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Learning Outcomes

• Mahasiswa akan dapat mengaplikasikan model simulasi ke berbagai permasalahan khususnya untuk simulasi atrian. Simulasi persediaan dalam berbagai contoh..

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Outline Materi:

• Pengertian • Simulasi Atrian• Simulasi Persediaan• Simulasi Transpostrasi• Contoh penggunaan

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• General Principles– The system is broken down into suitable components or

entities– The entities are modeled separately and are then connected

to a model describing the overall system A bottom-up approach!

• The basic principles apply to all types of simulation models– Static or Dynamic– Deterministic or Stochastic– Discrete or continuous

• In BPD (Birth and Death Processes) and OM situations computer based Stochastic Discrete Event Simulation (e.g. in Extend) is the natural choice– Focuses on events affecting the state of the system and skips

all intervals in between

Building a Simulation Model

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Steps in a BPD Simulation Project

8. Experimental Design

9. Model runs and analysis

10. More runsNoYes

3. Model conceptualization 4. Data Collection

5. Model Translation

6. Verified

7. Validated

Yes

No

No No

Yes

Phase 3

Experimentation

1. Problem formulation

2. Set objectives and overall project plan

Phase 1

Problem Definition

Phase 2

Model Building

11. Documentation, reporting and

implementation

Phase 4

Implementation

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• Verification (efficiency)– Is the model correctly built/programmed?– Is it doing what it is intended to do?

• Validation (effectiveness)– Is the right model built?– Does the model adequately describe the reality you want to model?– Does the involved decision makers trust the model?

Two of the most important and most challenging issues in performing a simulation study

Model Verification and Validation

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• Find alternative ways of describing/evaluating the system and compare the results– Simplification enables testing of special cases with predictable

outcomes Removing variability to make the model deterministic Removing multiple job types, running the model with one job type at a time Reducing labor pool sizes to one worker

• Build the model in stages/modules and incrementally test each module– Uncouple interacting sub-processes and run them separately– Test the model after each new feature that is added– Simple animation is often a good first step to see if things are working

as intended

Model Verification Methods

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Validation - an Iterative Calibration Process

The Real System

Conceptual Model1. Assumptions on system components2. Structural assumptions which define the

interactions between system components3. Input parameters and data assumptions

Conceptualvalidation

Operational Model(Computerized representation)

Modelverification

Calibration and Validation

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• Assume a small branch office of a local bank with only one teller.

• Empirical data gathering indicates that inter-arrival and service times are exponentially distributed.

– The average arrival rate = = 5 customers per hour – The average service rate = = 6 customers per hour

• Using our knowledge of queuing theory we obtain = the server utilization = 5/6 0.83– Lq = the average number of people waiting in line– Wq = the average time spent waiting in line

Lq = 0.832/(1-0.83) 4.2 Wq = Lq/ 4.2/5 0.83

• How do we go about simulating this system?– How do the simulation results match the analytical ones?

Example 1: Simulation of a M/M/1 Queue

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Example 2: Antrian saluran Tunggal

Misalkan data empiris tentang distribusi kurun waktu antara pertibaan dan distribusi waktu pelayanan sbb:

Variabel acak yang harus disimulasi secara langsung ialah :a. Kurun waktu antara pertibaan (T)b. Kurun waktu pelayanan (L), laluc) Buatlah SIMULASI untuk menggambarkan satu periode

waktu yg mencakup 10 pertibaan ?

Kurun waktu antara

Pertibaan (menit)

Peluang Kurun waktu pelayanan

(menit)

Peluang

0 - 4 0,4 0 - 2 0,4

4 - 8 0,3 2 - 4 0,4

8 - 12 0,2 4 - 6 0,2

12 – 16 0,1

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Struktur Simulasi untuk T

Perlu dicatat bahwa titik tengah selang ditetapkan sebagai variabel acak..Kemudian untuk struktur simulasi L dapat dilihat berikut ini :

Harga variabel acak untuk waktu

pertibaan (b)

Peluang f(b)

Peluang kumulatif F(b)

Selang 0-1 bilangan acak terdistribusi. (1)

2 0,4 0,4 0,0 -- 0,4

6 0,3 0,7 0,4 – 0,7

10 0,2 0,9 0,7 – 0,9

14 0,1 1,0 0,9 -- 1,0

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Struktur Simulasi untuk L

Maka satu simulasi untuk satu periode waktu yang mencakup 10 pertibaan adalah seperti berikut ini :

Harga variabel acak untuk waktu

pelayanan (t)

Peluang f(t)

Peluang kumulatif F(t)

Selang 0-1 bilangan acak terdistribusi. (2)

1 0,4 0,4 0,0 -- 0,4

2 0,4 0,8 0,4 – 0,8

3 0,2 1,0 0,8 – 1,0

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Struktur Simulasi GI/G/1Pertibaan

U1 b Masuk sistem pd waktu ( I)

Panjang antrian

Waktu habis dlm antrian

Waktu servis pd waktu (II)

U2 t

Selesai servis pd waktu (III)

Waktu luang pelayanan

1 -- -- 0 0 0 0 0,612 3 3 0

2 0,900 14 14 0 0 14 0,484 3 17 11

3 0,321 2 16 0 1 17 0,048 1 18 0

4 0,211 2 18 0 0 18 0,605 3 21 0

5 0,021 2 20 0 1 21 0,583 3 24 0

6 0,198 2 22 0 2 24 0,773 3 27 0

7 0,383 2 24 0 3 27 0,054 1 28 0

8 0,107 2 26 1 2 28 0,853 5 33 0

9 0,799 10 36 0 0 36 0,313 1 34 3

10 0,439 6 42 0 0 42 0,200 1 43 5

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