved… until bounds were added, and then it solved in a flash.

Bound all Decisions

• Optimization is an excellent way to find data errors, but it really exploits them

• Moderation is a virtue

• Bonus! You never have to deal with the embarrassment (or the theory) ofunbounded models.

Key #3: Expect any Constraint to Become an Objective, and Vice Versa

Real-world models are notorious for multiple, conflicting objectives

Expert guidance from senior leaders is often interpreted as constraints

These “constraints” are often infeasibleDiscovering what can be done changes your concept of

what should be doneContrary to impression of textbooks, alternate optima are

the rule, not the exception.

Key #4: Sensitivity Analysis in the Real World Is Nothing Like Textbook SA

LP Sensitivity Analysis, Textbook Style

Disappointing in practice because theory creates limits. •  

Textbooks have sleek algorithms for one modification at a time, all else held constant, e.g.,

minimize Sj cj Xj + dXk

Not very exciting in practice. So why is this stuff in all the textbooks? What is worth talking about?

Sensitivity Analysis, Practitioner Style

Large-scale LP for optimizing airlift -- multiple time-space muticommodity networks, linked together with non-network constraints . Initial results on realistic scenario: only 65% of required cargo can be delivered on time. Analysis of result revealed most of the undelivered cargo was destined for City A from City B, so.. what if we redirect some of this cargo to City A’? Sensitivity analysis: add ~12,000 new rows and ~10,000 columns... on-time delivery improves to 85%.

Key #5: Bound the Dual VariablesElastic constraints, with a linear (or piece-wise linear) penalty per unit of violation, bound the dual variables

“I’m willing to satisfy this restriction (constraint),as long as it doesn’t get too expensive.Otherwise, forget it; I’ll deal with the consequences”

Key #6: Model Robustly

Your analysis should consider alternate future scenarios, and render a single robust solution.

There may be many contingency plans,but you only get one chance per yearto ask for the money to get ready.

Key #7: Eliminate Lots of Variables

Big models get to be big through Cartesian products of indices

Find rules for eliminating lots of index tuples before they are generated in the model

Sources of rules: mathematical reasoning and common sense based on understanding of the problem

You can often eliminate constraints too!

Example 1 of Variable Elimination

XD(a,i,r,t) = # of type a aircraft direct delivering cargo for customer i on route r departing at time t

Allow variable to exist only if Route r is a direct delivery route from customer i ’s origin to i ’s destination Aircraft type a is available at i ’s origin at t Aircraft type a can fly route r ’s critical legAircraft type a can carry some cargo type that customer i demandsTime t is not before i ’s available-to-load timeTime t is not after i ’s required delivery date + maxlate – travel time

Example 2 of Variable Elimination

Ann Bixby and Brian Downs of Aspen Technology developed real-time Capable-to-Promise model for large meatpacking company

One of their major efforts to bring solution times down low enough was variable elimination.

Key #8: Incremental Implementation

In a complex model, add features incrementally. Test each new feature on small instances and take no prisoners.

When new features don’t work, there is either a bug to be fixed or a new insight to be gained. Either way, treasure the learning experiences.

Incremental Implementation

Eliminate variables corresponding to airlifters switching from long-haul to shuttle status, if there are no foreseeable shuttle opportunities.

Feature tested with small example: removing the option to make a seemingly foolish decision actually caused degradation of objective function.What happened?

Euro

US SWA FOB

Key #9: Persistence

“Any prescriptive model that suggests a plan and then, when used again, ignores its own prior advice…… is bound to advise something needlessly different, and lose the faith of its beneficiaries.”

Jerry Brown

Illustration of Persistence

Customer Eqpt Type Site DistanceCust01 Eqpt-01 HHH 353Cust02 Eqpt-01 HHH 724Cust03 Eqpt-01 HHH 773Cust04 Eqpt-01 YYY 707Cust05 Eqpt-01 YYY 719Cust06 Eqpt-03 RRR 495Cust07 Eqpt-01 HHH 442Cust08 Eqpt-03 RRR 590

Results for Initial Case with 8 Customers

There are initially 8 customers to serve. We must choose serving site and equipment type.

Illustration of PersistenceJust a moment after this solution is announced, two high-priority customers call in. The model is rerun with the 10 customers.

There are not enough assets to cover all 10 customers.

The new solution requires a major reallocation of assets. Major changes in the solution are highlighted.

Illustration of Persistence

Customer Eqpt Type Site Dist (nm)Cust01 Eqpt-01 HHH 353Cust02 Eqpt-01 YYY 678Cust03 Eqpt-01 YYY 703Cust04Cust05 Eqpt-03 RRR 705Cust06 Eqpt-03 RRR 495Cust07 Eqpt-01 HHH 442Cust08Cust09 Eqpt-01 HHH 353Cust10 Eqpt-01 HHH 353

Results for 10 Customers without Persistence

NOT SERVED

NOT SERVED

Illustration of Persistence

A persistent version of the model is run to obtain a new optimal solution that discourages major changes from the original announced solution.

Add to objective function: penalties on deviations from original solution, weighted by severity of disruption.

Illustration of Persistence

Customer Eqpt Type Site Dist (nm)Cust01 Eqpt-01 HHH 353Cust02 Eqpt-01 HHH 724Cust03 Eqpt-01 HHH 773Cust04Cust05 Eqpt-01 YYY 719Cust06 Eqpt-02 RRR 495Cust07 Eqpt-01 HHH 442Cust08Cust09 Eqpt-01 YYY 380Cust10 Eqpt-01 RRR 363

Results for 10 Customers with Persistence

NOT SERVED

NOT SERVED

Illustration of Persistence

At a cost of 1% in the objective function, the persistent solution causes no disruption to the announced plans, other than substitution of the two new customers.

Orig.With persistence? - No YesCustomers 8 10 10Objective function value Customers not served 0 180.00 180.00 Original objective 206.67 151.75 155.20 Total 206.67 331.75 335.20

Comparison of Solutions Subsequent

Key #10: Common Sense

• Heuristics are easy --- so easy we are tempted to use them in lieu of more formal methods

• Heuristics may offer a first choice to assess a “common sense” solution

• But, heuristics should not be your only choice

Common Sense

A formal optimization model takes longer to develop, and solve

But it provides a qualitative bound on each heuristic solution

Without this bound, our heuristic advice is of completely unknown quality

This quality guarantee is key

Common Sense

It’s OK to use a heuristic, but you should pair it with a traditional, “calibrating” mathematical model

With no quality assessment, you are betting your reputation that nobody else is luckier than you are

10 Keys to Success in Optimization Modeling

#1 Write formulation, communicate with execs

#2 Bound decisions

#3 Objectives and constraints exchange roles (alt. optima likely)

#4 Forget about sensitivity analysis as you learned it

#5 Elasticize (bound duals)

#6 Model robustly

#7 Eliminate variables – avoid generating them when you can

#8 Incremental implementation

#9 Model persistence

#10 Bound heuristics with optimization

MODELLING PROCESS

Introduction

Definition

System analysis

Integration

Hypotheses

Conclusion

Modelling

Validation

ModelProcesses

Bounding

Word Models

Alternatives

Systems

Impacts

SpaceTimeNiche

Elements

FactorialConfounding

SeparateCombinations

Communication

Data

Analysis

Choices

Test

Estimates

PlottingOutliers

94

MODELLING PROCESSES HYPOTHESES

Relevance Processes

Species

Variable Linkages

Sub-systems

Relationships

Decision Table

Impacts Interactive

Linear

Non-Linear

A hypothesis (from Greek ὑπόθεσις; plural hypotheses) is a proposed explanation for an observable phenomenon. The term derives from the Greek, ὑποτιθέναι –

hypotithenai meaning "to put under" or "to suppose." For a hypothesis to be put forward as a scientific hypothesis, the scientific method requires that one can test

it. Scientists generally base scientific hypotheses on previous observations that cannot be satisfactorily explained with the available scientific theories. Even though the words "hypothesis" and "theory" are often used synonymously in

common and informal usage, a scientific hypothesis is not the same as a scientific theory – although the difference is sometimes more one of degree than

of principle.

HYPOTHESES

Hypotheses of Relevance: Mengidentifikasi dan mendefinisikan variabel dan subsistem yang relevan dengan permasalahan yang diteliti

Hypotheses of Processes: Menghubungkan subsistem (atau variabel) di dalam permasalahan yang diteliti dan mendefinisikan dampak (pengaruh) terhadap sistem yang diteliti

Hypotheses of relationships: Merumuskan hubungan-hubungan antar variabel dengan menggunakan formula-formula matematik (fungsi linear, non-linear, interaksi, dll)

Hypotheses of relationships

Diunduh dari: http://www.sciencedirect.com/science/article/pii/S0019850107001149 ……………

Determinants of the sophistication of SFA. In terms of specific hypotheses:

1. Hypothesis 1: There is a positive relationship between perceived strategic importance of sales decisions and level of information orientation.

2. Hypothesis 2: There is a positive relationship between organizational slack and level of information orientation.

3. Hypothesis 3: There is a negative relationship between organizational control and level of information orientation.

4. Hypothesis 4: There is a positive relationship between integration of IT and sales and level of information orientation.

5. Hypothesis 5: There is a positive relationship between perceived strategic importance of sales decisions and integration of IT and sales.

6. Hypothesis 6: There is a positive relationship between organizational slack and integration of IT and sales.

7. Hypothesis 7: There is a negative relationship between organizational control and integration of IT and sales.

8. Hypothesis 8: There is a positive relationship between level of information orientation and a count of the number of types of results of sales campaigns that are measured.

Diunduh dari: ……………http://www.sciencedirect.com/science/article/pii/S0038071797002071

Path model of hypothesized causal relationships among the lengths of

roots and mycorrhizal fungal hyphae, three soil C pools and the percentage

of water-stable soil aggregates in a chronosequence of prairie restorations. Fine roots are 0.2–1 mm dia; very fine roots are <0.2 mm dia.Single-headed

arrows indicate direct causal relationships and double-headed

arrows indicate unanalyzed correlations. Numbers are path

coefficients and proportion of total variance explained (r2; shown in bold

italics) for each endogenous (dependent) variable (n=49). The

numbers within ellipses represent the proportion of unexplained variance

[(1−r2)1/2] and, thus, indicate the relative contribution of all unmeasured or

unknown factors to each dependent variable

Hypotheses of relationships

98

MODELLING PROCESSES VALIDATION

Verification Critical Test

Objectivities

Subjectives

Experiments Reason-ableness

Sensitivity Analysis

Analysis

Interactions

Uncertainty

Resources

Model verification and validation (V&V) areessential parts of the model development

process if models to be accepted and used tosupport decision making

Model validation is possibly the most important step in the model building sequence. It is also one of the most overlooked.

Often the validation of a model seems to consist of nothing more than quoting the R2 statistic from the fit (which measures the fraction of the total variability in

the response that is accounted for by the model).

99

ROLE OF THE COMPUTER

Introduction

Speed

Roles

Conclusions

Data

Development

Algoritms

Reasons

SpeedData

Algoritm

Comparison

Implication

Waste

TechniquesErrors

Plotting

ManualCalculatorComputer

RepetitionChecking

9/10Modelling

Programming

Program

Language

Information

High level

Special

Machine code

FORTRANBASIC

ALGOL

DYNAMO. Etc.

100

ROLE OF THE COMPUTER

DATA

Cautions Availability

Format

Sampling

Reanalysis

Data banks

Format

Exchange

Magnetic

Punched card

Paper tape

Machine readable

Tape

Disc

101

D A T AData adalah kumpulan angka, fakta, fenomena atau keadaan atau lainnya,

merupakan hasil pengamatan, pengukuran, atau pencacahan dan sebagainya …

terhadap variabel suatu obyek, …..yang berfungsi dapat membedakan obyek yang satu dengan lainnya pada

variabel yang sama

Data adalah catatan atas kumpulan fakta.

Data merupakan bentuk jamak dari datum, berasal dari bahasa Latin yang berarti "sesuatu yang diberikan". Dalam penggunaan sehari-hari data berarti suatu

pernyataan yang diterima secara apa adanya. Pernyataan ini adalah hasil pengukuran atau pengamatan suatu variabel yang bentuknya dapat berupa

angka, kata-kata, atau citra.

Dalam keilmuan (ilmiah), fakta dikumpulkan untuk menjadi data. Data kemudian diolah sehingga dapat diutarakan secara jelas dan tepat sehingga dapat

dimengerti oleh orang lain yang tidak langsung mengalaminya sendiri, hal ini dinamakan deskripsi. Pemilahan banyak data sesuai dengan persamaan atau

perbedaan yang dikandungnya dinamakan klasifikasi.

102

NOMINAL • Komponen Nama (Nomos)

ORDINAL• Komponen Nama• Komponen Peringkat (Order)

RATIO• Komponen Nama• Komponen Peringkat (Order)• Komponen Jarak (Interval)• Komponen Ratio• Nilai Nol Mutlak

INTERVAL• Komponen Nama• Komponen Peringkat (Order)• Komponen Jarak (Interval)• Nilai Nol tidak Mutlak

JENIS DATA

103

REFERENSI

Russell L. Ackoff (1999) Ackoff's Best: His Classic Writings on Management. (Wiley) ISBN 0-471-31634-2 Russell L. Ackoff (2010) Systems Thinking for Curious Managers. (Triarchy Press). ISBN 978-0-9562631-5-5 Béla H. Bánáthy (1996) Designing Social Systems in a Changing World (Contemporary Systems Thinking). (Springer)

ISBN 0-306-45251-0 Béla H. Bánáthy (2000) Guided Evolution of Society: A Systems View (Contemporary Systems Thinking). (Springer)

ISBN 0-306-46382-2 Ludwig von Bertalanffy (1976 - revised) General System theory: Foundations, Development, Applications. (George Braziller)

ISBN 0-807-60453-4 Fritjof Capra (1997) The Web of Life (HarperCollins) ISBN 0-00-654751-6 Peter Checkland (1981) Systems Thinking, Systems Practice. (Wiley) ISBN 0-471-27911-0 Peter Checkland, Jim Scholes (1990) Soft Systems Methodology in Action. (Wiley) ISBN 0-471-92768-6 Peter Checkland, Jim Sue Holwell (1998) Information, Systems and Information Systems. (Wiley) ISBN 0-471-95820-4 Peter Checkland, John Poulter (2006) Learning for Action. (Wiley) ISBN 0-470-02554-9 C. West Churchman (1984 - revised) The Systems Approach. (Delacorte Press) ISBN 0-440-38407-9. John Gall (2003) The Systems Bible: The Beginner's Guide to Systems Large and Small . (General Systemantics Pr/Liberty)

ISBN 0-961-82517-0 Jamshid Gharajedaghi (2005) Systems Thinking: Managing Chaos and Complexity - A Platform for Designing Business

Architecture. (Butterworth-Heinemann) ISBN 0-750-67973-5 Charles François (ed) (1997), International Encyclopedia of Systems and Cybernetics, München: K. G. Saur. Charles L. Hutchins (1996) Systemic Thinking: Solving Complex Problems CO:PDS ISBN 1-888017-51-1 Bradford Keeney (2002 - revised) Aesthetics of Change. (Guilford Press) ISBN 1-572-30830-3 Donella Meadows (2008) Thinking in Systems - A primer (Earthscan) ISBN 978-1-84407-726-7 John Seddon (2008) Systems Thinking in the Public Sector. (Triarchy Press). ISBN 978-0-9550081-8-4 Peter M. Senge (1990) The Fifth Discipline - The Art & Practice of The Learning Organization. (Currency Doubleday)

ISBN 0-385-26095-4 Lars Skyttner (2006) General Systems Theory: Problems, Perspective, Practice (World Scientific Publishing Company)

ISBN 9-812-56467-5 Frederic Vester (2007) The Art of interconnected Thinking. Ideas and Tools for tackling with Complexity (MCB)

ISBN 3-939-31405-6 Gerald M. Weinberg (2001 - revised) An Introduction to General Systems Thinking. (Dorset House) ISBN 0-932-63349-8 Brian Wilson (1990) Systems: Concepts, Methodologies and Applications, 2nd ed. (Wiley) ISBN 0-471-92716-3 Brian Wilson (2001) Soft Systems Methodology: Conceptual Model Building and its Contribution. (Wiley) ISBN 0-471-89489-3

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