Transcript Decision Technology Modeling, Software and Applications Matthew J. Liberatore Robert L. Nydick John Wiley & Sons, Inc.

Decision Technology
Modeling, Software and
Applications
Matthew J. Liberatore
Robert L. Nydick
John Wiley & Sons, Inc.
THE AHP: OVERVIEW
What is the Analytic Hierarchy Process (AHP)?
The AHP, developed by Tom Saaty, is a
decision-making method for prioritizing
alternatives when multi-criteria must be
considered.
An approach for structuring a problem as a
hierarchy or set of integrated levels.
THE AHP: OVERVIEW
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.
If additional detail is needed to describe the problem (e.g.,
initial purchase price, estimated yearly maintenance, and
trade-in value) then subcriteria can be created.
Arguably the most important part of the entire AHP process
is creating the hierarchy.
THE AHP: OVERVIEW
How does AHP really work? Simply put, 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.
PAIRWISE COMPARISONS
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.
PAIRWISE COMPARISONS
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.
PAIRWISE COMPARISONS
Individual AHP judgments are called pairwise
comparisons.
These judgments can be based on objective or subjective
information.
When criteria are being compared (e.g., taste and # of
grams of fat if Chips Ahoy wants to evaluate a new
cookie recipe), comparisons may be based on
strategic issues.
Alternative pairwise comparisons require data (e.g.,
actual # of grams of fat for each recipe).
WEIGHTS
The AHP uses eigenvalues and eigenvectors to
compute criteria, subcriteria, and alternative
weights for each factor based on the pairwise
comparisons.
Final alternative weights are determined using a
simple weighted average computation.
Example: FINAL CAR WEIGHTS
CRITERIA WEIGHTS
COST
0.309
CARS
Honda
Mazda
Volvo
0.558
0.320
0.122
SAFETY
0.582
0.117
0.200
0.683
APPEARANCE
0.109
FINAL
0.761
0.158
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
CONSISTENCY
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.
DECISION LENS
AHP does not require perfect consistency,
however, it does provide a measure of
consistency.
Software (Decision Lens) is available to support
all AHP analysis.
As a decision support tool, Decision Lens helps
with the creation of the hierarchy as well as
conducting sensitivity analysis (measuring the
impact that changes to the criteria weights
have on the final alternative weights).
MULTI-LEVEL HIERARCHIES
Tom Saaty suggests that hierarchies be
limited to nine levels and nine items per
level.
Brainstorming can identify several dozen
criteria.
In this case, related items are grouped into
categories, creating additional levels in
the hierarchy, that is, criteria and
subcriteria. This also helps to keep
consistency acceptable.
RATINGS
If many alternatives need to be evaluated,
then typically a ratings approach is used.
The ratings approach requires setting up a
ratings scale under each criterion.
Pairwise comparisons are needed to
determine the relative importance of each
ratings scale category (intensity).
Alternatives are not pairwise compared in a
rating model, rather alternatives are rated
for each criterion.
GROUP DECISION MAKING
There are many ways of applying AHP to
support a group decision-making process.
For example, all of the parties discuss,
debate, and eventually agree on each
pairwise comparison entry.
Another approach is to achieve consensus
mathematically.
Each participant provides their own
judgments for each pairwise comparison
and the results must be averaged.
GROUP DECISION MAKING
For example, suppose two individuals compared
cost to safety and provide judgments of 9 and
1/9.
The arithmetic mean is 4.56 ((9+(1/9))/2). Do you
think this is the best estimate?
Probably not! Since both judgments are at
opposite ends of scale, we would expect the
combined judgment to be 1.00.
The geometric mean produces this result.
In general, if there are n individuals that provide
judgments, the geometric mean is defined as the
nth root of the product of the n judgments.
GROUP DECISION MAKING
As another example, in comparing cost to
safety suppose the judgments of three
individuals are 2, 4, and 8.
The geometric mean is the cube root of
their product (64) which is 4.
Decision Lens manages the entire group
decision making process and achieves
consensus mathematically by computing
the geometric mean.
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?
Health Technology Assessment
There was a need to perform a health technology
assessment for the selection of expensive
neonatal ventilators for a new women’s health
addition at a hospital.
The small size of premature babies (as little as 1
pound) presents many electromechanical
requirements.
Neonatal ventilators must be able to accurately
deliver rapid, tiny puffs of precisely blended air
and oxygen. If not, damage could be done to the
babies lungs.
Health Technology Assessment
Neonatal ventilators range in price from around
$18,000 to nearly $40,000 and features vary
widely. They also have a significant life-cycle
cost of ownership due to supplies and
maintenance, which can be much larger than the
original purchase price.
This hospital was looking to purchase 24 or more
units, thus making this a million-dollar
commitment.
Two senior department directors (Respiratory
Therapy (RT) and Clinical Engineering (CE))
worked on this project.
Health Technology Assessment
The RT provides the routine clinical staffing to
support the patients and the CE evaluates,
installs, inspects, repairs, and maintains the
devices.
Before meeting with the directors, we produced a
simplistic hierarchy (ventilator1.ahp). This is
important since neither director had any AHP
experience.
Each director then focused on the parts of the
hierarchy that most impacted their work,
changing, adding, or deleting criteria and
subcriteria.
Health Technology Assessment
These brainstorming sessions are critical to success
in that ideas need time to “ferment.”
There were five iterations and the final hierarchy is
provided in ventilator6.ahp.
Focus next shifted to the alternatives. Since there
were 46 bottom level subcriteria and possibly a
dozen ventilators, the ratings approach was used.
The directors created and defined the ratings scale
intensities. This allowed easy ventilator
evaluation as it was understood what
performance was required to achieve each rating.
Health Technology Assessment
Several of the ratings terms, descriptions, and
final weights are shown below. Hospital staff
can easily grasp the meaning of this information
and can also interpret the weights.
Health Technology Assessment
Subcriteria and criteria pairwise comparison were
next performed. Again, each director took the
lead for their part of the hierarchy.
This did not work for the criteria comparisons. In
this case, both directors worked together to reach
a consensus for these pairwise comparisons.
Criteria and subcriteria were ranked before
conducting pairwise comparisons. This way the
directors did not have to worry about the
direction of preference. It also helped with
consistency. They also chose the graphical
comparison mode.
Health Technology Assessment
Each director was shown the pairwise comparison
screen after the weights were computed. The
weights are visually depicted as shaded bars where
each criterion name appears. Each director had an
opportunity to make “minor” changes to the
weights if desired. The bars can be moved and
Expert Choice will determine the pairwise
comparisons that produced these revised weights.
Health Technology Assessment
The final weights for each ventilator appear in
ventilator7.ahp.
The directors felt comfortable with these results.
They believed that AHP allowed them to easily
identify what criteria were important to them and
then to capture their judgments that reflected the
importance of each factor.
The AHP results will be used to help them make a
final ventilator decision.
COPYRIGHT
Copyright  2003 Matthew J. Liberatore and Robert L. Nydick.
All rights reserved. Reproduction or translation of this work
beyond that named in Section 117 of the United States
Copyright Act without the express written consent of the
copyright owners is unlawful. Requests for further
information should be addressed to Matthew J. Liberatore and
Robert L. Nydick. Adopters of the textbook are granted
permission to make back-up copies for their own use only, to
make copies for distribution to students of the course the
textbook is used in, and to modify this material to best suit
their instructional needs. Under no circumstances can copies
be made for resale. Matthew J. Liberatore and Robert L.
Nydick assume no responsibility for errors, omissions, or
damages, caused by the use of these programs or from the use
of the information contained herein.