Materi II – System Dynamics - Universitas Muhammadiyah Yogyakarta

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Apakah Sistem Dinamik itu?
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Sistem dinamik: Pemodelan dan simulasi komputer untuk
mempelajari dan mengelola sistem umpan balik yang
rumit (complex feedback systems), seperti bisnis, sistem
lingkungan, sistem sosial, dsb.
Sistem:
–
–
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Kumpulan elemen yang saling berinteraksi, berfungsi bersama
untuk tujuan tertentu.
Umpan balik menjadi sangat penting
Masalah dinamik
–
–
–
Mengandung jumlah (kuantitas) yang selalu bervariasi
Variasi dapat dijelaskan dalam hubungan sebab akibat
Hubungan sebab akibat dapat terjadi dalam sistem tertutup yang
mengandung lingkaran umpan balik (feedback loops)
Sejarah
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Cybernetics (Wiener, 1948): studi yang mempelajari
bagaimana sistem biologi, rekayasa, sosial, dan
ekonomi dikendalikan dan diatur
Industrial Dynamics (Forrester, 1961): mengaplikasikan
prinsip “cybernetics” ke dalam sistem industri
System Dynamics: karya Forrester semakin meluas
meliputi sistem sosial dan ekonomi
Dengan perkembangan komputer yang sangat cepat,
Sistem Dinamik menyediakan kerangka kerja dalam
menyelesaikan permasalahan sistem sosial dan
ekonomi
Tahap Pemodelan Sistem Dinamik
1.
2.
3.
4.
5.
6.
Identifikasi masalah
Membangun hipotesis dinamik yang menjelaskan
hubungan sebab akibat dari masalah termaksud
Membuat struktur dasar grafik sebab akibat
Melengkapi grafik sebab akibat dengan informasi
Mengubah grafik sebab akibat yang telah dilengkapi
menjadi grafik alir Sistem Dinamik
Menyalin grafik alir Sistem Dinamik kedalam program
DYNAMO, Stella, Vensim, Powersim, atau persamaan
matematika
Aspek Penting
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Berfikir dalam terminologi hubungan sebab
akibat
Fokus pada keterkaitan umpan balik (feedback
linkages) diantara komponen-komponen sistem
Membuat batasan sistem untuk menentukan
komponen yang masuk dan tidak di dalam sistem
Hubungan Sebab Akibat
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Berfikir sebab akibat adalah kunci dalam mengorganisir
ide-ide dalam studi Sistem Dinamik
Gunakan kata `menyebabkan` atau `mempengaruhi`
untuk menjelaskan hubungan antar komponen di
dalam sistem
Contoh yang logis (misalnya hukum fisika)
– makan berat bertambah
– api  asap
Contoh yang tidak logis (sosiologi, ekonomi)
– Pakai sabuk pengaman  mengurangi korban fatal
dalam kecelakaan lalu lintas
Umpan balik (Feedback)
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Berfikir sebab akibat saja tidak cukup
Umpan balik: untuk mengatur/ mengendalikan
sistem, yaitu berupa suatu sebab yang terlibat
dalam sistem namun dapat mempengaruhi
dirinya sendiri
Umpan balik sangat penting dalam studi Sistem
Dinamik
Causal Loop Diagram (CLD)
CLD menunjukkan struktur umpan balik dari sistem
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 Lelah VS Tidur
Gaji VS Kinerja
–
–
Gaji
Gaji  Kinerja
Kinerja  Gaji
Kinerja
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Lelah
Lelah  tidur
Tidur  lelah ?
Tidur
Penanda CLD
+ : jika penyebab naik, akibat akan naik (pertumbuhan, penguatan),
jika penyebab turun, akibat akan turun
- : jika penyebab naik, akibat akan turun, jika penyebab turun, akibat
akan naik
+
+
Gaji
+
Kinerja
Lelah
-
Tidur
Pemahaman “Sebab” – “Akibat”
Sales are poor
Sales force is weak
Overworked
Number is limited
Augmenting CLD 2 - (Determining Loop
Polarity)
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Positive feedback (reinforcing) loops
–
–
–
–
–
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Have an even number of ‘–’ signs
Some quantity increase, a “snowball” effect takes over and that
quantity continues to increase
The “snowball” effect can also work in reverse
Generate behaviors of growth, amplify, deviation, and reinforce
Notation: place + symbol in the center of the loop
Negative feedback (balancing) loops
–
–
–
Have an odd number of “–” signs
Tend to produce “stable”, “balance”, “equilibrium” and “goalseeking” behavior over time
Notation: place - symbol in the center of the loop
Positive/Reinforcing Loops
 Accelerating growth
decline
or accelerating
Positive/Reinforcing Loops
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Salary  Performance, Performance  Salary
The more salary I get
The better I perform
The better I perform
Salary
The more salary I get
+
The more salary I get
The better I perform
+
+
Performance
Negative /Balancing Loop
 Tired  Sleep, Sleep  Tired
The more I sleep
The less tired I am
The less tired I am
The more tired I am
The less I sleep
The more I sleep
+
Tired
-
-
The less I sleep
Sleep
The more tired I am
Balancing Loops
Body Temperature
Desired Body
Temperature
Adjust Clothing
Temperature Gap
Balancing Loops
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System reverts to status quo
The goals are implicit
Loop Dominance
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There are systems which have more than one
feedback loop within them
The dominating loop might shift over time
When a feedback loop is within another, one loop
must dominate
Stable conditions will exist when negative loops
dominate positive loops
Combined Feedback Loops
(Case of Population Growth)
+
Birth rate
+
+
+
Polulation
-
-
Death rate
Exogenous Items
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Items that affect other items in the system but are not
themselves affected by anything in the system
Arrows are drawn from these items but there are no
arrows drawn to these items
+
Sunlight reaching
each plant
Sunlight
+
-
-
Density of plants
Delays: The Sluggish Shower
Current Water
Temperature
Shower Tap
Setting
Desired Water
Temperature
Temperature
Gap
Delays
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When you tell the story add the word
“eventually”
Cause the system to overshoot the target
Delays
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Systems often respond sluggishly
From the example below, once the trees are planted,
the harvest rate can be ‘0’ until the trees grow enough
to harvest
delay
-
# of growing trees
Planting rate
+
+
-
Harvest rate
System Thinking
System Structure
Pattern of Behaviour
Events
Basic System Behaviors
Exponential Growth
S-shaped Growth
Goal Seeking
S-shaped Growth with Overshoot
Oscillation
Overshoot and Collapse
Exponential Growth
Positive feedback loops generate growth, amplify deviations,
and reinforce change. An initial quantity of something
starts to grow, and the rate of growth increases.
Sys tem Le vel
Inflo w
Net incre as e rate
Goal Seeking
Negative feedback loops seek balance, equilibrium, and
static. The quantity of interest starts either above or
below a goal level and over time moves toward the goal.
Sys te m Le vel
Corre ctive Actio n
Discre pan cy
Rate o f ch ang e
Goal
Oscillation
Time delays cause the state of system to constantly
overshoots its goal or equilibrium state, reverses, then
undershoots, and so on. the quantity of interest fluctuates
around some level.
Sys te m Le vel
Corre ctive Actio n
Percep tio n
Percep tio n Delay
Discre pan cy
Rate o f ch ang e
Goal
S-shaped Growth
No real quantity can grow or decline forever, eventually one or
more constraints halt the growth. Initial exponential growth is
followed by goal-seeking behavior which results in the
variable leveling o°.
Sys te m Le vel
Net Incre as e Rate
Reso urce Ad eq uacy
Normal Growth Rate
Carryin g Capa city
S-Shaped Growth with Overshoot
Time delays in lead to the possibility that the state
of the system will overshoot and oscillate around
the carrying capacity.
Sys te m Le vel
Net Incre as e Rate
Reso urce Ad eq uacy
Delayed Res ou rce Effect
Normal Growth Rate
Carryin g Capa city
Overshoot and Collapse
The ability of the environment to support a growing
population is eroded or consumed by the population
itself.
Cons ump tio n rate
Carryin g Capa city
Erosio n of Carryin g Cap acity
Sys te m Le vel
Net Incre as e Rate
Normal Growth Rate
Reso urce Ad eq uacy
Stock & Flow Diagram
Stock & Flow Diagram
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Three different types of elements are (i)
stock/level/accumulation, (ii) flow/rate, and (iii)
information
The stock and flow diagram shows relationships
among variables which have the potential to
change over time (time based variables)
Unlike a causal loop diagram, a stock and flow
diagram distinguishes between different types
of variables
Stock & Flow Diagram
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A stock is an accumulation of something (as
representing physical entities/elements/units),
“state variable”  rectangular box
A flow is the movement of the “something" from one
stock to another  double line arrow
Rate of flow is controlled by “valve”
Information is symbolized by an “arrow”
Example : the money is a stock, and the transfer
operation for the money is a flow
Types of Stock & Flow
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Materials : this includes all stocks and flows of
physical goods which are part of a production and
distribution process, whether raw materials, inprocess inventories, or finished products.
Personnel : this generally refers to actual people,
for example; hours of labour.
Capital equipment : this includes such things as
factory space, tools, and other equipment
necessary for the production of goods and
provision of services.
Types of Stock & Flow
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Orders : this includes such things as orders for
goods, requisitions for new employees, and
contracts for new space or capital equipment.
Orders are typically the result of some
management decision which has been made,
but not yet converted into the desired result.
Money: this is used in the cash sense. That is, a
flow of money is the actual transmittal of
payments between different stocks of money.

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