Materi II – System Dynamics - Universitas Muhammadiyah Yogyakarta

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   

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 

 Lelah VS Tidur

Gaji VS Kinerja – –

Gaji

Gaji  Kinerja Kinerja  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

Pemahaman “Sebab” – “Akibat” Sales are poor Sales force is weak Overworked Number is limited

Augmenting CLD 2 - (Determining Loop Polarity) 

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 

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  

System reverts to status quo The goals are implicit

Loop Dominance    

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  

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  

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.