- LAB SISTEM DAN ... 1 Dwi purnomo Sistem dinamik: Pemodelan dan simulasi komputer untuk mempelajari...
Transcript of - LAB SISTEM DAN ... 1 Dwi purnomo Sistem dinamik: Pemodelan dan simulasi komputer untuk mempelajari...
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Dwi purnomo
www.labsistemtmip.wordpress.com
Sistem dinamik:
Pemodelan dan simulasi komputer untukmempelajari dan mengelola sistem umpanbalik yang rumit (complex feedback systems), seperti bisnis, sistem lingkungan, sistem sosial, dsb.
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• Kumpulan elemen yang saling berinteraksi, berfungsi
Sistem:
p y g g , gbersama untuk tujuan tertentu.
• Umpan balik menjadi sangat penting
• Mengandung jumlah (kuantitas) yang selalu bervariasi• Variasi dapat dijelaskan dalam hubungan sebab akibat
Masalah dinamik
Variasi dapat dijelaskan dalam hubungan sebab akibat• Hubungan sebab akibat dapat terjadi dalam sistem
tertutup yang mengandung lingkaran umpan balik(feedback loops)
Identifikasi masalahMembangun hipotesis
dinamik yang menjelaskanhubungan sebab akibatdari masalah termaksud
Membuat struktur dasargrafik sebab akibat
Melengkapi grafik sebabMengubah grafik sebab
akibat yang telah
Menyalin grafik alirSistem Dinamik kedalam
program DYNAMO, Melengkapi grafik sebabakibat dengan informasi
akibat yang telahdilengkapi menjadi grafik
alir Sistem Dinamik
program DYNAMO, Stella, Vensim, Powersim,
atau persamaanmatematika
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M b t
Berfikir dalam
Fokus padaketerkaitanumpan balik(feedback linkages) diantara
Membuatbatasansistem untukmenentukankomponenyang masukdan tidak didalam sistem
terminologihubungansebab akibat
diantarakomponen-komponensistem
Berfikir sebab akibat adalah kunci dalam mengorganisir ide-ide dalam studi Sistem Dinamik
Gunakan kata `menyebabkan` atau `mempengaruhi` untukmenjelaskan hubungan antar komponen di dalam sistem
Contoh yang logis (misalnya hukum fisika)• makan berat bertambah• i• api asap
Contoh yang tidak logis (sosiologi, ekonomi)• Pakai sabuk pengaman mengurangi korban fatal dalam kecelakaan lalu
lintas
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Berfikir sebab akibat sajatidak cukup• laut evaporasi awan
hujan laut …
Umpan balik: untukmengatur/ mengendalikansistem, yaitu berupa suatusebab yang terlibat dalam
sistem namun dapathi di i
Umpan balik sangat pentingdalam studi Sistem Dinamik
mempengaruhi dirinyasendiri
Lelah TidurGaji VS Kinerja
G ji Ki j
Lelah VS TidurL l h tid• Gaji Kinerja
• Kinerja Gaji• Lelah tidur• Tidur lelah ?
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jik b b ik kib tjika penyebab naik, akibatakan naik (pertumbuhan,
penguatan), jika penyebabturun, akibat akan turun
jika penyebab naik, akibatakan turun, jika penyebab
turun, akibat akan naik
+
+
+
-
Gaji Kinerja Kinerja Gaji
S ki b ik ki j
++
Semakin gaji naik
Semakin baik kinerja
Semakin baik kinerja
Gaji akan semakin naik
Semakin gaji naik
Semakin baik kinerja
+
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Lelah Tidur Tidur Lelah
The more tired I am
The more I sleep
The more I sleep The less tired I am
The less tired I am
The less I sleep
The less I sleep The more tired I am
+
-
-
-+
+ +
+ -
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Evaporation clouds rain
amount of evapor
ation
Sunshine
EvaporationA mount of
water on earthEarth’s
temperature- -
+
+
+
+-
ration water ation
RainClouds
++ +
+
+-
Items that affect other items in the system but are not themselves affected by anything in the systemArrows 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
# of gro ing trees Har est rate
+delay
# of growing trees Harvest rate
Planting rate + -
-
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 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 dominateone loop must dominate
Stable conditions will exist when negative loops dominate positive loops
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Work to do Project Model
Work To Do
work doneovertime hoursrequired
quality of work
fatigue
+-
+
++
-
requiredworkforce
actual workforce
productivity+
-
+
hiring delay
q ++ p y
Level
Rate
Auxiliary
Flow arc
Cause-and-effect arc
Source/Sink
Constant
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Stock, accumulation, or state variableA quantity that accumulates over timeq yChange its value by accumulating or integrating ratesChange continuously over time even when the rates are changing discontinuously
Flow, activity, movementChange the values of levelsChange the values of levelsThe 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 calculationsOften useful in formulating complex rate equationsUsed 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 the boundary of the modelySink is where flows terminate outside the system
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BirthsBirths
Population
+
-
Births
children
Children maturing
Adultschildren Adults
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RabbitPopulationbirths deaths
birth rate average lifetime
average lifetime = 8Units: Year
birth rate = 0.125Units: fraction/Year
births = Population * birth rateUnits: rabbit/Year
deaths = Population / average lifetimeUnits: rabbit/Year
Population = INTEG(births - deaths,1000)Units: rabbit
Flow GraphCausal Graph
Equations
R
L
Block Model
+
+R L
dL/dt = k1*R(t)
R(t) = k2*L(t)
dL/dt = k1*k2*L(t)
L’ L
k1*k2
∫
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EquationsFlow GraphR1
LdL/dt = R1 – R2
R2 = k2*L
R1 = k1
dL/dt = k1 - k2*LBlock Model
R2
L1’ L1
k2
- k1
∫
EquationsdL /dt = R R
Flow GraphdL1/dt = R1 – R2
dL2/dt = R2 – R3
R1 = k1
R2 = K2 * L1
R3 = K3 * L2
dL1/dt = k1 – k2*L1
dL /dt k *L K *L
R1
L1
R2
L2
R3
Block ModeldL2/dt = k2*L1 – K3*L2
L1’ L1
k2
-
-
k1
L2’ L2∫ ∫
k3
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Problem statementFixed area of available land for constructionNew buildings are constructed while old buildings are demolishedPrimary state variable will be the total number of buildings over time
Causal Graph
-
-
-
-
EquationsFlow GraphdBl/dt = Cr – Dr
Cr = f1(CF, Bl)
Dr = f2(AL,Bl)
CF = f3(FLO)
FLO = f4(LA,AA,Bl)
Industrial
Buildings (B)
Construction (C) Demolition (D)
Construction
Average lifetime for buildings (AL)
( , , l)fraction
(CF)Fraction of
land occupied
(FLO)Land available for industrial buildings (LA)
Average area per building (AA)
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Simulation Model Design and Execution, Fishwick, Prentice-Hall, 1995 (Textbook), ( )Introduction to Computer Simulation: A system dynamics modeling approach, Nancy Roberts et al, Addison-wesley, 1983Business Dynamics: Systems thinking and modeling for a complex world, John D. Sterman, McGraw-Hill,2000