Matakuliah
Tahun
: K0414 / Riset Operasi Bisnis dan Industri
: 2008 / 2009
Aplikasi Simulasi
Pertemuan 24 (GSLC)
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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Building a Simulation Model
• 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
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Steps in a BPD Simulation Project
Phase 1
1. Problem formulation
Problem Definition
2. Set objectives and overall project plan
4. Data Collection
3. Model conceptualization
Phase 2
Model Building
5. Model Translation
No
No
Phase 3
6. Verified
Yes
No
7. Validated
Yes
Experimentation
Phase 4
8. Experimental Design
Implementation
9. Model runs and analysis
Yes
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10. More runs
No
11. Documentation, reporting and
implementation
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Model Verification and Validation
• 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
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Model Verification Methods
• 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
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Validation - an Iterative Calibration Process
The Real System
Conceptual
validation
Calibration and
Validation
Conceptual Model
1. Assumptions on system components
2. Structural assumptions which define the
interactions between system components
3. Input parameters and data assumptions
Model
verification
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Operational Model
(Computerized representation)
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Example 1: Simulation of a M/M/1 Queue
• 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?
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Example 2: Antrian saluran Tunggal
Misalkan data empiris tentang distribusi kurun waktu antara pertibaan dan
distribusi waktu pelayanan sbb:
Kurun waktu antara
Pertibaan (menit)
Peluang
Kurun waktu pelayanan
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
Variabel acak yang harus disimulasi secara langsung ialah :
a. Kurun waktu antara pertibaan (T)
b. Kurun waktu pelayanan (L), lalu
c) Buatlah SIMULASI untuk menggambarkan satu periode waktu yg
mencakup 10 pertibaan ?
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Struktur Simulasi untuk T
Harga variabel acak untuk
pertibaan
(b)
Peluang f(b)
Peluang kumulatif
Selang 0-1 bilangan acak
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
Perlu dicatat bahwa titik tengah selang ditetapkan sebagai variabel
acak.
Kemudian untuk struktur simulasi L dapat dilihat berikut ini :
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Struktur Simulasi untuk L
Harga variabel acak untuk
pelayanan
(t)
Peluang f(t)
Peluang kumulatif F(t)
Selang 0-1 bilangan acak
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
Maka satu simulasi untuk satu periode waktu yang mencakup 10 pertibaan
adalah seperti berikut ini :
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Struktur Simulasi GI/G/1
Pertib
n
U1
b
Masuk sistem
waktu ( I)
Panjang
antrian
Waktu
dlm
Waktu
pd waktu
U2
t
Selesai
pd waktu
Waktu
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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