Pertemuan I – Konsep Dasar Riset Operasional

Riset Operasinal – 4010102053-Dewiyani

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

OR/MS? Remarks

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• 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

Who am I?

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

OR/MS? Remarks

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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

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Materi

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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

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Kesepakatan kita bersama……

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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 % retentionWhat 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

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Review Syllabus

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

OR/MS? Remarks

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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

RISET OPERASIONALMasalah : 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

OREM, Spring 2014. Dr. Gigi Yuen-Reed

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

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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

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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

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OREM, Spring 2014. Dr. Gigi Yuen-Reed

The Management Science Process

Figure 1.1 The Management Science Process19

Apakah itu Model ? Model adalah bentuk sederhana dari

suatu masalah. Biasanya ditulis dalam persamaan

matematika model matematika Disebut sebagai formulasi model

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Example of a Mathematical Model

Profit = Revenue - Expensesor

Profit = f(Revenue, Expenses)or

Y = f(X1, X2)

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A Generic Mathematical Model

Y = f(X1, X2, …, Xn)

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

Where:

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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. v10.000 + (8.v) = 23 v10.000 = 15 v v = (10,000)/(15) = 666.7 pairs

Model Building Illustration:Break-Even Analysis

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Figure 1.2

Model Building Illustration:Break-Even Analysis

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Graphical Solution

Figure 1.3

Model Building Illustration:Break-Even Analysis

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What if unit price increase from $23 to $30?

OREM, Spring 2014. Dr. Gigi Yuen-Reed

Things to Consider

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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

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 LINEAR1. Merumuskan masalah2. Membuat model matematika Komponen : - variabel keputusan - fungsi tujuan - fungsi pembatas3. Menentukan suatu penyelesaian, agar

diperoleh optimal solution4. Pengujian model dan solusi5. 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

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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-Spa Hydro-LuxPumps 1 1Labor 9 hours 6 hoursTubing 12 feet 16 feetUnit Profit $350 $300

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5 Steps In Formulating LP Models:

1. Understand the problem.

2. Identify the decision variables.X1=number of Aqua-Spas to

produceX2=number of Hydro-Luxes to

produce

3. State the objective function as a linear combination of the decision variables.

MAX: 350X1 + 300X232

5 Steps In Formulating LP Models(continued)

4. State the constraints as linear combinations of the decision variables.1X1 + 1X2 <= 200 } pumps9X1 + 6X2 <= 1566 } labor12X1 + 16X2 <= 2880 } tubing

5. Identify any upper or lower bounds on the decision variables.X1 >= 0

X2 >= 033

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

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Feasible/Infeasible Solutions

A feasible solution does not violate any of the constraints:

An infeasible solution violates at least one

of the constraints:

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Summary LP LP Components Steps to formulate an LP

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