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Pertemuan I – Konsep Dasar Riset Operasional Riset Operasinal – 4010102053-Dewiyani 1.

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Presentasi berjudul: "Pertemuan I – Konsep Dasar Riset Operasional Riset Operasinal – 4010102053-Dewiyani 1."— Transcript presentasi:

1 Pertemuan I – Konsep Dasar Riset Operasional Riset Operasinal – Dewiyani 1

2 Agenda  Introduction  Goals, Objectives and Expected outcome  What is management science?  What is Analytics, how does it relate to OR/MS?  Remarks 2

3 Dr. M.J. Dewiyani Sunarto Dosen tetap di STMIK STIKOM Surabaya Ruang Prodi S1 Sistem Informasi – Lantai 2 Gedung Merah Senin – Jumat : – Who am I? 3

4 Agenda  Introduction  Goals, Objectives and Expected outcome  What is management science?  What is Analytics, how does it relate to OR/MS?  Remarks 4

5 Goals, objectives and expected outcome  Capaian Pembelajaran : Setelah mengikuti mata kuliah riset operasional, mahasiswa dapat menganalisis persoalan optimasi dan pembentukan model dalam proses pengambilan keputusan dengan perhitungan manual maupun hasil output komputer 5

6 Materi 6  Dalam Mata kuliah ini mahasiswa akan mempelajari pokok bahasan- pokok bahasan sebagi berikut:  Konsep dasar riset operasional dan pembentukan model.  Pengantar program linier dan solusi grafik,  Solusi metode simpleks, Analisis post optimal,  Model transportasi dan penugasan,  Model arus jaringan,  Analytical hierarchy process (AHP),  Program dinamik,  Analisis markov,  Diagram pohon keputusan dan teori permainan.

7 Kesepakatan kita bersama……  Apa yang saya harapkan dari Anda ?  Datang tepat waktu – keterlambatan 0 menit  Persiapkan diri sebelum kuliah – baca Rancangan Pelaksanaan Pembelajaran (RPP).  Membaca referensi dan Berlatih soal sebanyak mungkin  Kumpulkan tugas tepat waktu.  Komposisi nilai : 30% UTS, 30% UAS, 40% Tugas  Nilai Minimal Kelulusan : B  3 sks berarti dalam seminggu :  3 x 50 menit persiapan  3 x 50 menit tatap muka  3 x 50 menit evaluasi 7

8 Kesepakatan kita bersama…… 8  Apa yang saya janjikan kepada Anda ?  Datang tepat waktu – keterlambatan 0 menit  Menfasilitasi belajar Anda  Mengembalikan pekerjaan/tugas Anda dalam waktu maksimal 2 minggu  3 sks berarti dalam seminggu :  3 x 50 menit persiapan  3 x 50 menit tatap muka  3 x 50 menit evaluasi

9 Don ’t be shy! Learning method% retention What one reads10% What one hears26% What one sees30% What one sees and hears 50% What one speaks70% J.E. Stice, Engineering Education, pp ,

10 Review Syllabus 10

11 Agenda  Introduction  Goals, Objectives and Expected outcome  What is management science?  What is Analytics, how does it relate to OR/MS?  Remarks 11

12 SEJARAH  PERANG DUNIA II --> ANGKATAN PERANG INGGRIS  TUJUAN : menentukan penggunaan sumber kemiliteran terbatas, dg cara paling efektif  Ditiru oleh Angkatan Perang Amerika ==> PENERAPAN ke MANAJEMEN BISNIS

13 RISET OPERASIONAL  Masalah : alokasi optimal sumber daya yang terbatas, dalam usaha mencapai hasil terbaik.  Optimal berarti : memaksimalkan laba, atau meminimalkan biaya.

14 DEFINISI  Riset Operasional merupakan suatu pendekatan ilmiah dalam pengambilan keputusan yang digunakan untuk mencari model terbaik dalam menjalankan suatu perusahaan guna mencapai tujuan, dalam kondisi ketersediaan sumber daya yang terbatas

15  Digunakan model matematis ( karena pendekatan ilmiah), berupa persamaan atau ketidaksamaan.  2 macam model matematis: - deterministik : bersifat pasti, semua komponen diketahui dengan pasti. - probabilistik : tidak pasti, lebih realistik, tapi sulit dianalisa

16 Home Runs in Management Science continued...  Sears, Roebuck & Company  One of the largest merchandise & service retailers in the world  Maintains 13,500 service and delivery vehicles, making approximately 20 million service and delivery calls annually  Combined OR techniques with GIS for more efficient service and delivery routes  Benefits:  Over $9 million in one time savings  Over $42 million in annual savings 16 OREM, Spring Dr. Gigi Yuen-Reed

17 Home Runs in Management Science continued...  Grantham, May, Van Otterloo and Co.  Boston-based investment firm with over $26 billion in assets  Developed a model to design portfolios that achieve investment objectives while minimizing custodial and transaction fees  Benefits:  40-60% reduction in the average number of stocks held  Number of trades reduced by 75-80%  Reduced annual trading costs by $4 million 17 OREM, Spring Dr. Gigi Yuen-Reed

18 Business Use of Management Science  Some application areas:  Project planning  Capital budgeting  Inventory analysis  Production planning  Scheduling  Interfaces - Applications journal published by Institute for Operations Research and Management Sciences 18 OREM, Spring Dr. Gigi Yuen-Reed

19 The Management Science Process Figure 1.1 The Management Science Process 19 OREM, Spring Dr. Gigi Yuen-Reed

20 Apakah itu Model ?  Model adalah bentuk sederhana dari suatu masalah.  Biasanya ditulis dalam persamaan matematika  model matematika  Disebut sebagai formulasi model 20

21 Example of a Mathematical Model Profit = Revenue - Expenses or Profit = f (Revenue, Expenses) or Y = f (X 1, X 2 ) 21

22 A Generic Mathematical Model Y = f (X 1, X 2, …, X n ) Y = dependent variable (a bottom line performance measure) X i = independent variables (inputs having an impact on Y) f (. ) = function defining the relationship between the X i and Y Where: 22

23 Example: Western Clothing Company Fixed Costs: c f = $10000 Variable Costs: c v = $8 per pair Price : p = $23 per pair The Break-Even Point is: FC + VC = p. v (8.v) = 23 v = 15 v v = (10,000)/(15) = pairs Model Building Illustration: Break-Even Analysis 23

24 Figure 1.2 Model Building Illustration: Break-Even Analysis 24 Graphical Solution

25 Figure 1.3 Model Building Illustration: Break-Even Analysis 25 What if unit price increase from $23 to $30?

26 Things to Consider OREM, Spring Dr. Gigi Yuen-Reed 26  Break-even is good, but how do we optimize profit?  How many pairs of jeans can we realistically sell given market condition?  Do we have sufficient resources to produce the desired quantity of products?  What is the impact of price elasticity? Above and Beyond

27 Formulasi model: PROGRAM LINEAR  Merupakan fungsi Linear  Mempunyai target memaksimumkan atau meminimumkan suatu nilai  Teknik Penyelesaian yang digunakan: - dua variabel : metoda grafik lebih dari dua variabel : metoda Simpleks  Model LP Secara Umum : - Variabel - Fungsi Tujuan - Fungsi Pembatas

28 TAHAPAN DALAM PROGRAM LINEAR 1. Merumuskan masalah 2. Membuat model matematika Komponen : - variabel keputusan - fungsi tujuan - fungsi pembatas 3. Menentukan suatu penyelesaian, agar diperoleh optimal solution 4. Pengujian model dan solusi 5. Pembuatan Implementasi

29 Linearitas  Suatu mesin memerlukan waktu 10 menit untuk memproses produk A dan 20 menit untuk memproses produk B. Jam operasi mesin : ………………  Biaya angkut per unit produk dari pabrik ke daerah pemasaran A,B dan C adalah Rp 2,-, Rp 4,- dan Rp 6,-. Biaya angkut total : ……………

30 General Form of a Linear Programming (LP) Problem MAX (or MIN): c 1 X 1 + c 2 X 2 + … + c n X n Subject to:a 11 X 1 + a 12 X 2 + … + a 1 n X n <= b 1 : a k 1 X 1 + a k 2 X 2 + … + a kn X n >=b k : a m 1 X 1 + a m 2 X 2 + … + a mn X n = b m 30

31 An Example LP Problem Blue Ridge Hot Tubs produces two types of hot tubs: Aqua-Spas & Hydro-Luxes. There are 200 pumps, 1566 hours of labor, and 2880 feet of tubing available. Aqua-SpaHydro-Lux Pumps11 Labor 9 hours6 hours Tubing12 feet16 feet Unit Profit$350$300 31

32 5 Steps In Formulating LP Models: 1. Understand the problem. 2. Identify the decision variables. X 1 =number of Aqua-Spas to produce X 2 =number of Hydro-Luxes to produce 3.State the objective function as a linear combination of the decision variables. MAX: 350X X 2 32

33 5 Steps In Formulating LP Models (continued) 4. State the constraints as linear combinations of the decision variables. 1X 1 + 1X 2 <= 200} pumps 9X 1 + 6X 2 <= 1566} labor 12X X 2 <= 2880} tubing 5. Identify any upper or lower bounds on the decision variables. X 1 >= 0 X 2 >= 0 33

34 Summary of the LP Model for Blue Ridge Hot Tubs MAX: 350X X 2 S.T.:1X 1 + 1X 2 <= 200 9X 1 + 6X 2 <= X X 2 <= 2880 X 1 >= 0 X 2 >= 0 34

35 Feasible/Infeasible Solutions  A feasible solution does not violate any of the constraints:  An infeasible solution violates at least one of the constraints: 35

36 Summary  LP  LP Components  Steps to formulate an LP 36


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