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Bina Nusantara Aplikasi Simulasi Peretemuan 25: Mata kuliah: K0194-Pemodelan Matematika Terapan Tahun: 2008.

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Presentasi berjudul: "Bina Nusantara Aplikasi Simulasi Peretemuan 25: Mata kuliah: K0194-Pemodelan Matematika Terapan Tahun: 2008."— Transcript presentasi:

1 Bina Nusantara Aplikasi Simulasi Peretemuan 25: Mata kuliah: K0194-Pemodelan Matematika Terapan Tahun: 2008

2 Bina Nusantara Learning Outcomes Mahasiswa akan dapat mengaplikasikan model simulasi ke berbagai permasalahan khususnya untuk simulasi atrian. Simulasi persediaan dalam berbagai contoh..

3 Bina Nusantara Outline Materi: Pengertian Simulasi Atrian Simulasi Persediaan Simulasi Transpostrasi Contoh penggunaan

4 Bina Nusantara 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

5 Bina Nusantara Steps in a BPD Simulation Project 8. Experimental Design 9. Model runs and analysis 10. More runs No Yes 3. Model conceptualization 4. Data Collection 5. Model Translation 6. Verified 7. Validated Yes 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

6 Bina Nusantara 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

7 Bina Nusantara 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

8 Bina Nusantara Validation - an Iterative Calibration Process The Real System Conceptual Model 1.Assumptions on system components 2.Structural assumptions which define the interactions between system components 3.Input parameters and data assumptions Conceptual validation Operational Model (Computerized representation) Model verification Calibration and Validation

9 Bina Nusantara 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 –L q = the average number of people waiting in line –W q = the average time spent waiting in line L q = 0.83 2 /(1-0.83)  4.2W q = L q /  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

10 Bina Nusantara 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), lalu c) Buatlah SIMULASI untuk menggambarkan satu periode waktu yg mencakup 10 pertibaan ? Kurun waktu antara Pertibaan (menit) PeluangKurun waktu pelayanan (menit) Peluang 0 - 40,40 - 20,4 4 - 80,32 - 40,4 8 - 120,24 - 60,2 12 – 160,1

11 Bina Nusantara 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) 20,4 0,0 -- 0,4 60,30,70,4 – 0,7 100,20,90,7 – 0,9 140,11,00,9 -- 1,0

12 Bina Nusantara 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) 10,4 0,0 -- 0,4 20,40,80,4 – 0,8 30,21,00,8 – 1,0

13 Bina Nusantara Struktur Simulasi GI/G/1 Perti baan U1bMasuk sistem pd waktu ( I) Panjang antrian Waktu habis dlm antrian Waktu servis pd waktu (II) U2 tSelesai servis pd waktu (III) Waktu luang pelayanan 1-- 00000,612 330 20,90014 00 0,484 31711 30,32121601170,048 1180 40,21121800 0,605 3210 50,02122001210,583 3240 60,19822202240,773 3270 70,38322403270,054 1280 80,10722612280,853 5330 90,799103600 0,313 1343 100,43964200 0,200 1435

14 Bina Nusantara

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