DIT 1141: OPERATIONS MANAGEMENT
DEPARTMENT OF DECISION AND
INFORMATION TECHNOLOGIES
COLLEGE OF COMMERCE AND FINANCE
VILLANOVA UNIVERSITY
INTRODUCTION
INTRODUCTION
Operations management is the process of obtaining
and utilizing resources to produce useful goods
and services so as to meet the goals of the
organization.
INTRODUCTION
Production management is concerned with the
manufacturing of goods:
Examples of goods:
cars
books
chairs
computers
houses
etc.
INTRODUCTION
Operations management is also concerned with the
management of service industries as well as the
manufacturing of goods.
INTRODUCTION
Examples of services:
retailing/food
banking
education
health care
utilities
insurance
government agencies
etc.
OVERVIEW OF OPERATIONS
MANAGEMENT MODEL
Input: resources
raw materials
machines
personnel
capital
land/buildings
utilities
information
etc.
Output
Transformation
Process
Control
Goods or
Services
OVERVIEW OF OPERATIONS
MANAGEMENT MODEL
Operations management considers how the input are
transformed into goods or services.
Control is when something is learned about the
goods or services that is used to more effectively
transform future goods or services.
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
Automobile factory
Input
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
Automobile factory
Input
steel, plastic
glass, paint
tools
equipment
machines
personnel, buildings
utilities, etc.
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
Automobile factory
Input
steel, plastic
glass, paint
tools
Transformation
equipment
process
machines
personnel, buildings
utilities, etc.
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
Automobile factory
Input
steel, plastic
glass, paint
tools
Transformation
equipment
process
machines
personnel, buildings
utilities, etc.
Output
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
Automobile factory
Input
steel, plastic
glass, paint
tools
Transformation
equipment
process
machines
personnel, buildings
utilities, etc.
Output
Car
OPERATIONS MANAGEMENT
QUESTIONS
1. How many items will be demanded next month?
2. How many items should be produced next month?
3. How many workers are needed to satisfy the
proposed production level?
OPERATIONS MANAGEMENT
QUESTIONS
4. If a plant is built, how should the activities be
scheduled so that the project is completed on time,
within budget, and with acceptable quality?
5. How is the quality of our output measured and
how is it improved?
6. If tires are needed, how many should be ordered?
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
Hospital
Input
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
Hospital
Input
patients, doctors
nurses, drugs
beds
building
medical equipment
support staff, computers
utilities, etc.
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
Hospital
Input
patients, doctors
nurses, drugs
Transformation
beds
Process
building
medical equipment
support staff, computers
utilities, etc.
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
Hospital
Input
Output
patients, doctors
nurses, drugs
Transformation
beds
Process
building
medical equipment
support staff, computers
utilities, etc.
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
Hospital
Input
Output
patients, doctors
A treated patient
nurses, drugs
Transformation
beds
Process
building
medical equipment
support staff, computers
utilities, etc.
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
University
Input
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
University
Input
students, professors
secretaries
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
University
Input
students, professors
secretaries, drugs
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
University
Input
students, professors
secretaries, drugs
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
University
Input
students, professors
secretaries, lab equipment
dormitories
staff, computers
buildings
etc.
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
University
Input
students, professors
secretaries, lab equipment
dormitories
staff, computers
Transformation
buildings
process
etc.
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
University
Input
Output
students, professors
secretaries, lab equipment
dormitories
staff, computers
Transformation
buildings
process
etc.
EXAMPLE OF OPERATIONS
MANAGEMENT PROCESS
University
Input
students, professors
secretaries, lab equipment
dormitories
staff, computers
Transformation
buildings
process
etc.
Output
A more highly
educated
student
DECISION MAKING IN
OPERATIONS:
THE ANALYTIC
HIERARCHY PROCESS
INTRODUCTION
What is the Analytic Hierarchy Process (AHP)?
The AHP, developed by Tom Saaty, is a decisionmaking method for prioritizing alternatives when
multi-criteria must be considered.
An approach for structuring a problem as a hierarchy
or set of integrated levels.
INTRODUCTION
AHP problems are structured in at least three levels:
The goal, such as selecting the best car to purchase,
The criteria, such as cost, safety, and appearance,
The alternatives, namely the cars themselves.
INTRODUCTION
The decision-maker:
measures the extent to which each alternative
achieves each criterion, and
determines the relative importance of the criteria in
meeting the goal, and
synthesizes the results to determine the relative
importance of the alternatives in meeting the goal.
APPROACH
How does AHP capture human judgments?
AHP never requires you to make an absolute
judgment or assessment. You would never be
asked to directly estimate the weight of a stone in
kilograms.
AHP does require you to make a relative assessment
between two items at a time. AHP uses a ratio
scale of measurement.
APPROACH
Suppose the weights of two stones are being
assessed. AHP would ask: How much heavier (or
lighter) is stone A compared to stone B?
AHP might tell us that, of the total weight of stones
A and B, stone A has 65% of the total weight,
whereas, stone B has 35% of the total weight.
APPROACH
Individual AHP judgments are called pairwise
comparisons.
These judgments can be based on objective or
subjective information.
For example, smoothness might be a subjective
criterion used to compare two stones. Pairwise
comparisons could be based on touch.
APPROACH
However, suppose stone A is a diamond worth
$1,000.00 and stone B is a ruby worth $300.00.
This objective information could be used as a basis
for a pairwise comparison based on the value of
the stones.
APPROACH
Consistency of judgments can also be measured.
Consistency is important when three or more
items are being compared.
Suppose we judge a basketball to be twice as large as
a soccer ball and a soccer ball to be three times as
large as a softball.
To be perfectly consistent, a basketball must be six
times as large as a softball.
APPROACH
AHP does not require perfect consistency, however,
it does provide a measure of consistency.
We will discuss consistency in more detail later.
AHP APPLICATIONS
AHP has been successfully applied to a variety of
problems.
1. R&D projects and research papers;
2. vendors, transport carriers, and site locations;
3. employee appraisal and salary increases;
4. product formulation and pharmaceutical licensing;
5. capital budgeting and strategic planning;
6. surgical residents, medical treatment, and
diagnostic testing.
AHP APPLICATIONS
The product and service evaluations prepared by
consumer testing services is another potential
application.
Products and services, such as self propelled lawn
mowers are evaluated.
Factors include: bagging, mulching, discharging,
handling, and ease of use.
An overall score for each mower is determined.
AHP APPLICATIONS
Would you make your purchasing decision based
solely on this score?
Probably not! Some of the information will be
helpful.
Some additional questions are:
How important is each criterion?
Would you weigh the criteria the same way?
Are all of the criteria considered important to you?
Are there other criteria that are important to you?
Have you ever thought about these issues?
RANKING SPORTS RECORDS
The AHP has been used to rank outstanding season,
career, and single event records across sports.
Season
1. Babe Ruth, 1920: .847 slugging average
2. Joe DiMaggio, 1944: 56 game hitting streak
3. Wilt Chamberlain, 1961-62: 50.4 points per game
scoring average
RANKING SPORTS RECORDS
Career
1. Johnny Unitas, 1956-70: touchdown passes in 47
consecutive games
2. Babe Ruth, 1914-35: .690 slugging average
3. Walter Payton, 1975-86: 16,193 rushing yardage
Single event
1. Wilt Chamberlain, 1962: 100 points scored
2. Norm Van Brocklin, 1951: 554 passing yards
3. Bob Beamon, 1968: 29' 2.5" long jump
RANKING SPORTS RECORDS
How do we compare records from different sports?
It all depends on the criteria that you select!
Golden and Wasil (1987) used the following criteria:
1. Duration of record - years record has stood, years
expected to stand
2. Incremental improvement - % better than previous
record
3. Other record characteristics - glamour, purity
(single person vs. team)
RANKING SPORTS RECORDS
Did this article end all arguments about sports
records?
Absolutely not!
In bars and living rooms across the country, people
still argue about sports.
AHP provides a methodology to structure the debate.
Different criteria and different judgments could
produce different results.
A FINAL POINT ABOUT SPORTS
In reading the sports pages we often see discussion
of how well teams match up across different
positions.
These match-ups are often used to predict a winner.
Match-ups is a pairwise comparison concept!
AHP APPLICATIONS
Our culture is obsessed with quantitative rankings of
all sorts of things.
There are many measurement problems associated
with rankings of products, sports teams,
universities, and the like.
Many of these issues are discussed on a web site at:
http://www.expertchoice.com/annie.person.
APPLES AND ORANGES
The discussion of how to compare records from
different sports recalls a saying from childhood:
APPLES AND ORANGES
The discussion of how to compare records from
different sports recalls a saying from childhood:
You can’t compare apples and oranges. All you
get is mixed fruit!
APPLES AND ORANGES
The discussion of how to compare records from
different sports recalls a saying from childhood:
You can’t compare apples and oranges. All you
get is mixed fruit!
After the discussion about sports, do you still believe
this statement?
APPLES AND ORANGES
The discussion of how to compare records from
different sports recalls a saying from childhood:
You can’t compare apples and oranges. All you
get is mixed fruit!
After the discussion about sports, do you still believe
this statement?
We hope not!!!
APPLES AND ORANGES
What criteria might you use when comparing apples
and oranges?
There are a vast set of criteria that may change
depending upon time of day or season of year:
taste,
ripeness,
shape,
cost.
texture,
juiciness,
weight,
Can you think of others?
smell,
nutrition,
color, and
APPLES AND ORANGES
The point is that people are often confronted with the
choice between apples and oranges.
Their choice is based on some psychological
assessment of:
relevant criteria,
their importance, and
how well the alternatives achieve the criteria.
CAR PURCHASE EXAMPLE
We now consider a motivating example.
After completing this example, you will have an
understanding of the basics of AHP and its
application through Expert Choice
(www.expertchoice.com).
We want to apply the AHP to help a couple decide
which car they should purchase.
CAR PURCHASE EXAMPLE
The couple is considering three criteria: cost, safety,
and appearance.
They have narrowed their alternatives to three
specific cars: Honda, Mazda, and Volvo.
We demonstrate how to build the AHP hierarchy in
Expert Choice.
EXPERT CHOICE: FILE SETUP
Select the File, New option and enter a file name
such as CARS.EC1. (You must use the EC1 file
extension.)
Choose the Direct option to create the model. Next,
specify the description of the goal, such as, “Select
the best car.”
EXPERT CHOICE: FILE SETUP
To enter the criteria, use the Edit, Insert command.
Use the Esc key when finished entering the
criteria.
To add the alternative cars under the cost node,
simply highlight the cost node and again use the
Edit, Insert command. Use the Esc key when
finished.
EXPERT CHOICE: FILE SETUP
To include the same alternatives under the other
criteria nodes, first highlight the cost node, then
select Edit, Replicate children of current node, To
Peers, Yes.
Double-click on the goal node to display the
complete hierarchy.
Additional details can be found in the Expert Choice
tutorial provided with the software.
ANALYZING THE HIERARCHY
1. Determine the weights of the alternatives for each
criterion.
2. Determine the priorities or weights of the criteria
in achieving the goal.
3. Determine the overall weight of each alternative in
achieving the goal. This is accomplished by
combining the results of the first two stages and is
called synthesis.
HYPOTHETICAL DATA FOR CAR
PURCHASE EXAMPLE
Car
Honda
Mazda
Volvo
Cost
$22,000
28,500
33,000
Safety*
28
39
52
Appearance
Sporty
Slick
Dull
* Safety Rating from a consumer testing service - the
higher the number, the safer the car.
DETERMINING PRIORITIES
The couple begins by making pairwise comparison
judgments between each pair of cars for the cost
criterion.
In our example, three judgments are needed: Honda
to Mazda, Mazda to Volvo, and Honda to Volvo.
STANDARD 1 - 9 MEASUREMENT SCALE
Intensity of Importance
1
3
Definition
Equal importance
Moderate importance
5
Strong importance
7
Very strong
9
Extreme importance
2, 4, 6, 8
1.1 - 1.9
Reciprocals of above
For compromise
values
For tied activities
If activity A has
one of the above
numbers assigned
to it when compared
with activity B,
then B has the
reciprocal value
when compared to A.
Explanation
Two activities contribute equally
Experience and judgment slightly favor one
activity over another
Experience and judgment strongly favor one
activity over another
An activity is favored very strongly over
another
The evidence favoring one activity over
another is of the highest possible order
of affirmation
Sometimes one needs to interpolate a
compromise between the above judgment
numerically because there is no good
word to describe it
When elements are close and nearly
indistinguishable; moderate is 1.3 and
extreme is 1.9
For example, if the pairwise comparison of
A to B is 3.0, then the pairwise comparison
of B to A is 1/3
COST PAIRWISE COMPARISONS
The pairwise comparisons are represented in the
form of pairwise comparison matrices.
The computation of the weights are also shown.
Consider the pairwise comparison matrix to compare
the cars for the cost criterion.
Remember that the costs of the three cars are:
$22000, $28500, and $33000, respectively.
COST PAIRWISE COMPARISONS
If we compare the Honda to the Honda, obviously
they are equal.
Therefore, a 1 (equal preferred) is placed in the first
row, first column entry of the matrix.
COST PAIRWISE COMPARISONS
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
22K
Honda
1
28.5K
Mazda
33K
Volvo
Volvo
COST PAIRWISE COMPARISONS
The other entries along the main diagonal of the
matrix are also 1.
This simply means that everything is equally
preferred to itself.
COST PAIRWISE COMPARISONS
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
22K
Honda
1
28.5K
Mazda
1
33K
Volvo
Volvo
1
COST PAIRWISE COMPARISONS
Suppose we believe the Honda ($22000) is equally
to moderately preferred to the Mazda ($28500).
Place a 2 in the row 1, column 2 entry.
Some might argue that the Honda should be 1.295
times better than the Mazda (28,500/22,000).
COST PAIRWISE COMPARISONS
Do you agree?
It depends!
For some, $28,500 is significantly greater than
$22,000, implying a judgments greater than 1.295.
Others with a lot of money may perceive virtually no
difference between the two costs, implying a
judgment somewhere between 1 and 1.295.
COST PAIRWISE COMPARISONS
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
22K
Honda
1
2
28.5K
Mazda
1
33K
Volvo
Volvo
1
COST PAIRWISE COMPARISONS
If the Honda is 2 times better than the Mazda, this
implies that the Mazda ($28500) is one half as
good as the Honda ($22000).
The reciprocal judgment, (1/2), should be placed in
the row 2, column 1 entry of the matrix.
COST PAIRWISE COMPARISONS
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
22K
Honda
1
2
28.5K
Mazda
1/2
1
33K
Volvo
Volvo
1
COST PAIRWISE COMPARISONS
Suppose that we judge the Mazda ($28500) to be
equally to moderately preferred to the Volvo
($33000).
The following judgments would be entered in the
matrix.
COST PAIRWISE COMPARISONS
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
22K
Honda
1
2
28.5K
Mazda
1/2
1
33K
Volvo
1/2
Volvo
2
1
COST PAIRWISE COMPARISONS
Assuming perfect consistency of judgments, we
would expect that the Honda ($22000) is 4 times
(that is, moderately to strongly) preferred to the
Volvo ($33000).
We will relax this assumption later.
COST PAIRWISE COMPARISONS
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
22K
Honda
1
2
28.5K
Mazda
1/2
1
33K
Volvo
1/4
1/2
Volvo
4
2
1
COST PAIRWISE COMPARISONS
The matrix is now complete and the weights for each
car (for the cost criterion) can be computed.
The exact computational procedure is implemented
in Expert Choice. For details see Expert Choice
homepage and download AHPDEMO.EXE.
COST PAIRWISE COMPARISONS
A simple three step procedure can be used to
approximate the weights for each alternative.
Essentially, this procedure normalizes the ratios of
the judgments between any pair of alternatives.
COST PAIRWISE COMPARISONS
1.
2.
3.
SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.
COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
22K
Honda
1
2
28.5K
Mazda
1/2
1
33K
Volvo
1/4
1/2
------------COLUMN TOTALS
Volvo
4
2
1
-------
COST PAIRWISE COMPARISONS
1.
2.
3.
SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.
COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
22K
Honda
1
2
28.5K
Mazda
1/2
1
33K
Volvo
1/4
1/2
------------COLUMN TOTALS
7/4
7/2
Volvo
4
2
1
------7
COST PAIRWISE COMPARISONS
1.
2.
3.
SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.
COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
22K
Honda
1
2
28.5K
Mazda
1/2
1
33K
Volvo
1/4
1/2
------------COLUMN TOTALS
7/4
7/2
Volvo
4
2
1
------7
COST PAIRWISE COMPARISONS
1.
2.
3.
SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.
COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
22K
Honda
1
2
28.5K
Mazda
1/2
1
33K
Volvo
1/4
1/2
------------COLUMN TOTALS
7/4
7/2
Volvo
4
2
1
------7
B. ADJUSTED COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
Honda
4/7*
4/7
Mazda
2/7
2/7
Volvo
1/7
1/7
Volvo
4/7
2/7
1/7
* This entry is obtained by dividing the Honda entry in the original matrix (1)
by the Honda column total (7/4).
COST PAIRWISE COMPARISONS
Notice that no variation is seen across the rows
because the judgments are perfectly consistent.
For the third column, judgments totaling 7 were
awarded. The Honda received 4 of 7 (57.1%), the
Mazda 2 of 7 (28.6%), and the Volvo 1 of 7
(14.3%) of the weight.
Similar comparisons can be made for the other two
columns.
COST PAIRWISE COMPARISONS
1.
2.
3.
SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.
COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
22K
Honda
1
2
28.5K
Mazda
1/2
1
33K
Volvo
1/4
1/2
------------COLUMN TOTALS
7/4
7/2
Volvo
4
2
1
------7
B. ADJUSTED COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
Honda
4/7*
4/7
Mazda
2/7
2/7
Volvo
1/7
1/7
Volvo
4/7
2/7
1/7
* This entry is obtained by dividing the Honda entry in the original matrix (1)
by the Honda column total (7/4).
COST PAIRWISE COMPARISONS
1.
2.
3.
SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.
COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
22K
Honda
1
2
28.5K
Mazda
1/2
1
33K
Volvo
1/4
1/2
------------COLUMN TOTALS
7/4
7/2
B. ADJUSTED COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
Honda
4/7*
4/7
Mazda
2/7
2/7
Volvo
1/7
1/7
Volvo
4
2
1
------7
Volvo
4/7
2/7
1/7
TOTAL
WEIGHTS
(ROW AVG.)
0.571
0.286
0.143
--------1.000
* This entry is obtained by dividing the Honda entry in the original matrix (1)
by the Honda column total (7/4).
EXPERT CHOICE: Entering Judgments
Expert Choice offers a variety of modes for entering
the judgments.
Highlight the cost node, select Assessment.
There are three options: Pairwise, Data, and Ratings.
Ratings will be discussed later.
EXPERT CHOICE: Entering Judgments
The Data option allows the user to enter data items
for each alternative, for example, costs, miles per
gallon, and number of defects.
Expert Choice takes the ratio of these data items and
converts them into pairwise comparisons.
What assumption are you making if you use the Data
option?
The data items have a linear preference scale, that
is, a $20,000 car is twice as good as a $40,000 car.
EXPERT CHOICE: Entering Judgments
To enter our cost judgments choose Pairwise.
When comparing alternatives select Preference for
Type; for criteria select Importance.
Modes options are: Verbal, Matrix (numerical),
Questionnaire, and Graphic.
Assessment, Pairwise, Matrix is demonstrated.
Enter judgments, Calculate and Record.
INCONSISTENCY OF JUDGMENTS
Since our pairwise comparisons were perfectly
consistent, Expert Choice reports
INCONSISTENCY RATIO = 0.0.
If this ratio is greater than 0.1 some revision of
judgments is required.
Select Inconsistency (within Assessment, Pairwise)
to identify the most inconsistent judgments.
INCONSISTENCY OF JUDGMENTS
Inconsistency of judgments may result from:
problems of estimation;
errors between the comparisons;
or, the comparisons may be naturally inconsistent.
INCONSISTENCY OF JUDGMENTS
One example of natural inconsistency is in a sporting
contest.
If team A is twice as likely to beat team B, and if
team B is three times as likely to beat team C, this
does not necessarily imply that team A is six times
as likely to beat team C.
This inconsistency may result because of the way
that the teams “match-up” overall.
INCONSISTENCY OF JUDGMENTS
The point is not to stop inconsistency from
occurring.
Make sure that the level of inconsistency remains
within some reasonable limit.
INCONSISTENCY OF JUDGMENTS
How does a judgment change affect the car weights?
Suppose the Mazda to Volvo changes from 2 to 3.
This obviously changes the comparison for Volvo to
Mazda from (1/2) to (1/3).
The judgments are now somewhat inconsistent.
COST PAIRWISE COMPARISONS
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
22K
Honda
1
2
28.5K
Mazda
1/2
1
33K
Volvo
1/4
1/3
Volvo
4
3
1
COST PAIRWISE COMPARISONS
1.
2.
3.
SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.
COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
22K
Honda
1
2
28.5K
Mazda
1/2
1
33K
Volvo
1/4
1/3
------------COLUMN TOTALS
7/4
10/3
Volvo
4
3
1
------8
COST PAIRWISE COMPARISONS
1.
2.
3.
SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.
COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
22K
Honda
1
2
28.5K
Mazda
1/2
1
33K
Volvo
1/4
1/3
------------COLUMN TOTALS
7/4
10/3
Volvo
4
3
1
------8
B. ADJUSTED COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
Honda
4/7*
6/10
Mazda
2/7
3/10
Volvo
1/7
1/10
Volvo
4/8
3/8
1/8
* This entry is obtained by dividing the Honda entry in the original matrix (1)
by the Honda column total (7/4).
COST PAIRWISE COMPARISONS
1.
2.
3.
SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.
COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
22K
Honda
1
2
28.5K
Mazda
1/2
1
33K
Volvo
1/4
1/3
------------COLUMN TOTALS
7/4
10/3
B. ADJUSTED COST PAIRWISE COMPARISON MATRIX
Honda
Mazda
Honda
4/7*
6/10
Mazda
2/7
3/10
Volvo
1/7
1/10
Volvo
4
3
1
------8
Volvo
4/8
3/8
1/8
TOTAL
WEIGHTS
(ROW AVG.)
0.557
0.320
0.123
-------1.000
* This entry is obtained by dividing the Honda entry in the original matrix (1)
by the Honda column total (7/4).
INCONSISTENCY OF JUDGMENTS
The new weights are: 0.557, 0.320, and 0.123. The
inconsistency resulted in some change in the
original weights of 0.571, 0.286, and 0.143.
As expected, the weight for the Mazda increased
while the weight for the Volvo decreased.
The weights now vary across each row. Essentially,
inconsistency measures the degree of variation
across the rows.
EXPERT CHOICE: Revising Judgments
Highlight cost node, select Assessment, Pairwise.
Enter a 3 in the Mazda to Volvo cell then Calculate.
The weights of 0.558, 0.320, and 0.122 are slightly
different from the three-step procedure weights.
This is not due to rounding -- Expert Choice gives
the exact results.
The INCONSISTENCY RATIO is now 0.02.
INCONSISTENCY OF JUDGMENTS
The weights can also be used to measure the
effectiveness of the alternatives.
For example, based on all pairwise comparisons, we
determined that the Honda is 1.74 (0.558/0.320)
times better than the Mazda.
Why is this ratio 1.74 and not the pairwise
comparison of 2?
Inconsistency in the judgments!
REMAINING COMPUTATIONS
Next, the cars must be pairwise compared for the
safety criterion and then for the appearance
criterion.
These judgments are shown on the next page.
Since the Mazda to Honda safety comparison is 2,
highlight the Honda to Mazda cell, click Invert,
and enter 2.
This judgment now appears in red.
SAFETY & APPEARANCE JUDGMENTS
Safety Pairwise Comparison Matrix
Honda
Mazda
28
Honda
1
1/2
39
Mazda
2
1
52
Volvo
5
4
Appearance Pairwise Comparison Matrix
Honda
Mazda
SportyHonda
1
5
Slick Mazda
1/5
1
Dull Volvo
1/9
1/2
Volvo
1/5
1/4
1
Volvo
9
2
1
REMAINING COMPUTATIONS
Next, the criteria must be pairwise compared.
These judgments are shown on the next page.
There are no data to support these judgments since
they are purely a reflection of your preferences.
CRITERIA JUDGMENTS
Original Criteria Pairwise Comparison Matrix
Cost
Safety
Appearance
Cost
1
1/2
3
Safety
2
1
5
Appearance 1/3
1/5
1
REMAINING COMPUTATIONS
The last stage computes the final weights for each car.
Multiply the criteria weight by the car weight for each
criterion and then sum over all criteria.
This is nothing more than a weighted average.
The computational results are shown next.
FINAL CAR WEIGHTS
CARS
Honda
Mazda
Volvo
CRITERIA WEIGHTS
COST
SAFETY
APPEARANCE
0.309
0.582
0.109
FINAL WEIGHTS
0.558
0.117
0.761
0.320
0.200
0.158
0.122
0.683
0.082
FINAL CAR WEIGHTS
CARS
Honda
Mazda
Volvo
CRITERIA WEIGHTS
COST
SAFETY
APPEARANCE
0.309
0.582
0.109
FINAL WEIGHTS
0.558
0.117
0.761
0.324
0.320
0.200
0.158
0.122
0.683
0.082
Honda: (0.558)(0.309) + (0.117)(0.582) + (0.761)(0.109) = 0.324
0.173
0.068
0.083
FINAL CAR WEIGHTS
CARS
Honda
Mazda
Volvo
CRITERIA WEIGHTS
COST
SAFETY
APPEARANCE
0.309
0.582
0.109
FINAL WEIGHTS
0.558
0.117
0.761
0.324
0.320
0.200
0.158
0.232
0.122
0.683
0.082
Honda: (0.558)(0.309) + (0.117)(0.582) + (0.761)(0.109) = 0.324
0.173
0.068
0.083
Mazda: (0.320)(0.309) + (0.200)(0.582) + (0.158)(0.109) = 0.232
0.099
0.116
0.017
FINAL CAR WEIGHTS
CARS
Honda
Mazda
Volvo
CRITERIA WEIGHTS
COST
SAFETY
APPEARANCE
0.309
0.582
0.109
FINAL
0.558
0.117
0.761
0.320
0.200
0.158
0.122
0.683
0.082
WEIGHTS
0.324
0.232
0.444
Honda: (0.558)(0.309) + (0.117)(0.582) + (0.761)(0.109) = 0.324
0.173
0.068
0.083
Mazda: (0.320)(0.309) + (0.200)(0.582) + (0.158)(0.109) = 0.232
0.099
0.116
0.017
Volvo: (0.122)(0.309) + (0.683)(0.582) + (0.082)(0.109) = 0.444
0.038
0.397
0.009
LOCAL VS GLOBAL WEIGHTS
For cost, the local weights for the cars are 0.558, 0.320,
and 0.122 and sum to 1.000.
The global weights are computed by multiplying the cost
criterion weight by the local car weights.
The global weights are 0.173, 0.099, and 0.038 and sum to
the cost criterion weight of 0.309.
EXPERT CHOICE: Synthesis
To compute the final weights select Synthesis (from
GOAL).
Choose Distributive Mode and Display Summary.
Details provides the global weights.
The output can also be exported to a spreadsheet
using the Utilities, Export Model(s) to Spreadsheet
commands.
EXPERT CHOICE: Printing
The Print icon can be used to select certain options.
The recommended print options are: Entire Tree,
Tree Views, Judgments/Data, and Synthesis.
INTERPRETING THE RESULTS
The final weights provide a measure of the relative
performance of each alternative.
It is important to properly interpret the meaning of
these numbers.
The Volvo is ranked first, the Honda second, and
Mazda third.
The Volvo is preferred 1.37 (0.444/0.324) times
more than the Honda.
INTERPRETING THE RESULTS
Should we buy the Volvo?
The output is a decision-making aid and cannot
replace the decision-maker.
The results can be used to support discussion and
possibly the judgments will be revised.
This iterative process is quite normal.
AHP can help to facilitate communication and
generate consensus between different groups.
SENSITIVITY ANALYSIS
Sensitivity analysis is an important aspect of any
decision-making process.
Sensitivity analysis determines whether small changes
in judgments affects the final weights and rankings
of the alternatives.
If so, the decision-maker may want to review the
sensitive judgments.
EXPERT CHOICE: Sensitivity Analysis
In Expert Choice sensitivity analysis from the GOAL
shows how the weights and the rankings of the
alternatives change if some or all of the criteria
weights change.
There are five graphical sensitivity analysis modes
available: Performance, Dynamic, Gradient, TwoDimensional, and Difference.
The first three show how a change in a criterion
weight affects the final weights of the alternatives.
EXPERT CHOICE: Sensitivity Analysis
The last two show how the alternatives perform with
respect to any two criteria.
Performance: places all sensitivity information on a
single chart with horizontal line graphs for the
alternatives linked to vertical bars for the criteria.
Dynamic: two sets of dynamically linked horizontal
bar graphs: one for criteria and one for
alternatives.
EXPERT CHOICE: Sensitivity Analysis
Gradient: a line graph that shows how the weights of
the alternatives vary according to the weight
assigned to a specific criterion. (Use the X-Axis to
change the selected criterion.)
Two-Dimensional: shows how well the alternatives
perform with respect to any two criteria.
Difference: a graph that shows the differences
between any two alternatives for any criterion.
EXPERT CHOICE: Sensitivity Analysis
An important use of sensitivity analysis is to
determine how much a given criterion weight
must change before there is a change in the
rankings of the two highest alternatives.
This type of breakeven analysis can be easily done in
Expert Choice.
EXPERT CHOICE: Sensitivity Analysis
Choose Dynamic from the Sensitivity-Graphs option.
Drag the cost criterion bar 30.9% to approximately
45.9%, and see that the Volvo and Honda have the
same highest final weight.
The final rankings are relatively insensitive to a
change in the cost criterion weight because the
cost weight had to be increased by almost 50% to
get a change in the rankings.
NEW PRODUCT INTRODUCTION
CHOCK-FUL-O-CHIPS developed the following
hierarchy and data that can be used to help decide
which chocolate chip recipe they should use.
Select the best recipe
Taste
Cost
Fat Content
Recipe 1
Recipe 1
Recipe 1
Recipe 2
Recipe 2
Recipe 2
Recipe 3
Recipe 3
Recipe 3
Recipe 4
Recipe 4
Recipe 4
RECIPE DATA
Recipe
1
2
3
4
Cost*
$0.166
0.099
0.265
0.224
Taste
Fat Content
Rating** (Grams)*
54%
8.0
24%
7.0
20%
3.5
43%
6.0
* Per one ounce cookie
** Percentage of people who rated a cookie either an 8 or 9
on a 9-point scale, where 9 means extremely liked, 8
means liked very much, and down to one which means
extremely disliked.
TASTE PAIRWISE COMPARISON
MATRIX
Recipe 1
Recipe 2
Recipe 3
Recipe 4
54%
24%
20%
Recipe 1 Recipe 2 Recipe 3
1
1
1
43%
Recipe 4
1
COST PAIRWISE COMPARISON
MATRIX
Recipe 1
Recipe 2
Recipe 3
Recipe 4
0.166
0.099
0.265
Recipe 1 Recipe 2 Recipe 3
1
1
1
0.224
Recipe 4
1
FAT CONTENT PAIRWISE
COMPARISON MATRIX
Recipe 1
Recipe 2
Recipe 3
Recipe 4
8.0
7.0
3.5
Recipe 1 Recipe 2 Recipe 3
1
1
1
6.0
Recipe 4
1
CRITERIA PAIRWISE
COMPARISON MATRIX
Taste
Cost
Fat Content
Taste
1
Cost
Fat Content
1
1
FINAL WEIGHTS FROM EXPERT
CHOICE
Criteria Weights
Taste
Cost
Fat Content
Final
Weights
Recipe 1
Recipe 2
Recipe 3
Recipe 4
SUMMARY
In this chapter:
we provided an overview of operations management;
and
offered the AHP as a decision-making process with
application in operations management.
SUMMARY
AHP benefits include:
natural way to elicit judgments;
measure degree of inconsistency;
easy to use;
allows broad participation; and
fully supported by Expert Choice.