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METODE SIMULASIMETODE SIMULASIDALAM KAJIAN DALAM KAJIAN LINGKUNGANLINGKUNGAN

Pmpslp ppsub 2011

soemarno

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SIMULASI

A simulation is an 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.

Historically, the word had negative connotations:…for Distinction Sake, a Deceiving by Words, is commonly called a Lye, and

a Deceiving by Actions, Gestures, or Behavior, is called Simulation… Robert South (1643–1716)

However, the connection between simulation and dissembling later faded out and is now only of linguistic interest.

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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.

Key issues in simulation include acquisition of valid source information about the referent, selection of key characteristics and behaviours, the

use of simplifying approximations and assumptions within the simulation, and fidelity and validity of the simulation outcomes.

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KLASIFIKASI & TERMINOLOGI

Historically, simulations used in different fields developed largely independently, but 20th century studies of Systems theory and Cybernetics combined with spreading use of computers across all those fields have led

to some unification and a more systematic view of the concept.

SIMULASI FISIK & SIMULASI INTERAKTIF

Physical simulation refers to simulation in which physical objects are substituted for the real thing. These physical objects are often chosen because they are smaller or cheaper than the actual object or system.

Interactive simulation is a special kind of physical simulation, often referred to as a human in the loop simulation, in which physical

simulations include human operators, such as in a flight simulator or a driving simulator.

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SIMULASI KOMPUTER

A computer simulation is an attempt to model a real-life or hypothetical situation on a computer so that it can be studied to

see how the system works. By changing variables, predictions may be made about the

behaviour of the system.

An interesting application of computer simulation is to simulate computers using computers.

The related software is called computer architecture simulators, which can be further divided into instruction set

simulators or full system simulators.

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Computer simulation has become a useful part of modeling many natural systems in physics, chemistry and biology, and

human systems in economics and social science (the computational sociology) as well as in engineering to gain

insight into the operation of those systems.

A good example of the usefulness of using computers to simulate can be found in the field of network traffic simulation.

In such simulations the model behaviour will change each simulation according to the set of initial parameters assumed

for the environment. Computer simulations are often considered to be human out of

the loop simulations.

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Traditionally, the formal modeling of systems has been via a

mathematical model, which attempts to find analytical solutions enabling

the prediction of the behaviour of the system from a set of parameters and

initial conditions.

Computer simulation is often used as an adjunct to, or substitution for,

modeling systems for which simple closed form analytic solutions are not

possible.

There are many different types of computer simulation, the common feature they all share is the attempt

to generate a sample of representative scenarios for a model in which a complete enumeration of

all possible states would be prohibitive or impossible.

serc.carleton.edu/.../Analytical.html

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Various industries use discrete event simulation to model

systems of interest in commerce, health, defence,

manufacturing, logistics etc., for example the value-adding

business processes.

Imagine a business, where each person could do 30 tasks, where

thousands of products or services involved dozens of tasks in a sequence, where customer demand varied

seasonally and forecasting was inaccurate — this is the domain

where such simulation helps with business decisions across

all functions.

www.rar.duhs.duke.edu/wiki/index.php/Discrete...

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Related topics include Theory of Constraints, bottlenecks, and management consulting.

Several software packages exist for running computer-based simulation modeling (e.g. Monte Carlo simulation and

stochastic modeling) that makes the modeling almost effortless.

It is increasingly common to hear simulations of many kinds referred to as "synthetic environments".

This label has been adopted to broaden the definition of "simulation" to encompass virtually any computer-based

representation.

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SIMULASI DALAM ILMU KOMPUTER

In computer science, simulation has an even more specialized meaning: Alan Turing uses the term "simulation" to refer to what happens when a digital computer runs a state transition table (runs a program) that describes the state transitions, inputs

and outputs of a subject discrete-state machine. The computer simulates the subject machine.

In computer architecture, a simulator is often used to execute a program that has to run on some inconvenient type of computer, or in a

tightly controlled testing environment (see Computer architecture simulator). For example, simulators are usually used to debug a microprogram or sometimes commercial application programs.

Since the operation of the computer is simulated, all of the information about the computer's operation is directly available to the programmer, and the speed and

execution of the simulation can be varied at will.

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Simulators may also be used to interpret fault trees, or test VLSI logic designs before they are constructed.

Symbolic simulation that uses variables to stand for unknown values.

In theoretical computer science the term simulation represents a relation between state transition systems.

This is useful in the study of operational semantics.

In the field of optimization, simulations of physical processes are often used in conjunction with evolutionary computation to

optimize control strategies.

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SIMULASI DALAM TRAINING

Simulation is often used in the training of civilian and military personnel.

This usually occurs when it is prohibitively expensive or simply too dangerous to allow trainees to use the real equipment in the real world. In such situations they will spend time learning valuable

lessons in a "safe" virtual environment.

Often the convenience is to permit mistakes during training for a safety-critical system.

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Model SIMULASI unit Pengolahan Air minum

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Training simulations typically come in one of three categories:

"live" simulation (where real people use simulated (or "dummy") equipment in the real world);

"virtual" simulation (where real people use simulated equipment in a simulated world (or "virtual environment")), or

"constructive" simulation (where simulated people use simulated equipment in a simulated environment).

Constructive simulation is often referred to as "wargaming" since it bears some resemblance to table-top war games in which players command armies of soldiers and equipment that move

around a board.

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CONTOH-CONTOH

Truck Simulator

A truck simulator provides an opportunity to reproduce the characteristics of real vehicles in a virtual environment. It replicates the external factors and conditions with which a

vehicle interacts enabling a driver to feel as if they are sitting in the cab of their own vehicle.

Scenarios and events are replicated with sufficient reality to ensure that drivers become fully immersed in the experience rather than simply viewing it as an educational programme.

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Closed-Loop Transportation Simulation in Multi-Robot System

http://www.deyangzhao.com/closed-loop-transportation-simulation-in-multi-robot-system.html

the state flow that describes the robot's behavior.

The robot is located at the middle of the lane before started, the present value

from the three light sensors are stored as the set values. Then during the robot is

moving, the NXT Brick reads values from the light sensors continually, as actual

values. The controller attempts to minimize the error by adjusting the

process control inputs, here which means the output of the controller is added to the inputs to the motors, converting to PWM signal finally. The left motor and the right motor are given different inputs therefore they generate torques to drive the robot, adjusting the direction. As a result, the actual values from the sensors change

and form a close-loop control with feedback.

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Healthcare (Clinical) Simulators

Medical simulators are increasingly being developed and deployed to teach therapeutic and diagnostic procedures as well as medical concepts

and decision making to personnel in the health professions.

Simulators have been developed for training procedures ranging from the basics such as blood draw, to laparoscopic surgery and trauma care.

They are also important to help on prototyping new devices for biomedical engineering problems.

Currently, simulators are applied to research and development of tools for new therapies, treatments and early diagnosis in medicine.

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Many medical simulators involve a computer connected to a plastic

simulation of the relevant anatomy.

Sophisticated simulators of this type employ a life size mannequin

that responds to injected drugs and can be programmed to create

simulations of life-threatening emergencies.

In others simulations, visual components of the procedure are reproduced by computer graphics techniques, while touch-based

components are reproduced by haptic feedback devices combined with physical simulation routines

computed in response to the user's actions.

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Medical simulations of this sort will often use 3D CT or MRI scans of patient data to enhance realism.

Some medical simulations are developed to be widely distributed

(such as web-enabled simulations that can be viewed via standard web

browsers) and can be interacted with using standard computer interfaces,

such as the keyboard and mouse.

Another important medical application of a simulator — although, perhaps, denoting a slightly different meaning of

simulator — is the use of a placebo drug, a formulation that simulates

the active drug in trials of drug efficacy.

pharmrev.aspetjournals.org/.../503/F3.expansion

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History of Simulation in Healthcare

The first medical simulators were simple models of human patients.

Since antiquity, these representations in clay and stone were used to demonstrate clinical features of disease states and their

effects on humans.

Models have been found from many cultures and continents. These models have been used in some cultures (e.g., Chinese

culture) as a "diagnostic" instrument, allowing women to consult male physicians while maintaining social laws of

modesty. Models are used today to help students learn the anatomy of the

musculoskeletal system and organ systems.

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MODEL-MODEL AKTIF

Active models that attempt to reproduce living anatomy or physiology are recent developments.

The famous “Harvey” mannikin was developed at the University of Miami and is able to recreate many of the physical findings of the cardiology examination, including palpation, auscultation, and electrocardiography.

MODEL INTERAKTIF

More recently, interactive models have been developed that respond to actions taken by a student or physician. Until recently, these simulations

were two dimensional computer programs that acted more like a textbook than a patient. Computer simulations have the advantage of allowing a student to make judgements, and also to make errors. The process of

iterative learning through assessment, evaluation, decision making, and error correction creates a much stronger learning environment than

passive instruction.

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SIMULATOR-KOMPUTER

Simulators have been proposed as an ideal tool for assessment of students for clinical skills.

Programmed patients and simulated clinical situations, including mock disaster drills, have been used extensively for education and evaluation.

These “lifelike” simulations are expensive, and lack reproducibility.

A fully functional "3Pi" simulator would be the most specific tool available for teaching and measurement of clinical skills.

Such a simulator meets the goals of an objective and standardized examination for clinical competence.

This system is superior to examinations that use "standard patients" because it permits the quantitative measurement of competence, as well as

reproducing the same objective findings.

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The "classroom of the future"

The "classroom of the future" will probably contain several kinds of simulators, in addition to textual and visual learning tools. This will allow students to enter the

clinical years better prepared, and with a higher skill level. The advanced student or postgraduate will have a more concise and comprehensive method of retraining — or of incorporating new clinical procedures into their skill set — and regulatory

bodies and medical institutions will find it easier to assess the proficiency and competency of individuals.

The classroom of the future will also form the basis of a clinical skills unit for continuing education of medical personnel; and in the same way that the use of

periodic flight training assists airline pilots, this technology will assist practitioners throughout their career.

The simulator will be more than a "living" textbook, it will become an integral a part of the practice of medicine. The simulator environment will also provide a

standard platform for curriculum development in institutions of medical education.

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FinanceIn finance, computer simulations are often used for scenario

planning. Risk-adjusted net present value, for example, is computed from well-defined but not always known (or fixed) inputs. By

imitating the performance of the project under evaluation, simulation can provide a distribution of NPV over a range of

discount rates and other inputs.

http://www.12manage.com/methods_npv.htmlThe Net Present Value (NPV) of an investment (project) is the difference between the sum of the discounted cash flows which are expected from

the investment, and the amount which is initially invested. It is a

traditional valuation method (often for a project) used in the

Discounted Cash Flow measurement methodology

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Sophisticated Irrigation Technology And Biotechnology Adoption: Impacts On Ground Water Conservation

Talah S. Arabiyat, Eduardo Segarra, and David B. WillisTexas Tech University

Net present value of returns and ground water use levels associated with the BASELINE simulation and

scenarios A to D.

The optimal levels of NPVR and ground water use for scenarios A, B,

and C are as follows. Scenario A achieves a NPVR $2,891.50 per acre

and water use of 26.04 feet/acre; scenario B achieves a NPVR

$2,953.35 per acre and water use of 17.87 feet/per acre; and scenario C

achieves a NPVR $3,624.46 per acre and water use of 17.87 feet/acre.

http://www.agbioforum.org/v2n2/v2n2a11-segarra.htm

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Home-built Flight Simulators

Some people who use simulator software, especially flight simulator software, build their own simulator at home.

Some people in order to further the realism of their homemade simulator, buy used cards and racks that still run the exact same

software they did before they were disassembled from the actual machine itself.

Though this brings along the problem of matching hardware and software, and the fact that hundreds of cards plug into many different

racks, still, many find that is it well worth it.

Some are very serious in building their simulator by buying real aircraft parts like complete nose sectionals of written off aircraft at aircraft

boneyards. This permits people who are unable to perform their hobby in real life to simulate it.

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Engineering (Technology) simulation or Process simulation

Simulation is an important feature in engineering systems or any system that involves many processes.

For example in electrical engineering, delay lines may be used to simulate propagation delay and phase shift caused by an

actual transmission line.

Similarly, dummy loads may be used to simulate impedance without simulating propagation, and is used in situations

where propagation is unwanted.

A simulator may imitate only a few of the operations and functions of the unit it simulates.

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Most engineering simulations entail mathematical modeling and computer assisted investigation.

There are many cases, however, where mathematical modeling is not reliable.

Simulation of fluid dynamics problems often require both mathematical and physical simulations.

In these cases the physical models require dynamic similitude.

Physical and chemical simulations have also direct realistic uses, rather than research uses;

in chemical engineering, for example, process simulations are used to give the process parameters immediately used for

operating chemical plants, such as oil refineries.

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Model Sistem Pengelolaan Air Minum

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Simulation and games

Strategy games — both traditional and modern — may be viewed as simulations of abstracted decision-making for the purpose of training

military and political leaders.

In a narrower sense, many video games are also simulators, implemented inexpensively.

These are sometimes called "sim games". Such games can simulate various aspects of reality, from economics to piloting vehicles, such as

flight simulators (described above).

Another type of simulation is a government simulation, which can be used to help the player understand certain aspects of political science —

specifically cause and effect.

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Model Simulasi Sistem Pengelolaan Sumberdaya Air

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Simulation in education

Simulations in education are somewhat like training simulations. They focus on specific tasks. In the past, video has been used for

teachers and education students to observe, problem solve and role play; however, a more recent use of simulations in education include

animated narrative vignettes (ANV).

ANVs are cartoon-like video narratives of hypothetical and reality-based stories involving classroom teaching and learning.

ANVs have been used to assess knowledge, problem solving skills and dispositions of children, and pre-service and in-service teachers.

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MODEL SISTEM DINAMIKHere is a simplified systems dynamic model of what I think is going on in the world. The circles

are, roughly speaking, processes identified by their predominant feature(s).

The arrows show the flow of cause or influence. The 'plus' signs indicate positive influence or pressure to increase the effects. The 'minus'

signs show a pressure to diminish - negative feedback. So, for example,

the positive arrow from human nature to population, labeled 'br', causes an increase in population (sub-served

by the supply of energy and technology). Eventually, however, at large enough population sizes and densities the effects of toxins and

resource depletion feedback negatively reducing the population through disease, starvation, etc.

http://questioneverything.typepad.com/question_everything/2008/04/a-model-of-busi.html

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Sustainability and resilience: toward a systems approach

http://sspp.proquest.com/archives/vol2iss2/0608-028.fiksel.html

Structure and feedback loops in Threshold 21 system dynamics

model.

The Millennium Institute has applied system dynamics to develop the Threshold 21 (T21) model, which

combines proven economic-sector models into an integrated framework (Sterman, 2000). The approach uses

differential equations to represent changes in stocks and flows, and

considers nonlinearity, feedback, and delays. Customized T21 models have been created at a national

scale for the United States and Italy, for less-developed countries

(Bangladesh, Malawi), and at a regional level in Africa and

Indonesia.

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Integrated Approaches to Systems Modeling and Management

http://sspp.proquest.com/archives/vol2iss2/0608-028.fiksel.html

Modeling of coupled parameters in a lake system.

A multidisciplinary research team at The Ohio State University (OSU) is investigating the complex interactions among biological, physical, and human components of large

lake ecosystems (OSU, 2004). Figure illustrates some of these interactions.

While a large lake provides amenities, or ecological services, that support economic

growth, such growth can degrade these amenities.

This team of biologists, ecologists, physicists, economists, geographers, and

others is attempting to model the patterns of socio-economic activity, and the potential

impacts of policies to protect natural amenities, in the Lake Erie region. Beginning with simple equilibrium models, the project is

investigating increasingly sophisticated techniques, including agent-based

simulation.

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Analytic Hierarchy Process: AHP

The Analytic Hierarchy Process (AHP) is a decision making technique developed by

Thomas Saaty.

He claimed AHP allows for the rational evaluation of pros. and cons. concerning different

alternative solutions to a multi-goal problem.

AHP is based on a series pairwise comparions and then those comparisons are checked for internal

consistency.

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The Analytic Hierarchy Process (AHP) was developed by Thomas L. Saaty in the 1970s. It is basically a decision support system, derived from the decision making theory. The goal of an AHP is to find the appropriate alternative out of a range of given

alternatives in order to solve a decision problem. Furthermore, an AHP can show the importance of the defined criteria regarding their impact on the solution of the problem.

http://en.wikipedia.org/wiki/Analytic_hierarchy_process

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The process of analytic decision making

Modeling a hierarchy is the most important task when using the

decision part of questfox. There are several levels of modeling to be

considered:

1. Hierarchy itself2. Meta Hierarchy: the master plan of routing the hierarchies3. Semantics of the hierarchy: question texts4. Design issues5. Hierarchy routing6. Adaptive hierarchy design

http://questfox.com/help/questfox_manu

al.html?AnalyticHierarchyProcessAHP.html

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The procedure can be summarized as:

Decision makers are asked their preferences of attributes of

alternatives.

For example, if the alternatives are comparing potential real-estate purchases, the investors might say they prefer location

over price and price over timing.

Then they would be asked if the location of alternative "A" is

preferred to that of "B", which has the preferred timing, and so

on.

http://cfpub.epa.gov/ncer_abstracts/index.cfm/fuseaction/display.abstractDetail/abstract/5961/report/1999

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Criticisms

AHP has had many challenges to its theoretical and practical

shortcomings from those who have a more thurough grounding

in all the decision sciences.

Some have maintained that AHP assigns arbitrary or ordinal measures to the pairwise

comparisons.

Proponents maintain that while this is true of the 'verbal' mode of

AHP, it has been demonstrated that in situations where there is

adequate variety and redundancy, accurate ratio scale priorities can be derived from such judgments.

The limitation of the AHP is the simulation of market shares and pricing

questions. These are only possible in combination with other methods. questfox offers the

opportunity of the Price-Sensitivity Meter integrated for live calculations.

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RATIONAL PLANNING PROCESS

http://www.fao.org/docrep/007/y5648e/y5648e06.htm

In relation to aquaculture development, each step of the process is however

rarely encountered, as it depends largely on the advancement of the

sector in a given country. Countries wishing to develop their yet marginal

aquaculture sector may only possess a framework, whilst those at a more

advanced stage will have formulated strategies and plans to guide and

manage aquaculture development at the national level. The country documents obtained ranged from frameworks to

plans, with production targets and corresponding activities. Their close

examination however revealed a great deal of confusion over appropriate use

of planning terms and development logic.

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AHP, like many systems based on pairwise comparisons, can produce "rank reversal" outcomes.

That is a situation where the order of preference is, for example, A, B, C then D. But if C is eliminated for other reasons, the order of A and B

could be reversed so that the resulting priority is then B, A, then D.

It has been proven that any pairwise comparison system will still have rank-reversal solutions even when the pair preferences are consistent .

Proponents argue that rank reversal may still be desirable but this is also controversial.

Given the example, this would be the position that if C were elliminated, the preference of A over B should be switched.

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Another strong theoretical problem of AHP was found by Perez, et. al.

This has to do with what they identify as an "indiferent criterion"

flaw.

Indiferent criterion requires that once A, B, C and D are ranked

according to criteria, say, W, X, Y, adding another criterion for which A, B, C, and D are equal, should have no bearing on the ranks.

Yet, Perez et al prove that such an outcome is possible.

Note that this flaw, too, is a shortcoming of any pairwise

comparison process, not just AHP. But AHP's consistency-checking methods offer no guarantee such

flaws cannot occur, since there are solution sets with these flaws even when preferences are consistent.

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Many alternatives to AHP are economically viable, especially for

larger, riskier decision.

Methods from decision theory and various economic modeling methods

can be applied.

A scoring method that has a superior track record of improving decisions was developed by Egon Brunswik in

the 1950's.

Other methods such as Applied Information Economics quantify risk, cost and value in

economically meaningful terms even where AHP considers them to be

"immeasurable".

horan.asu.edu/cfedm/chapter8.php

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Comparison of racing simulators

DissimulationEmulator

Experimentation in silico Futures studies

Mathematical model Merger simulation Mining Simulation

Monte Carlo simulation Network Simulator

PlaceboPlacebo (origins of

technical term) Similitude (model) Simulated reality

Simulation language Scientific modeling

www.designnews.com/article/48957-Mechatronic_...

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Identifying improvement areas when implementing green initiatives using a multitier AHP approach

http://www.emeraldinsight.com/journals.htm?articleid=1863554&show=html

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MODEL MATEMATIK

A mathematical model is a description of a system using mathematical concepts and language. The process of

developing a mathematical model is termed mathematical modeling.

Mathematical models are used not only in the natural sciences (such as physics, biology, earth science, meteorology)

and engineering disciplines (e.g. computer science, artificial intelligence), but also in the social sciences (such as

economics, psychology, sociology and political science); physicists, engineers, statisticians, operations research analysts and economists use mathematical models most extensively.

http://en.wikipedia.org/wiki/Mathematical_model

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. MODEL MATEMATIK

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. In general,

mathematical models may include logical models, as far as logic is taken as a part of mathematics.

In many cases, the quality of a scientific field depends on how well the mathematical models developed on the

theoretical side agree with results of repeatable experiments. Lack of agreement between theoretical mathematical models

and experimental measurements often leads to important advances as better theories are developed.

http://en.wikipedia.org/wiki/Mathematical_model

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CONTOH MODEL MATEMATIK

Population Growth. A simple (though approximate) model of population growth is the Malthusian growth model. A slightly more realistic and largely used population growth model is the logistic function, and its

extensions.

Model of a particle in a potential-field. In this model we consider a particle as being a point of mass which describes a trajectory in space which is modeled by a function giving its coordinates in space as a function of

time. The potential field is given by a function V : R3 → R and the trajectory is a solution of the differential equation

Note this model assumes the particle is a point mass, which is certainly known to be false in many cases in which we use this model; for

example, as a model of planetary motion.

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A SIGMOID (S-SHAPED) POPULATION GROWTH CURVE. 

The sigmoid graph showing the population growth of a species has three phases which are; the exponential phase, the transitional phase and the plateau phase. At the start of

the sigmoid curve we can see the exponential phase. This is where there is a rapid increase in population growth as natality rate exceeds

mortality rate. The reason for this is because there are abundant resources available such as food for all members of the population and diseases as well as predators are rare. As time passes, the population reaches the transitional phase. This is where the

natality rate starts to fall and/or the mortality rate starts to rise. It is the result of a decrease in the abundance of resources, and an increase in the number of predators and diseases. However, even though population growth has decreased compared to the exponential phase, it is still increasing as natality rate still exceeds mortality rate.

Finally, the population reaches the plateau phase. Here, the population size is constant so no more growth is occurring. This is the result of natality rate being equal to mortality

rate and is caused by resources becoming scarce as well as an increase in predators, diseases and parasites. These are the limiting factors to the population growth. If

natality rate starts to drop then mortality rate will drop too as more resources become available.

As natality rate starts to increase again so does mortality rate as resources become scarce. This keeps the population number relatively stable. If a population is limited by

a shortage of resources then we say that it has reached the carrying capacity of the environment. 

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A SIGMOID (S-SHAPED) POPULATION GROWTH CURVE.

ibguides.com

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MODEL PERTUMBUHAN POPULASI

Today in Biology we looked at population growth, graphing populations of bacteria

(hypothetical), bees in a hive, deer and the human population. The rate of population

growth is dependent on four factors – births and immigration (increase) and deaths and emigration (decrease). In the hypothetical situation of bacterial growth with no limits,

we saw that the population increased exponentially. Bees showed a gradual

increase and then reached their equilibrium around the ‘carrying capacity’ of the hive. The ‘carrying capacity’ is dependent on environmental pressures such as space

and nutrient availablity. Other environmental factors that will affect population growth

include predation, disease (parasites and pathogens), catastrophic weather events (drought, flood, fire, storms) and habitat

destruction. The deer population showed a more gradual increase, a peak and then a

sharp decline..

http://vcebiology.edublogs.org/2009/09/16/population-growth/

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CONTOH MODEL MATEMATIK

Model of rational behavior for a consumer. In this model we assume a consumer faces a choice of n commodities labeled 1,2,...,n each with a market price p1, p2,..., pn.

The consumer is assumed to have a cardinal utility function U (cardinal in the sense that it assigns numerical values to utilities), depending on the amounts of

commodities x1, x2,..., xn consumed. The model further assumes that the consumer has a budget M which is used to

purchase a vector x1, x2,..., xn in such a way as to maximize U(x1, x2,..., xn).

The problem of rational behavior in this model then becomes an optimization problem, that is:

subject to:

This model has been used in general equilibrium theory, particularly to show existence and Pareto efficiency of economic equilibria. However, the fact that this

particular formulation assigns numerical values to levels of satisfaction is the source of criticism (and even ridicule). However, it is not an essential ingredient of the theory

and again this is an idealization.

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CONTOH MODEL MATEMATIK

Neighbour-sensing model explains the mushroom formation from the initially chaotic fungal network.

Computer Science: models in Computer Networks, data models, surface model,...

Mechanics: movement of rocket model,...

http://en.wikipedia.org/wiki/Mathematical_model

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SIMULASI KOMPUTER

A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system. Computer simulations have become a useful part

of mathematical modeling of many natural systems in physics (computational physics), astrophysics, chemistry and

biology, human systems in economics, psychology, social science, and engineering.

Simulations can be used to explore and gain new insights into new technology, and to estimate the performance of

systems too complex for analytical solutions.

http://en.wikipedia.org/wiki/Computer_simulation

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SIMULATION Vs. MODELING

Traditionally, building large models of systems has been via a statistical model, which attempts to find analytical solutions to

problems and thereby enable the prediction of the behavior of the system from a set of parameters and initial conditions.

The term computer simulation is broader than computer modeling; the latter implies that all aspects are being modeled in the computer

representation. However, computer simulation also includes generating inputs from simulated users in order to run actual

computer software or equipment, with only part of the system being modeled.

An example would be a flight simulator that can run machines as well as actual flight software.

Computer simulations are used in many fields, including science, technology, entertainment, health care, and business planning and

scheduling.http://en.wikipedia.org/wiki/Computer_simulation

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MODEL KONSEPTUAL

In the most general sense, a model is anything used in any way to represent anything else. Some models are physical objects, for instance, a toy model which may be assembled, and may even be made to work

like the object it represents. They are used to help us know and understand the subject matter they represent.

The term conceptual model may be used to refer to models which are represented by concepts or related concepts which are formed after a

conceptualization process in the mind. Conceptual models represent human intentions or semantics.

Conceptualization from observation of physical existence and conceptual modeling are the necessary means human employ to think and solve problems. Concepts are used to convey semantics during

various natural languages based communication. Since that a concept might map to multiple semantics by itself, an explicit formalization is usually required for identifying and locating the intended semantic

from several candidates to avoid misunderstandings and confusions in conceptual models.

http://en.wikipedia.org/wiki/Conceptual_model

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SCIENTIFIC MODELS

A scientific 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

http://en.wikipedia.org/wiki/Conceptual_model

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STATISTICAL MODELS

A statistical model is a probability distribution function proposed as generating data. In a parametric model, the probability distribution

function has variable parameters, such as the mean and variance in a normal distribution, or the coefficients for the various exponents of the

independent variable in linear regression.

A nonparametric model has a distribution function without parameters, such as in bootstrapping, and is only loosely confined by assumptions.

Model selection is a statistical method for selecting a distribution function within a class of them, e.g., in linear regression where the dependent variable is a polynomial of the independent variable with parametric

coefficients, model selection is selecting the highest exponent, and may be done with nonparametric means, such as with cross validation.

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MATHEMATICAL MODELS

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.

A more comprehensive type of mathematical model[5] uses a linguistic version of category theory to model a given situation. Akin to entity-relationship models, custom categories or sketches can be directly

translated into database schemas.

The difference is that logic is replaced by category theory, which brings powerful theorems to bear on the subject of modeling, especially useful

for translating between disparate models (as functors between categories).

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ECONOMIC MODELS

In economics, a model is a theoretical construct that represents economic processes by a set of variables and a

set of logical and/or quantitative relationships between them.

The economic model is a simplified framework designed to illustrate complex processes, often but not always using

mathematical techniques.

Frequently, economic models use structural parameters. Structural parameters are underlying parameters in a model or class of models. A model may have various parameters

and those parameters may change to create various properties.

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TEORI ILMIAH

A scientific theory is a set of principles that explain and predict phenomena. Scientists create scientific theories with the scientific

method, when they are originally proposed as hypotheses and tested for accuracy through observations and experiments. Once a

hypothesis is verified, it becomes a theory.

The term "theory" is a polyseme, even among scientists. While most scientists reserve the term for verifiable principles, others use it to refer to hypothetical frameworks. Colloquially, it is often

used to refer to a guess. In the humanities, the concept is called a philosophical theory and is intended to explain noumena. Philosophical theories can refer to

a set of principles or a set of propositions.

http://en.wikipedia.org/wiki/Scientific_theory

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THEORIES AS MODELS

The previously dominant position in philosophy of science -- the received view of theories -- which was prevalent in logical empiricism has in the course of the

second half of the 20th century been replaced by the semantic view of theories which identifies scientific theories with models rather than propositions.

A model of the solar system, for example, might consist of abstract objects that

represent the sun and the planets. These objects have associated properties, e.g., positions, velocities, and masses.

Functions defined on this set of objects, e.g., Newton's Law of Gravitation, determine how the positions and velocities change with time.

This model can be tested; astronomers can verify that the positions of the model's objects over time match the actual positions of the planets. For most planets, they do match; for Mercury, if the model is based on Newton's Law of Gravitation, they

don't.In this approach, the theory is the model. More precisely, a theory is a collection of similar models. One can use language to describe a model; however, the theory is

the model, not the description of the model.The word "semantic" refers to the way that a model represents the real world.