diabstraksikan oleh: smno.psl.ppsub.sept2012

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1 diabstraksikan oleh: smno.psl.ppsub.sept2012
PEMODELAN SISTEM Dalam KAJIAN LINGKUNGAN diabstraksikan oleh: smno.psl.ppsub.sept2012

2 MAKNA SUMBERDAYA ALAM “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 merata 2. Pemanfaatannya tgt teknologi 3. Kalau diolah menghasilkan produk dan limbah

3 The Comprehensive Model
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 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. The Comprehensive Model

4 FIVE GEOMETRIES in Resources use system
Natural resources geometry Human demand geometry NATURAL RESOURCES USE GEOMETRY Resources Degradation Geometry Natural Resources Geometry

5 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.

6 FILOSOFI “Sistem”: Gugusan elemen-elemen yg saling berinteraksi dan terorganisir peri-lakunya ke arah tujuan tertentu 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. “Tiga prasyarat aplikasinya”: 1. Tujuan dirumuskan dengan jelas 2. Proses pengambilan keputusan sentralisasi logis 3. Sekala waktu jangka panjang

7 PROSEDUR “Tahapan Pokok”: 1. Analisis Kelayakan 2. Pemodelan Abstrak
3. Disain Sistem 4. Implementasi Sistem 5. Operasi Sistem 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". Need Assesment Tahapan Pokok: - Evaluasi Outcomes

8 ALAT -BANTU “Model Abstrak”:
Perilaku esensialnya sama dengan dunia nyata “digunakan dalam”: 1. Perancangan / Disain Sistem 2. Menganalisis SISTEM ……………strukturnya INPUT …...…….. beragam STRUKTUR …….. fixed OUTPUT ……….. Diamati perilakunya 3. Simulasi SISTEM untuk sistem yang kompleks

9 A model is a simplified abstract view of the complex reality.
SIMULASI SISTEM: OPERASINYA “Penggunaan Komputer ”: Simulasi Komputer: Disain Sistem Strategi Pengelolaan Sistem 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. MODEL SISTEM programming PROGRAM KOMPUTER

10 “Model dasar”: Model Matematik
SIMULASI SISTEM: METODOLOGI “Model dasar”: Model Matematik Model lain diformulasikan menjadi model matematik “tahapan”: 1. Identifikasi subsistem / komponen sistem 2. Peubah input ( U(t) ) ……….. Stimulus 3. 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 eksogen 7. Interaksi antar komponen ………… DIAGRAM LINGKAR 8. Verifikasi model …….. Uji ……. Revisi 9. 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

11 MODEL KONSEP MATEMATIKA
“Pemodelan”: Serangkaian kegiatan pembuatan model MODEL: abstraksi dari suatu obyek atau situasi aktual PEMODELAN SISTEM: RUANG LINGKUP MODEL KONSEP 1. Hubungan Langsung 2. Hubungan tidak langsung 3. Keterkaitan Timbal-balik / Sebab-akibat / Fungsional 4. Peubah - peubah 5. Parameter MATEMATIKA Operasi Matematik: Formula, Tanda, Aksioma

12 JENIS-JENIS MODEL “MODEL IKONIK” : “MODEL ANALOG” : Model Fisik
“MODEL SIMBOLIK” : Simbol-simbol Matematik Angka Simbol “Persamaan” Rumus Ketidak-samaan Fungsi JENIS-JENIS MODEL “MODEL IKONIK” : Model Fisik 1. 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.

13 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

14 FUNGSI MODEL MODEL DESKRIPTIF
Deskripsi matematik dari kondisi dunia nyata 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 “MODEL ALOKATIF” : Komparasi alternatif untuk mendapatkan “optimal solution”

15 TAHAPAN PEMODELAN 1. Seleksi Konsep 2. Konstruksi Model: a. Black Box b. Structural Approach 3. Implementasi Komputer 4. Validasi (keabsahan representasi) 5. Sensitivitas 6. Stabilitas 7. Aplikasi Model 1. Asumsi Model 2. Konsistensi Internal 3. Data Input hitung parameter 4. Hubungan fungsional antar peubah-peubah 5. 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

16 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

17 Mengapa kita gunakan Analisis Sistem?
1. Kompleksitas obyek / fenomena /substansi penelitian Multi-atribute Multi fungsional Multi dimensional Multi-variabel 2. Interaksi rumit yg melibatkan banyak hal Korelasional Pathways Regresional Struktural 3. Interaksi dinamik: Time-dependent , and Constantly changing 4. Feed-back loops Negative effects vs. Positive effects Proses Abstraksi & Simplifikasi

18 Alternatives: Separate - Combination
PROSES PEMODELAN INTRODUCTION SISTEM - MODEL - PROSES Bounding - Word Model Alternatives: Separate - Combination DEFINITION Relevansi : Indikator - variabel - subsistem Proses : Linkages - Impacts Hubungan : Linear - Non-linear - interaksi Decision table: HYPOTHESES MODELLING Data : Plotting - outliers Analisis : Test - Estimation Choice : VALIDATION Verifikasi: Subyektif - reasonable Uji Kritis: Eksperiment - Analisis/Simulasi Sensitivity: Uncertainty - Resources - - Interaksi INTEGRATION Communication Conclusions

19 Proses Pemodelan SISTEM: Approach Simulasi Sistem Analisis Sistem
Model vs. Pemodelan Mathematical models: An exact science, Its Practical Application: 1. A high degree of intuition 2. Practical experiences 3. Imagination 4. “Flair” 5. Problem define & bounding Modelling 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

20 DEFINITION & BOUNDING The whole systems vs. sets of sub-systems
IDENTIFIKASI dan PEMBATASAN Masalah penelitian 1. Alokasi sumberdaya penelitian 2. Aktivitas penelitian yang relevan 3. Kelancaran pencapaian tujuan Proses pembatasan masalah: 1. Bersifat iteratif, tidak mungkin “sekali jadi” 2. Make a start in the right direction 3. Sustain initiative and momentum System bounding: SPACE - TIME - SUB-SYSTEMS Sample vs. Population The whole systems vs. sets of sub-systems

21 Proses Pengujian Model Hipotetik
COMPLEXITY AND MODELS The real system sangat kompleks The hypotheses to be tested MODEL Sub-systems Trade-off: complexity vs. simplicity Proses Pengujian Model Hipotetik The process of evaluating a model A 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

22 Simbolisasi kata-kata atau istilah Pengembangan Model simbolik
WORD MODEL Masalah penelitian dideskripsikan secara verbal, dengan meng-gunakan kata (istilah) yang relevan dan simple Simbolisasi kata-kata atau istilah Setiap 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). Pengembangan Model simbolik Hubungan-hubungan verbal dipresentasikan dengan simbol-simbol yang relevan

23 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).

24 HYPOTHESES Penjelasan / justifikasi Hipotesis
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. 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. Penjelasan / justifikasi Hipotesis Justifikasi secara teoritis Justifikasi berdasarkan hasil-hasil penelitian yang telah ada

25 MODEL CONSTRUCTION Konstruksi Model
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. Proses seleksi / uji alternatif yang ada

26 VERIFICATION & VALIDATION
VERIFIKASI MODEL 1. 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 sistem 3. Verifikasi: subjective assessment of the success of the modelling 4. Inkonsistensi antara perilaku model dengan real-system harus dapat diberikan penjelasannya VALIDASI MODEL 1. Sampai seberapa jauh output dari model sesuai dengan perilaku sistem yang sesungguhnya 2. Uji prosedur pemodelan 3. Uji statistik untuk mengetahui “adequacy of the model” 4. Proses Pemodelan

27 Validasi MODEL SENSITIVITY ANALYSIS
Perubahan input variabel dan perubahan parameter menghasilkan variasi kinerja model (diukur dari solusi model) ……… analisis sensitivitas 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 Validasi MODEL 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).

28 PLANNING & INTEGRATION
Integrasi 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 development 2. Antara simulasi model dengan implementasi model 3. Antara hasil prediksi model dengan implementasi model 4. Antara management practices dengan pengembangan hipotesis yang baru 5. Implementasi hasil uji coba dengan hipotesis yg baru DEVELOPMENT of MODEL 1. Kualitas data dan pemahaman terhadap fenomena sebab- akibat (proses yang di model) umumnya POOR 2. Analisis sistem dan pengumpulan data harus dilengkapi dengan mekanisme umpan-balik 3. Pelatihan dalam analisis sistem sangat diperlukan 4. Model sistem hanya dapat diperbaiki dengan jalan mengatasi kelemahannya 5. Tim analisis sistem seyogyanya interdisiplin

29 PEMODELAN KUANTITATIF : MATEMATIKA DAN STATISTIKA
MODEL STATISTIKA: FENOMENA STOKASTIK MODEL MATEMATIKA: FENOMENA DETERMINISTIK

30 Deterministic Model Example
. 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. Diunduh dari: ……………

31 Conceptual modelling framework
Diunduh dari: ……………

32 WHAT IS SYSTEM MODELLING ? Sensitivity & Assumptions
Worthwhile Recognition Problems Amenable Compromise Complexity Definitions Bounding Simplification Objectives Hierarchy Identification Priorities Goals Generality Solution Family Generation Selection Modelling Inter-relationship Feed-back Stopping rules Evaluation Sensitivity & Assumptions Implementation

33 PHASES OF SYSTEM MODELLING
Recognition Definition and bounding of the problems Identification of goals and objectives Generation of solution MODELLING Evaluation of potential courses of action Implementation of results Model evaluation A 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.

34 Fit to empirical data Usually 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.

35 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.

36 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.

37 MODEL & MATEMATIK: Term Modelling and Simulation
Tipe Konstante Variabel Parameter Likelihood Dependent Populasi Probability Analitik Independent Maximum Sampel Simulasi Regressor 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.

38 JENIS VARIABEL Intervening (Mediating) Moderator Control Concomitant
Independent Dependent INTRANEOUS EXTRANEOUS Confounding Control Concomitant

39 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

40 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.

41 MODEL & MATEMATIK: Definition
Preliminary Goodall Mathematical Mapping Rules Formal Expression Representational Maynard-Smith Predicted values Words Homomorph Model Comparison Physical Symbolic Mathematical Simulation Data values Simplified 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.

42 MODEL & MATEMATIK: Relatives
Advantages Disadvantages Distortion Precise Opaqueness Abstract Complexity Transfer Replacement Communication 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

43 A mathematical model uses mathematical language to describe a system.
MODEL & MATEMATIK: Families Types Basis Choices 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). Dynamics Compartment Stochastic Multivariate Network

44 PARAMETER: Nilai-nilai karakteristik dari populasi
BEBERAPA PENGERTIAN MODEL 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 PARAMETER: Nilai-nilai karakteristik dari populasi KONSTANTE, KOEFISIEAN: nilai-nilai karakteristik yang dihitung dari SAMPEL 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.

45 BEBERAPA PENGERTIAN MODEL 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 MULTIVARIATE EXPERIMENTAL DESIGN STANDARD DISTRIBUTION, etc SIMULATION MODEL: Model yang formula-formulanya diturunkan dengan serangkaian operasi arithmatik, misal: Solusi persamaan diferensial Aplikasi matrix Penggunaan 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.

46 DYNAMIC MODEL MODELLING Dynamics SIMULATION Equations Computer FORMAL
Language ANALYSIS Special General DYNAMO CSMP CSSL BASIC

47 DYNAMIC MODEL SYMBOLS DIAGRAMS RELATIONAL AUXILIARY VARIABLES LEVELS
MATERIAL FLOW RATE EQUATIONS PARAMETER INFORMATION FLOW SINK 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 Discriminant Function
DYNAMIC MODEL: ORIGINS Abstraction Computers Equations Steps Hypothesis Discriminant Function Simulation Undestanding Other functions Exponentials Logistic

49 MATRIX MODEL MATHEMATICS Operations Matrices Eigen value Elements
Dominant Additions Substraction Multiplication Inversion Types Eigen vector Square Rectangular Diagonal Identity Vectors Scalars Row Column

50 MATRIX MODEL DEVELOPMENT Interactions Groups Stochastic
Materials cycles Size Markov Models Development stages 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 Other Models
Statistical method Dynamics Stability 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 Pisson Poisson
Negative Binomial Binomial Negative Binomial Others 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 Error Estimates
Analysis Parameter Orthogonal Variance Effects Block Experimental Significance Treatments

54 Linear/ Non-linear functions
STOCHASTIC MODEL REGRESSION Model Example Decomposition Equation Error Linear/ Non-linear functions Theoritical base Oxygen uptake Reactions Experimental Empirical base Assumptions 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 Transition probabilities
STOCHASTIC MODEL MARKOV Analysis Example Assumptions Advantages Analysis Disadvantage Transition probabilities Raised mire 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 Principal Component Analysis Discriminant Analysis
MULTIVARIATE MODELS METHODS VARIATE Variable Classification Dependent Descriptive Predictive Principal Component Analysis Discriminant Analysis Independent Cluster Analysis Reciprocal averaging Canonical Analysis

59 PRINCIPLE COMPONENT ANALYSIS
MULTIVARIATE MODEL PRINCIPLE COMPONENT ANALYSIS Requirement Example Correlation Objectives Environment Eigenvalues Eigenvectors Organism Regions 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 Multivariate space
CLUSTER ANALYSIS Example Spanning tree Multivariate space Demography Rainfall regimes Minimum Similarity Single linkage Distance Settlement patern 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 CANONICAL CORRELATION
MULTIVARIATE MODEL Example Correlation Partitioned Watershed Urban area Eigenvalues Eigenvectors Irrigation regions 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 Discriminant Function
MULTIVARIATE MODEL Discriminant Function Example Discriminant Calculation Villages Vehicles 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.

63 OPTIMIZATION MODEL OPTIMIZATION Dynamic Meanings Indirect Non-Linear
Simulation Objective function Minimization Constraints Experimentation Solution Examples Maximization Optimum Transportation Routes Optimum irrigation scheme Optimum Regional Spacing

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

65 Ten Keys to Success in Optimization Modeling
Richard E. Rosenthal Operations Research Department Naval Postgraduate School INFORMS Atlanta, October 2003

66 Key #1: Communicate Early and Often
Mathematical formulation – kept up to date Verbal description of formulation Executive summary – in the right language

67 Mathematical Formulation
Index use Given data (and units) in lower case Decision Variables (and units) in UPPER CASE Objectives and constraints

68 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.

69 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?

70 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.

71 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) of unbounded models.

72 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 infeasible Discovering what can be done changes your concept of what should be done Contrary to impression of textbooks, alternate optima are the rule, not the exception.

73 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?

74 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%.

75 Key #5: Bound the Dual Variables
Elastic 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”

76 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 year to ask for the money to get ready.

77 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!

78 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 leg Aircraft type a can carry some cargo type that customer i demands Time t is not before i ’s available-to-load time Time t is not after i ’s required delivery date + maxlate – travel time

79 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.

80 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.

81 Incremental Implementation
Eliminate variables corresponding to airlifters switching from long-haul to shuttle status, if there are no foreseeable shuttle opportunities. Euro US SWA FOB Feature tested with small example: removing the option to make a seemingly foolish decision actually caused degradation of objective function. What happened?

82 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

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

84 Illustration of Persistence
Just 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.

85 Illustration of Persistence

86 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.

87 Illustration of Persistence

88 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.

89 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

90 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

91 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

92 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

93 MODELLING PROCESS Definition Modelling Validation Hypotheses Data
System analysis Introduction Processes Model Space Time Niche Elements Bounding Systems Definition Word Models Impacts Factorial Confounding Alternatives Separate Combinations Hypotheses Data Plotting Outliers Modelling Analysis Test Choices Estimates Validation Conclusion Integration Communication

94 MODELLING PROCESSES HYPOTHESES Decision Table Relevance Processes
Relationships Variable Linkages Linear Species Non-Linear Impacts Sub-systems Interactive 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.

95 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)

96 Hypotheses of relationships
Determinants of the sophistication of SFA. In terms of specific hypotheses: Hypothesis 1: There is a positive relationship between perceived strategic importance of sales decisions and level of information orientation. Hypothesis 2: There is a positive relationship between organizational slack and level of information orientation. Hypothesis 3: There is a negative relationship between organizational control and level of information orientation. Hypothesis 4: There is a positive relationship between integration of IT and sales and level of information orientation. Hypothesis 5: There is a positive relationship between perceived strategic importance of sales decisions and integration of IT and sales. Hypothesis 6: There is a positive relationship between organizational slack and integration of IT and sales. Hypothesis 7: There is a negative relationship between organizational control and integration of IT and sales. 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: ……………

97 Hypotheses of relationships
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 Diunduh dari: ……………

98 MODELLING PROCESSES VALIDATION Verification Critical Test
Sensitivity Analysis Subjectives Uncertainty Analysis Resources Objectivities Reason-ableness Experiments Interactions Model verification and validation (V&V) are essential parts of the model development process if models to be accepted and used to support 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 Algoritms Data Program
Roles Speed Data Algoritm Introduction Reasons Manual Calculator Computer Comparison Speed Techniques Errors Plotting Implication Repetition Checking Waste 9/10 Modelling Data FORTRAN BASIC ALGOL Program High level Algoritms Language Machine code Special DYNAMO. Etc. Information Development Conclusions Programming

100 ROLE OF THE COMPUTER DATA Machine readable Cautions Availability
Format Sampling Punched card Exchange Paper tape Format Reanalysis Magnetic Tape Data banks Disc

101 D A T A Data adalah catatan atas kumpulan fakta.
Data 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 JENIS DATA INTERVAL Komponen Nama Komponen Peringkat (Order)
Komponen Jarak (Interval) Nilai Nol tidak Mutlak NOMINAL Komponen Nama (Nomos) ORDINAL Komponen Nama Komponen Peringkat (Order) RATIO Komponen Nama Komponen Peringkat (Order) Komponen Jarak (Interval) Komponen Ratio Nilai Nol Mutlak

103 REFERENSI Russell L. Ackoff (1999) Ackoff's Best: His Classic Writings on Management. (Wiley) ISBN Russell L. Ackoff (2010) Systems Thinking for Curious Managers. (Triarchy Press). ISBN Béla H. Bánáthy (1996) Designing Social Systems in a Changing World (Contemporary Systems Thinking). (Springer) ISBN Béla H. Bánáthy (2000) Guided Evolution of Society: A Systems View (Contemporary Systems Thinking). (Springer) ISBN Ludwig von Bertalanffy ( revised) General System theory: Foundations, Development, Applications. (George Braziller) ISBN Fritjof Capra (1997) The Web of Life (HarperCollins) ISBN Peter Checkland (1981) Systems Thinking, Systems Practice. (Wiley) ISBN Peter Checkland, Jim Scholes (1990) Soft Systems Methodology in Action. (Wiley) ISBN Peter Checkland, Jim Sue Holwell (1998) Information, Systems and Information Systems. (Wiley) ISBN Peter Checkland, John Poulter (2006) Learning for Action. (Wiley) ISBN C. West Churchman ( revised) The Systems Approach. (Delacorte Press) ISBN John Gall (2003) The Systems Bible: The Beginner's Guide to Systems Large and Small. (General Systemantics Pr/Liberty) ISBN Jamshid Gharajedaghi (2005) Systems Thinking: Managing Chaos and Complexity - A Platform for Designing Business Architecture. (Butterworth-Heinemann) ISBN 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 Bradford Keeney ( revised) Aesthetics of Change. (Guilford Press) ISBN Donella Meadows (2008) Thinking in Systems - A primer (Earthscan) ISBN John Seddon (2008) Systems Thinking in the Public Sector. (Triarchy Press). ISBN Peter M. Senge (1990) The Fifth Discipline - The Art & Practice of The Learning Organization. (Currency Doubleday) ISBN Lars Skyttner (2006) General Systems Theory: Problems, Perspective, Practice (World Scientific Publishing Company) ISBN Frederic Vester (2007) The Art of interconnected Thinking. Ideas and Tools for tackling with Complexity (MCB) ISBN Gerald M. Weinberg ( revised) An Introduction to General Systems Thinking. (Dorset House) ISBN Brian Wilson (1990) Systems: Concepts, Methodologies and Applications, 2nd ed. (Wiley) ISBN Brian Wilson (2001) Soft Systems Methodology: Conceptual Model Building and its Contribution. (Wiley) ISBN

104 PEMODELAN SISTEM DALAM KAJIAN LINGKUNGAN
FOTO: smno.kampus.ub.juli2012