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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