Apakah System Dynamics itu? 0 System Dynamics: Pemodelan dan simulasi
komputer untuk mempelajari dan mengelola sistem umpan balik yang rumit (complex feedback systems), seperti sistem ekonomi, sistem lingkungan, sistem sosial, dll. 0 Sistem: 0 Kumpulan elemen yang saling berinteraksi, berfungsi
bersama untuk tujuan tertentu. 0 Umpan balik menjadi sangat penting
0 Masalah dinamik
0 Mengandung jumlah (kuantitas) yang selalu bervariasi 0 Variasi dapat dijelaskan dalam hubungan sebab akibat 0 Hubungan sebab akibat dapat terjadi dalam sistem tertutup
yang mengandung lingkaran umpan balik (feedback loops)
Sejarah 0 Cybernetics (Wiener, 1948): studi yang
mempelajari bagaimana sistem biologi, rekayasa, sosial, dan ekonomi dikendalikan dan diatur 0 Industrial Dynamics (Forrester, 1961): mengaplikasikan prinsip “cybernetics” ke dalam sistem industri 0 System Dynamics: karya Forrester semakin meluas meliputi sistem sosial dan ekonomi 0 Dengan perkembangan komputer yang sangat cepat, System Dynamics menyediakan kerangka kerja dalam menyelesaikan permasalahan sistem sosial dan ekonomi
Tahap Pemodelan System Dynamics 1. Identifikasi masalah 2. Membangun hipotesis dinamik yang menjelaskan 3. 4. 5. 6.
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 System Dynamics Menyalin grafik alir System Dynamics ke dalam program komputer (DYNAMO, Stella, Vensim, Powersim) atau persamaan matematika
Aspek penting 0 Berfikir dalam terminologi hubungan sebab akibat
0 Fokus pada keterkaitan umpan balik (feedback
linkages) diantara komponen-komponen sistem 0 Membuat batasan sistem untuk menentukan komponen yang masuk dan tidak di dalam sistem
Hubungan Sebab Akibat 0 Berfikir sebab akibat adalah kunci dalam
mengorganisir ide-ide dalam studi System Dynamics 0 Gunakan kata `menyebabkan` atau `mempengaruhi` untuk menjelaskan hubungan antar komponen di dalam sistem 0 Contoh yang logis (misalnya hukum fisika) 0 makan berat bertambah 0 api asap 0 Contoh yang tidak logis (sosiologi, ekonomi) 0 Pakai sabuk pengaman mengurangi korban fatal dalam kecelakaan lalu lintas
Umpan balik (Feedback) 0 Berfikir sebab akibat saja tidak cukup 0 laut evaporasi awan hujan laut …
0 Umpan balik untuk mengatur/mengendalikan
sistem, yaitu berupa suatu sebab yang terlibat dalam sistem namun dapat mempengaruhi dirinya sendiri 0 Umpan balik sangat penting dalam studi System Dynamics
Causal Loop Diagram (CLD) CLD menunjukkan struktur umpan balik dari sistem 0 Gaji VS Kinerja
Lelah VS Tidur
0 Gaji Kinerja
0 Kinerja Gaji
Gaji
Kinerja
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
CLD dengan Positive Feedback Loop 0 Gaji Kinerja, Kinerja Gaji Semakin gaji naik
Semakin baik kinerja
+
Semakin baik kinerja Gaji akan semakin naik
Semakin gaji naik Semakin baik kinerja
Gaji +
+
Kinerja
Lelah Tidur, Tidur Lelah
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
The less I sleep
+
Lelah -
-
Tidur
The more tired I am
CLD with Combined Feedback Loops (Population Growth)
+
Birth rate +
+
+
Population -
-
Death rate
CLD with Nested Feedback Loops (Self-Regulating Biosphere) Evaporation clouds rain amount of water evaporation … -
+
-
Sunshine
+ +
+
Earth’s temperature
-
Evaporation
+
+ Clouds
+
A mount of water on earth
Rain
+
+
Exogenous Items 0 Items that affect other items in the system but are not
themselves affected by anything in the system 0 Arrows are drawn from these items but there are no arrows drawn to these items +
Sunlight reaching each plant +
Sunlight
-
-
Density of plants
Delays 0 Systems often respond sluggishly (dgn malas=tidak
seketika) 0 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
Loop Dominance 0 There are systems which have more than one
feedback loop within them 0 A particular loop in a system of more than one loop is most responsible for the overall behavior of that system 0 The dominating loop might shift over time 0 When a feedback loop is within another, one loop must dominate 0 Stable conditions will exist when negative loops dominate positive loops
Example Work to do Project Model + -
quality of work
Work To Do
required workforce
hiring delay +
-
actual workforce
fatigue +
+
overtime hours required
-
work done +
+
productivity
Stock and Flow Diagram
Level
Rate
Flow arc
Auxiliary
Cause-and-effect arc
Source/Sink
Constant
Level/Stock 0 Stock, accumulation, or state variable 0 A quantity that accumulates over time 0 Change its value by accumulating or integrating rates 0 Change continuously over time even when the rates
are changing discontinuously
Rate/Flow: 0 Flow, activity, movement
0 Change the values of levels 0 The value of a rate is 0 Not dependent on previous values of that rate 0 But dependent on the levels in a system along with exogenous influences
Auxiliary: 0 Arise when the formulation of a level’s influence
on a rate involves one or more intermediate calculations 0 Often useful in formulating complex rate equations 0 Used for ease of communication and clarity 0 Value changes immediately in response to changes in levels or exogenous influences
Source and Sink: 0 Source represents systems of levels and rates outside
the boundary of the model 0 Sink is where flows terminate outside the system
Example 1 (Population and birth) + Births
Population
+
Births Population
Example 2 (Children and adults) + Births +
Children -
+
-
+
Children maturing
Adults
+
Children maturing
Births children
Adults
births
Rabbit Population
birth rate
0 average lifetime = 8 0 Units: Year
0 birth rate = 0.125 0 Units: fraction/Year 0 births = Population * birth rate 0 Units: rabbit/Year 0 deaths = Population / average lifetime 0 Units: rabbit/Year 0 Population = INTEG(births - deaths,1000) 0 Units: rabbit
deaths average lifetime
From Causal Loop Diagram To Simulation Models 1 Causal Graph
Flow Graph R
+ R
L
L +
Equations dL/dt = k1*R(t) R(t) = k2*L(t) dL/dt = k1*k2*L(t)
Block Model L’
∫
L k1*k2
From Causal Loop Diagram To Simulation Models 2 Flow Graph R1
Equations R2
L
dL/dt = R1 – R2 R2 = k2*L
R1 = k1 dL/dt = k1 - k2*L
Block Model L1’
∫ -
L1 k2 k1
From Causal Loop Diagram To Simulation Models 3 Equations
Flow Graph R2
R1
dL1/dt = R1 – R2
R3
dL2/dt = R2 – R3
L2
L1
R1 = k1 R2 = K2 * L1 R3 = K3 * L2 dL1/dt = k1 – k2*L1
Block Model L1’
∫ -
dL2/dt = k2*L1 – K3*L2
L1 k2 k1
-
L2’
∫
L2 k3
References 0 Asep Sofyan, Teknik Lingkungan ITB,
[email protected] 0 Simulation Model Design and Execution, Fishwick,
Prentice-Hall, 1995 (Textbook) 0 Introduction to Computer Simulation: A system dynamics modeling approach, Nancy Roberts et al, Addison-wesley, 1983 0 Business Dynamics: Systems thinking and modeling for a complex world, John D. Sterman, McGraw-Hill,2000
