1-introductionOPERARION RESEARCH TECHNIQUES.ppt

OPERATIONS RESERCH(OR)/
MANAGEMENT SCIENCE(MS)
Department of Industrial Engineering and
Management
02, 2004
Instructor : Ching-Fang Liaw
E-mail Address : cfliaw@mail.cyut.edu.tw
Office : E-503
Office 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
18
2
3
12
2
0
4
0
1
5
3
2
1
2
1
2
1
2
1
2
1









x
x
x
x
x
x
x
x
x
x
Maximize
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).

1
x 2
x 3
x 4
x 5
x
Z
3
x
4
x
5
x
(0)
(1)
(2)
(3)
2
1 5
3 x
x
Z 

1
x 3
x

2
x 4
x

2
1 2
3 x
x  5
x
 18
12
4
0




(0)
(1)
(2)
(3)
(a) Algebraic Form
(b) Tabular Form
Coefficient of: Right
Side
Basic Variable
Z
Eq.
1 -3 -5 0 0 0 0
0 1 0 1 0 0 0
0 2 0 0 1 0 12
0 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
j
j
j x
c
Z
1
, 


m
i
i
i y
b
W
1
,



n
j
i
j
ij b
x
a
1
, 


m
i
j
i
ij c
y
a
1
,
,
0
xj 
Maximize Minimize
subject to subject to
,
0

i
y
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
L
K
4
10
4 7
6
7
9
8
5
4
6
2
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).

Strategy
Player 2
1 2
1 -1
-1 1
Player 1
1
2
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

a
e
d
c
b
f
g
h
decision fork
chance 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:
.
1
0
0
0
0
3
1
0
3
2
0
0
0
3
1
0
3
2
0
0
0
3
1
0
3
2
0
0
0
0
1

















p
State 0 1 2 3 4
0
1
2
3
4
3
1
3
2

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.

S
S Service
S facility
S
C
C
C
C
Served customers
Served customers
C C C C C C
Queueing system
Customers
Queue
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
at
Q 
Time t
Inventory
level
Batch
size
a
Q
a
Q
2
0

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
Monthly
sales
(units
sold)
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

Number
of
customers
4
3
2
1
0
Outcome of the simulation run
for a queueing system
Time
Cycle 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:

1-introductionOPERARION RESEARCH TECHNIQUES.ppt

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