OPERATIONS RESERCH(OR)/

MANAGEMENT SCIENCE(MS)

Department of Industrial Engineering and Management

02, 2004

Instructor : Ching-Fang LiawE-mail Address : cfliaw@mail.cyut.edu.twOffice : E-503Office Hour : Tue, Thu: 10:30 ~ 12:00

1. Course Description:

The purpose of this course is to introduce Operations

Research (OR) / Management Science (MS)

techniques for manufacturing, services, and public

sector.

OR/MS includes a variety of techniques used in

modeling business applications for both better

understanding the system in question and making

best decisions.

OR/MS techniques have been applied in many

situations, ranging from inventory management

in manufacturing firms to capital budgeting in

large and small organizations.

Public and Private Sector Applications

The main objective of this course is to provide

engineers with a variety of decisional tools

available for modeling and solving problems in a

real business and/or nonprofit context.

In this class, each individual will explore how to

make various business models and how to solve

them effectively.

2. Text and References :

Text:

(1) Hillier and Lieberman

Introduction to Operations Research (2001),

Seven Edition, McGraw-Hill. （滄海）

(2) 潘昭賢 葉瑞徽 譯 作業研究 (上 ) (2003) （滄海）

References :

(1) Lawrence and Pasternack Applied Management Science (2001) Second Edition, John Wiley&Sons. （西書）

(2) Hillier, Hillier and Lieberman,

Introduction to Management Science: A Modeling and Case Studies Approach with Spreadsheets (2000), McGraw-Hill . （華泰）

3. Grading:

Quizzes 40%

Midterm 25%

Final 25%

Homework/Attendance 10%

========================

Total 100%

4. Topic Outline:

Unit Topic(s)

1 Introduction and Overview

2 Linear Programming Formulation

3 Solving Linear Programming

4 Theory of Simplex

5 Duality Theory

6 Project Scheduling: PERT-CPM

7 Game Theory

Unit Topic(s)

8 Decision Analysis

9 Markov Chain Model

10 Queuing Theory

11 Inventory Theory

12 Forecasting

13 Simulation

Linear Programming (LP):

A mathematical method that consists of an objective

function and many constraints.

LP involves the planning of activities to obtain an

optimal result, using a mathematical model, in

which all the functions are expressed by a linear

relation.

0,0

1823

1220

401

53

21

21

21

21

21

xx

xx

xx

xx

xxMaximize

subject to

A standard Linear Programming Problem

Applications: Man Power Design, Portfolio Analysis

Simplex method:

A remarkably efficient solution procedure for

solving various LP problems.

Extensions and variations of the simplex method

are used to perform postoptimality analysis

(including sensitivity analysis).

1x 2x 3x 4x 5xZ

3x4x5x

(0)(1)(2)(3)

21 53 xxZ 1x 3x

2x 4x21 23 xx 5x 18

12

4

0

(0)

(1)

(2)

(3)

(a) Algebraic Form

(b) Tabular Form

Coefficient of: RightSide

Basic VariableZ

Eq.

1 -3 -5 0 0 0 00 1 0 1 0 0 00 2 0 0 1 0 120 3 2 0 0 1 18

Duality Theory:

An important discovery in the early development

of LP is Duality Theory.

Each LP problem, referred to as ” a primal

problem” is associated with another LP problem

called “a dual problem”.

One of the key uses of duality theory lies in the

interpretation and implementation of sensitivity

analysis.

n

jjj xcZ

1

,

m

iii ybW

1

,

n

jijij bxa

1

,

m

ijiij cya

1

,

,0x j

Maximize Minimize

subject to subject to

,0iy

for i = 1, 2,…, m for j = 1, 2,…, n

for i = 1, 2,…, m.for j = 1, 2,…, n.

Primal Problem Dual Problem

PERT (Program Evaluation and Review

Technique)-CPM (Critical Path Method):

PERT and CPM have been used extensively to

assist project managers in planning, scheduling,

and controlling their projects.

Applications: Project Management, Project

Scheduling

A 2

B

C

E

M N

START

FINISH

H

G

D

J

I

F

LK

4

10

4 76

7

9

8

54

62

5

0

0

Critical Path

2 + 4 + 10 + 4 + 5 + 8 + 5 + 6 = 44 weeks

Game Theory:

A mathematical theory that deals with the general

features of competitive situations (in which the

final outcome depends primarily upon the

combination of strategies selected by the

opponent).

StrategyPlayer 2

1 2 1 -1-1 1

Player 112

Payoff table for the odds and evens game

Applications: Corporate Scheduling, Group Ware,

Strategy

Each player shows either one finger or two fingers. If the total number is even, player 1 wins the bet $1 to player 2. If the total number is odd, then player 1 pays $1 to player 2.

Decision Analysis:

An important technique for decision making in

uncertainty.

It divides decision making between the cases

of without experimentation and with

experimentation.

Applications: Decision Making, Planning

Oil0.5 0.3Favorable

0.75Dry

0.85Dry

a

e

d

c

b

f

g

h

Drill

Sell

Drill

Sell

Sell

DrillOil0.14

Oil0.25

0.5DryDo

seism

ic

surv

ey

Unfavorable

0.7

No seismic survey

decision forkchance fork

Markov Chain Model:

A special kind of a stochastic process.

It has a special property that probabilities,

involving how a process will evolve in

future, depend only on the present state of

the process, and so are independent of events

in the past.

Applications: Inventory Control, Forecasting

Suppose that two players (A and B), each having $2, agree to keep playing the game and betting $1 at a time until one player is broke.

The probability of A winning:

The probability of B winning:

.

100003

103200

03103

20

003103

200001

p

State 0 1 2 3 4

0

1

2

3

4

31

32

Queueing Theory:

This theory studies queueing systems by

formulating mathematical models of their

operation and then using these models to derive

measures of performance.

This analysis provides vital information for

effectively designing queueing systems that

achieve an appropriate balance between the

cost of providing a service and the cost

associated with waiting for the service.

SS ServiceS facilityS

CCCC

Served customers

Served customers

C C C C C C

Queueing system

CustomersQueue

Applications: Waiting Line Design, Banking, Network Design

Inventory Theory:

This theory is used by both wholesalers and retailers

to maintain inventories of goods to be available for

purchase by customers.

The just-in-time inventory system is such an example

that emphasizes planning and scheduling so that the

needed materials arrive “just-in-time” for their use.

Applications: Inventory Analysis, Warehouse Design

Economic Order Quantity (EOQ) model

Q

Q

atQ

Time t

Inventory level

Batchsize

a

Q

a

Q20

Forecasting:

When historical sales data are available, statistical

forecasting methods have been developed for using

these data to forecast future demand.

Several judgmental forecasting methods use expert

judgment.

Applications: Future Prediction, Inventory Analysis

1/99 4/99 7/99 10/99 1/00 4/00 7/00

The evolution of the monthly sales of a product illustrates a time series

Mon

thly

sal

es (

unit

s so

ld)

10,000

8,000

6,000

4,000

2,000

0

Simulation:

This technique is widely used for estimating the

performance of complex stochastic systems if

contemplated designs or operating policies are to

be used.

Applications: Risk Analysis, Future Prediction

Num

ber

of c

usto

mer

s

4

3

2

1

0

Outcome of the simulation run for a queueing system

TimeCycle 1 C.2 Cycle 3 C.4 C.5

Introduction to MS/OR

MS: Management Science

OR: Operations Research

Key components: (a) Modeling/Formulation

(b) Algorithm

(c) Application

OR/MS:

(1) A discipline that attempts to aid managerial

decision making by applying a scientific approach

to managerial problems that involve quantitative

factors.

(2) OR/MS is based upon mathematics, computer

science and other social sciences like economics

and business.

General Steps of OR/MS:

Step 1: Define problem and gather data

Step 2: Formulate a mathematical model to

represent the problem

Step 3: Develop a computer based procedure

for deriving a solution(s) to the

problem

Step 4: Test the model and refine it as needed

Step 5: Apply the model to analyze the

problem and make recommendation

for management

Step 6: Help implementation

WWII: The British and U.S. Military Operations

The Simplex Method: George Dantzig, 1947

Computer Revolution (Hardware/Software).

Origin of OR/MS: