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

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

Who am I? Dr. M.J. Dewiyani Sunarto dewiyani@stikom.edu 08563062843 Dosen tetap di STMIK STIKOM Surabaya Ruang Prodi S1 Sistem Informasi – Lantai 2 Gedung Merah Senin – Jumat : 07.30 – 16.30

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

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

Materi 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.

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

Kesepakatan kita bersama…… 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

Don’t be shy! Learning method % retention What one reads 10% What one hears 26% What one sees 30% What one sees and hears 50% What one speaks 70% J.E. Stice, Engineering Education, pp. 291-296, 1987

Review Syllabus

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

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

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

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

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

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 OREM, Spring 2014. Dr. Gigi Yuen-Reed

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 OREM, Spring 2014. Dr. Gigi Yuen-Reed

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 OREM, Spring 2014. Dr. Gigi Yuen-Reed

The Management Science Process Observation - Identification of a problem that exists in the system or organization. Definition of the Problem - problem must be clearly and consistently defined showing its boundaries and interaction with the objectives of the organization. Important to define this in respect to the business needs. Model Construction - Development of the functional mathematical relationships that describe the decision variables, objective function and constraints of the problem. This includes identifying and gathering the right data Model Solution - Models solved using management science techniques. Model Implementation - Actual use of the model or its solution. Figure 1.1 The Management Science Process OREM, Spring 2014. Dr. Gigi Yuen-Reed

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

Example of a Mathematical Model Profit = Revenue - Expenses or Profit = f(Revenue, Expenses) Y = f(X1, X2)

A Generic Mathematical Model Y = f(X1, X2, …, Xn) Where: Y = dependent variable (a bottom line performance measure) Xi = independent variables (inputs having an impact on Y) f(.) = function defining the relationship between the Xi and Y

Model Building Illustration: Break-Even Analysis Example: Western Clothing Company Fixed Costs: cf = $10000 Variable Costs: cv = $8 per pair Price : p = $23 per pair The Break-Even Point is: FC + VC = p. v 10.000 + (8.v) = 23 v 10.000 = 15 v v = (10,000)/(15) = 666.7 pairs

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

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

Things to Consider Break-even is good, but how do we optimize profit? Above and Beyond 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? OREM, Spring 2014. Dr. Gigi Yuen-Reed

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

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

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 : ……………

General Form of a Linear Programming (LP) Problem MAX (or MIN): c1X1 + c2X2 + … + cnXn Subject to: a11X1 + a12X2 + … + a1nXn <= b1 : ak1X1 + ak2X2 + … + aknXn >=bk am1X1 + am2X2 + … + amnXn = bm

An Example LP Problem Blue Ridge Hot Tubs produces two types of hot tubs: Aqua-Spas & Hydro-Luxes. Aqua-Spa Hydro-Lux Pumps 1 1 Labor 9 hours 6 hours Tubing 12 feet 16 feet Unit Profit $350 $300 There are 200 pumps, 1566 hours of labor, and 2880 feet of tubing available.

5 Steps In Formulating LP Models: 1. Understand the problem. 2. Identify the decision variables. X1=number of Aqua-Spas to produce X2=number of Hydro-Luxes to produce 3. State the objective function as a linear combination of the decision variables. MAX: 350X1 + 300X2

5 Steps In Formulating LP Models (continued) 4. State the constraints as linear combinations of the decision variables. 1X1 + 1X2 <= 200 } pumps 9X1 + 6X2 <= 1566 } labor 12X1 + 16X2 <= 2880 } tubing 5. Identify any upper or lower bounds on the decision variables. X1 >= 0 X2 >= 0

Summary of the LP Model for Blue Ridge Hot Tubs MAX: 350X1 + 300X2 S.T.: 1X1 + 1X2 <= 200 9X1 + 6X2 <= 1566 12X1 + 16X2 <= 2880 X1 >= 0 X2 >= 0

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

Summary LP LP Components Steps to formulate an LP