29/05/2011
Dwi purnomo
www.labsistemtmip.wordpress.com
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.
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29/05/2011
Sistem: p g saling g berinteraksi,, berfungsi g • Kumpulan elemen yyang 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)
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
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Berfikir dalam terminologi hubungan sebab akibat
Fokus pada keterkaitan umpan balik (feedback linkages) diantara komponenkomponen sistem
Membuat M b t batasan sistem untuk menentukan komponen yang masuk dan tidak di dalam sistem
Berfikir sebab akibat adalah kunci dalam mengorganisir ideide dalam studi Sistem Dinamik
Gunakan kata `menyebabkan` atau `mempengaruhi` untuk menjelaskan hubungan antar komponen di dalam sistem Contoh yang logis (misalnya hukum fisika) • makanÆ berat bertambah • apii Æ asap
Contoh yang tidak logis (sosiologi, ekonomi) • Pakai sabuk pengaman Æ mengurangi korban fatal dalam kecelakaan lalu lintas
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Berfikir sebab akibat saja tidak cukup • laut Æ evaporasi Æ awan Æ hujan Æ laut Æ …
Umpan balik: untuk mengatur/ mengendalikan sistem, yaitu berupa suatu sebab yang terlibat dalam sistem namun dapat mempengaruhi hi di dirinya i sendiri
Gaji VS Kinerja j • G Gajiji Æ Ki Kinerja • Kinerja Æ Gaji
Umpan balik sangat penting dalam studi Sistem Dinamik
Lelah VS Tidur
Lelah Tidur l h Æ tid • LLelah tidur • Tidur Æ lelah ?
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jika jik penyebab b b naik, ik akibat kib t akan naik (pertumbuhan, penguatan), jika penyebab turun, akibat akan turun
jika penyebab naik, akibat akan turun, jika penyebab turun, akibat akan naik
+
+
+
Gaji
-
Kinerja
Kinerja
Gaji
Semakin gaji naik
+
Semakin baik kinerja S ki b ik ki j Semakin baik kinerja Gaji akan semakin naik
+ +
Semakin gaji naik Semakin baik kinerja
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Lelah
Tidur
Tidur
The more I sleep
Lelah
The less tired I am
The more tired I am
The less tired I am
The more I sleep
The less I sleep The less I sleep
The more tired I am
+ -
+
+ -
+
+
-
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Evapo ration
clouds
Sunshine -
amount of water
rain
+
+
Earth’s temperature
evapor ation
+
+
+
+
A mount of water on earth
-
Evaporation
-
+
+
Clouds
Rain +
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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 +
+
-
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Systems often respond sluggishly (dgn malas) From the example below, once the trees are planted, the harvest rate can be ‘0’ until the trees grow enough to harvest
delay
# of gro growing ing trees Planting rate
+
-
+ Har est rate Harvest
-
There are systems which have more than one feedback loop within them A particular loop in a system of more than one loop is most responsible for the overall behavior of that system 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
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Work to do Project Model + -
quality of work
Work To Do
required workforce
hiring delay +
-
actual workforce
fatigue +
+
overtime hours required q
-
work done +
+
productivity p y
Level
Rate
Flow arc
Auxiliary
Cause-and-effect arc
Source/Sink Constant
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` ` `
Stock, accumulation, or state variable y that accumulates over time Aq quantity Change its value by accumulating or integrating rates Change continuously over time even when the rates are changing discontinuously
Flow, activity, movement Change the values of levels The value of a rate is ◦ Not dependent on previous values of that rate ◦ But dependent on the levels in a system along with exogenous influences
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` ` `
`
`
Arise when the formulation of a level’s influence on a rate involves one or more intermediate calculations Often useful in formulating complex rate equations Used for ease of communication and clarity Value changes immediately in response to changes in levels or exogenous influences
Source represents systems of levels and rates outside y of the model the boundary Sink is where flows terminate outside the system
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Births Population
+
Children maturing
Births children
Adults
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Rabbit Population
births
deaths
birth rate ` ` ` ` ` ` ` ` ` `
average lifetime
average lifetime = 8 Units: Year birth rate = 0.125 Units: fraction/Year births = Population * birth rate Units: rabbit/Year deaths = Population / average lifetime Units: rabbit/Year Population = INTEG(births - deaths,1000) Units: rabbit
Causal Graph
Flow Graph R
+ R
L
L +
Equations dL/dt = k1*R(t) R(t) = k2*L(t) Æ dL/dt = k1*k2*L(t)
Block Model L’
∫
L k1*k2
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Flow Graph R1
Equations R2
dL/dt = R1 – R2
L
R2 = k2*L R1 = k1 Æ dL/dt = k1 - k2*L
Block Model L1’
L1
∫
k2 k1
-
Equations
Flow Graph R2
R1
dL1/dt = R1 – R2
R3
dL2/dt = R2 – R3
L2
L1
R1 = k1 R2 = K2 * L1 R3 = K3 * L2 Æ dL1/dt = k1 – k2*L1
Block Model L1’
∫ -
Æ dL2/dt = k2*L1 – K3*L2
L1 k2
-
L2’
∫
L2 k3
k1
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Problem statement Fixed area of available land for construction New buildings are constructed while old buildings are demolished Primary state variable will be the total number of buildings over time
Causal Graph -
-
Equations
Flow Graph Construction (C)
Demolition (D) Industrial
dBl/dt = Cr – Dr Cr = f1(CF, Bl)
Buildings (B)
Dr = f2(AL,Bl) Average lifetime for buildings (AL)
Construction fraction (CF) Land available for industrial buildings (LA)
CF = f3(FLO) FLO = f4(LA,AA,B ( , , l)
Fraction of land occupied (FLO)
Average area per building (AA)
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Simulation Model Design and Execution, Fishwick, PrenticeHall,, 1995 ((Textbook)) Introduction to Computer Simulation: A system dynamics modeling approach, Nancy Roberts et al, Addison-wesley, 1983 Business Dynamics: Systems thinking and modeling for a complex world, John D. Sterman, McGraw-Hill,2000
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