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T H E A N A L Y T I C H I E R A R C H Y P R O C E S S
USER'S GUIDE AND REFERENCE MANUAL
Release 3.01
___________________________________________________________________________
This software is provided to you for evaluation use only. If you
find the software useful, please register it. With your registration
you will not only receive technical support and the latest version
of software, but you will also be sponsoring the continued support
and future enhancements of this product.
___________________________________________________________________________
AHP - Analytic Hierarchy Process, Release 3.01
The Modern Art of Decision Making
Program Serial No. 9312400
Changes are periodically made to the information herein; these changes will
be incorporated in new editions of this publication.
A Product Comment Form is provided at the front of this publication. If
this form has been removed, you can mail any comments to the address below:
Armada Systems
P.O. Box 637, Station A
Downsview, Ontario
M3M 3A9
Canada
DAS, DMM, PCM, DME and MyBASE are Trademarks of Armada Systems.
Copyright (C) 1986-1993, Armada Systems
All Rights Reserved
Made in Canada
For your records:
NAME ____________________________ TITLE __________________________________
COMPANY _________________________ DEPARTMENT _____________________________
DATE PROGRAM RECEIVED ___________ OBTAINED FROM __________________________
TABLE OF CONTENTS
PAGE
ARMADA SYSTEMS LICENSE AGREEMENT ....................... i
PRODUCT COMMENT FORM ................................... ii
GETTING STARTED ........................................ iii
CREATING A WORKING COPY OF AHP iii
DISK CONTENTS iv
1.0 THE ANALYTIC HIERARCHY PROCESS .................... 1
1.1 INTRODUCTION 1
1.2 THEORY OF OPERATION 2
1.2.1 Pairwise comparisons and inconsistency 2
1.2.2 Example 2
1.3 USING THE AHP 4
1.3.1 Pairwise comparisons for level 1 5
1.3.2 Pairwise comparisons for level 2 7
1.3.3 Relative impact on overall goal 8
1.4 SAMPLE PROBLEMS 9
1.4.1 Estimating relative lengths of lines 9
1.4.2 Benefit/Cost analysis 11
1.4.3 Application to psychotherapy 18
1.4.4 Calculating expected values 19
1.4.5 Determining optimum type of coal plant 20
2.0 PROGRAM CONFIGURATION ............................. 21
3.0 ABOUT ARMADA SYSTEMS .............................. 22
3.1 THE DECISION MATRIX EXPERT (DME) 23
3.1.1 Applications 23
3.1.2 System requirements 23
3.2 MyBASE 24
3.2.1 Quick overview of features 24
3.2.2 System requirements 25
4.0 ORDERING SOFTWARE: WHAT YOU WILL RECEIVE ........... 26
ARMADA SYSTEMS SOFTWARE REGISTRATION AND ORDER FORM .... 27
REFERENCES ............................................. 28
AHP i
ARMADA SYSTEMS LICENSE AGREEMENT
Read this agreement carefully. Use or distribution of this product consti-
tutes your acceptance of the terms and conditions of this agreement!
GENERAL LICENSE TERMS
This documentation and the software described in it are copyrighted with
all rights reserved worldwide by Armada Systems. Under the copyright laws,
neither the documentation nor the software may be copied, photocopied,
reproduced, translated, modified, reverse engineered, or reduced to any
electronic medium or machine readable form, in whole or in part, except as
specifically authorized below, without the prior written consent of Armada
Systems.
Armada Systems specifically authorizes individuals and organizations to
make complete unaltered copies of this software, for the purpose of free
distribution to other individuals or organizations. This software and
documentation may not be sold, no fee must be involved in the distribution
of this software except, for a small reasonable fee to cover the cost of
any distribution media and service charges. This software which consists of
application programs, data files and documentation, are a complete entity
which must not be separated or altered in any way shape or form.
Individuals or organizations who wish to distribute or market this software
for the purpose of financial or other material gain, must first receive the
authorization to do so by contacting Armada Systems.
Armada Systems authorizes the use of this software for non-commercial,
educational, and evaluation purposes only. If you are using or intend to
use this software for any other purposes, then you must register with
Armada Systems by purchasing the commercial version of the software.
Copying (except for back-up purposes) and distribution of software provided
to registered users is not permitted.
DISCLAIMER
This documentation and the software described in it are provided "as is,"
without any warranty as to their performance, accuracy, or freedom from
error, or as to any results generated through their use. Armada Systems
excludes without limitation any and all implied warranties, including
warranties of merchantability and fitness for a particular purpose. You
assume the entire risk as to the results and performance of the software
and documentation.
Armada Systems will under no circumstances be liable for any direct,
indirect, special, incidental, or consequential damages arising out of the
use or inability to use the software or documentation, even if advised of
the possibility of such damages.
GENERAL
Should you have any questions concerning this Agreement, you may contact
Armada Systems by writing to the address given at the front of this manual.
3.01 - 9312400 AHP ii
PRODUCT COMMENT FORM
Use this form if you have any comments or suggestions regarding the AHP
program or this manual. Mail your comments to:
Armada Systems
P.O. Box 637, Station A
Downsview, Ontario
M3M 3A9
Canada
NAME_________________________________ TITLE________________________________
COMPANY______________________________ DEPARTMENT___________________________
ADDRESS____________________________________________________________________
CITY_________________________________ STATE/PROVINCE_______________________
ZIP/POSTAL CODE______________________ COUNTRY______________________________
PHONE________________________________ FAX__________________________________
COMPUTER TYPE________________________ DOS VERSION__________________________
DATE PROGRAM RECEIVED________________ OBTAINED FROM________________________
COMMENTS/SUGGESTIONS:
AHP iii
GETTING STARTED
Before doing anything, we suggest that you make a working copy of the disk
supplied to you. You should then keep the original disk as a back-up copy,
in a safe place where it will not come in contact with any heat, dust, or
magnetic radiation. In the event that your working copy is ever damaged or
destroyed, you can always make a new copy from the original disk.
CREATING A WORKING COPY OF AHP
To make a working copy of AHP, simply follow one of the procedures below
corresponding to your computer system:
Hard disk system:
1. Boot-up DOS operating system
(you should see the C> prompt appear on screen).
2. Insert AHP floppy disk into drive A.
3. Type the following:
MD\AHP
CD\AHP
COPY A:*.* C:
4. To start using AHP, type the following:
CD\AHP
AHP
Floppy disk system:
1. Insert your DOS diskette into drive A.
2. Boot-up DOS operating system by either turning computer on, or
if already on, push the CTRL, ALT and DEL keys simultaneously
(you should see the A> prompt on screen).
3. Insert a blank diskette into drive B
4. Type the following:
FORMAT B:/S
5. When finished, replace the DOS disk in drive A with the AHP
diskette
6. Type the following:
COPY A:*.* B:
7. To start using AHP, do the following: insert the working copy
of AHP into drive A, boot-up computer and type AHP
AHP iv
DISK CONTENTS
AHP.EXE
Analytic Hierarchy Process program.
MANUAL.EXE
Program for printing this manual.
AHP.TXT
This manual.
AHP.CFG
Program configuration file defining screen colors and printer control
codes.
CAR.AHP
Sample file illustrating the use of the AHP in a car purchase problem.
LINE.AHP
File contains subjective pairwise comparisons of various lines in order
that their relative lengths may be estimated. See section 1.4.
BENEFIT.AHP & COST.AHP
These two files contain the hierarchical structure and subjective pairwise
comparisons of the benefits and costs associated with three large scale
transportation projects. Results are used in a benefit/cost analysis of
these projects. See section 1.4.
XYZCOMP.AHP
This sample file shows how a comparative performance evaluation of a
company's branch-plant offices may be conducted using AHP. The hierarchy
for this problem consists of braking the company down into major
departments (engineering, sales, manufacturing, etc...), considering
performance factors (productivity, quality, profitability, etc...), and
finally the various branch-plant offices.
AHP Pg. 1
1.0 ANALYTIC HIERARCHY PROCESS
1.1 INTRODUCTION
More often than not, the decisions you make in your personal or
professional life can be made without a lot of fuss. Either your best
choice is clear to you without much analysis, or the decision is not
important enough to warrant any great amount of attention. Occasionally,
however, you probably find yourself in a situation where you feel it is
worth your time and effort to think systematically and hard about the
different courses of action you might pursue. It is in these cases that the
Analytic Hierarchy Process (AHP) will be of most help to you.
When faced with a problem of choice, the AHP will help you in selecting an
alternative that is consistent with your personal basic judgments and
preferences. The AHP is designed to deal specifically with subjective
assessments and evaluations of alternatives and criteria. This package will
be most beneficial when you wish to model complex problems, and the only
data available to solve these problems is your own subjective judgments or
those of a group. The AHP is not only useful in decision making problems,
but also in any other area where you find it difficult to quantify
subjective data.
In addition to the AHP, a companion decision analysis program, the Decision
Matrix Expert (DME), is available separately from Armada Systems. Designed
to be used with primarily tangible and easily quantifiable data, the DME
models decisions by representing the problem in a matrix containing all the
information required to arrive at a final decision. The columns of this
matrix portray the criteria which are important to the decision, while the
rows depict the various alternatives being considered. Through its analysis
of the decision matrix, the DME will provide you with an unbiased ranking
of alternatives. In addition, by discarding dominated or substandard
alternatives, the DME will enable you to quickly narrow down the set of
alternatives you need to consider. See section 3.1 in this manual for more
details on this package and how to order it.
The AHP program will be most useful when data is not readily available or
when data is highly qualitative or subjective in nature. For those
occasions where you would like to be as objective as possible in a decision
problem, or where physical data is readily available, you should consider
obtaining the Decision Matrix Expert software package from Armada Systems.
The next section will provide an explanation of the method used by the AHP
to model problems. We will then proceed to a hands-on application of the
program, illustrating a practical example to clarify the method in greater
detail. Finally, a number of additional examples will be presented to
illustrate how the AHP may be used in many different applications. It is
strongly recommended that you look at these examples, as they are a source
of much information.
AHP Pg. 2
1.2 THEORY OF OPERATION
The technique used by the AHP is a proven scientific method, originally
developed by Thomas L. Saaty at the Wharton School and described in his
book "The Analytic Hierarchy Process" published by McGraw-Hill, 1980. We
will not go into the actual theory and mathematical formulations of the
method, because it is fairly involved. The interested reader can however
consult the book "The Analytic Hierarchy Process" for much greater detail
and more examples. Here, we shall be primarily concerned with the
application of the method.
The AHP requires that a problem be decomposed into a hierarchical model,
structured so as to capture it's basic elements. Hierarchical decomposition
involves setting up levels, where each level contains a set of elements.
These elements are grouped in such a way that those of a lower level
directly influence the elements in the immediately higher level, these in
turn must influence elements in the next level and so on up to the goal of
the hierarchy. The objective is to derive a set of quantitative weights for
elements in the last level which reflect, as best as possible, their
relative impact on the goal of the hierarchy. The way we accomplish this,
is to compare, in pairs, elements in each level, with respect to those
elements in the immediately higher level.
The advantage of setting up a problem in a hierarchical structure is that
it helps you in focusing your attention on each part of the problem
separately. Keep in mind however, that results obtained with the use of
this program will only be as good as the model you have constructed and the
data you have entered into it.
1.2.1 Pairwise comparisons and inconsistency
Pairwise comparisons are made using a 1 to 9 numerical scale. For example,
if elements A and B are being compared, a 1 would indicate that they are
both equal and a 9 would indicate that A is extremely better than B.
Intermediate values are used to arrive at a compromise between these two
extreme points. When we compare N elements in a level with respect to an
element in the immediately higher level, we would require N(N-1)/2
comparisons. That is, if 4 elements are being compared with each other,
then a total of 6 pairwise comparisons are needed. These pairwise
comparisons are entered into what is called a pairwise comparison matrix.
As well as being able to calculate subjective weights based on your
pairwise comparisons, the software will also provide you with an indication
of your judgment consistency, or inconsistency as it is referred to in the
program. Inconsistency in pairwise comparison judgments can best be
described with the following example: If you were comparing the weight of
three stones, and were to say that; stone A is heavier than stone B which
is heavier than C, and then say that stone C is heavier than A, then your
judgments would be inconsistent. In real life situations, one can not
escape the fact that many things are in fact inconsistent. For example, in
a game of sport team A can beat team B, team B can beat team C, but team C
can nevertheless beat team A. In general, a pairwise comparison matrix with
AHP Pg. 3
an inconsistency index of 1.0 or less is acceptable, and up to 1.5 can be
tolerated in some cases, but any more than this should result in a review
of the judgments. If the judgments are found to be a true representation of
the actual system, then the matrix should be left as is, though you should
remember the consequent higher margin of error when analyzing the results.
1.2.2 Example
Let's look at an example. Suppose your goal is to purchase a car and you
wish to model this decision using AHP. The first question you must ask
yourself is, what factors will influence your goal. Thinking a little bit
about this, you would probably come up with things such as price, fuel
economy, styling, reliability and so on. These would form the elements of
the first level. You would then ask yourself a similar question as before;
what factors would influence the price, fuel economy, styling and
reliability. The answer is obvious that a particular car will influence the
factors of level1. Therefore the second level in your decision hierarchy
will be comprised of the different types of cars which you are considering,
ie. your alternatives. Figure 1.1 illustrates this hierarchy in graphical
form:
╔════════╗
Level 0 ║ GOAL ║
╚════╤═══╝
│
┌───────────────┬────────┴───────┬───────────────┐
┌───┴───┐ ┌──────┴───────┐ ┌────┴────┐ ┌──────┴──────┐
Level 1 │ PRICE │ │ FUEL ECONOMY │ │ STYLING │ │ RELIABILITY │
└───┬───┘ └──────┬───────┘ └────┬────┘ └──────┬──────┘
│ │ │ │
├───────────────┼────────────────┼───────────────┤
│ │ │ │
┌───┴───┐ ┌───┴───┐ ┌───┴───┐ ┌───┴───┐
Level 2 │ CAR A │ │ CAR B │ │ CAR C │ │ CAR D │
└───────┘ └───────┘ └───────┘ └───────┘
Figure 1.1. Hierarchy for a car purchase problem.
This particular problem requires only 2 levels in the model to describe.
Highly complex models can however be created with up to 5 levels and 16
elements per level using the AHP program. The technique used in creating a
complex model would be the same as the one explained above.
Once the hierarchical model has been created, pairwise comparison data must
be entered into the computer. Elements in level 1 are first compared (in
pairs) with respect to the overall goal (level 0). For example, with
respect to a goal of purchasing a car, you would need to compare the
elements; price, fuel economy, styling and reliability with each other, in
pairs. The program will use these pairwise comparisons to arrive at a
quantitative weight for each element in level 1, which will depict that
element's subjective preference with respect to level 0.
AHP Pg. 4
The next step involves performing a pairwise comparison of elements in
level 2 (alternatives) with respect to elements in level 1 (price, fuel
economy, styling, etc...). Again this data will be used by the program to
arrive at a set of quantitative weights for each alternative with respect
to each criteria in level 1. When you have finished inputting all pairwise
comparison data, the program can calculate preference weights for the
alternatives (level 2) with respect to the overall goal (level 0). The
alternative with the highest score should be the alternative selected.
1.3 USING THE AHP
This section is intended to be used as a tutorial in learning how to use
the AHP program. A car purchase problem which is supplied on your diskette,
will be analyzed.
Once you have loaded the AHP, push F8, and type x followed by CAR (x is the
drive letter indicating where the file CAR.AHP is to be found) followed by
RTN. Once the file has been loaded, the computer display screen will look
something like this:
┌──────────────────────────────────────────────────────────────────────────────────┐
│ FILE:> C:CAR .AHP Copyright (C) 1986-1993, ARMADA SYSTEMS │
│ Decision Tree Hierarchy │
│ GOAL: To purchase a car. │
│ ╔══════════════╤══════════════╤══════════════╤══════════════╤══════════════╗ │
│ ║ Level 1 │ Level 2 │ Level 3 │ Level 4 │ Level 5 ║ │
│ ╔═══╬══════════════╪══════════════╪══════════════╪══════════════╪══════════════╣ │
│ ║ 1 ║Price │Mustang GT │ │ │ ║ │
│ ║ 2 ║Fuel econ. │Tempo Sport │ │ │ ║ │
│ ║ 3 ║Acceleraton │Prelude │ │ │ ║ │
│ ║ 4 ║Braking │Corolla GTS │ │ │ ║ │
│ ║ 5 ║Handling │VW GTI │ │ │ ║ │
│ ║ 6 ║Styling │ │ │ │ ║ │
│ ║ 7 ║ │ │ │ │ ║ │
│ ║ 8 ║ │ │ │ │ ║ │
│ ║ 9 ║ │ │ │ │ ║ │
│ ║10 ║ │ │ │ │ ║ │
│ ║11 ║ │ │ │ │ ║ │
│ ║12 ║ │ │ │ │ ║ │
│ ║13 ║ │ │ │ │ ║ │
│ ║14 ║ │ │ │ │ ║ │
│ ║15 ║ │ │ │ │ ║ │
│ ║16 ║ │ │ │ │ ║ │
│ ╚═══╩══════════════╧══════════════╧══════════════╧══════════════╧══════════════╝ │
│ │
│ 1HELP 2DATA 3NEXT 4GRAPH 5RUN 6PRINT 7ERASE 8OPEN 9SAVE 10QUIT │
└──────────────────────────────────────────────────────────────────────────────────┘
As indicated on the second line of the screen, this represents the decision
tree hierarchy. Compare the method used to express this hierarchy on
screen, with the method presented in Figure 1.1.
The bottom line lists the active function keys. To get a little more
information on what each key does push F1-HELP. Your computer display
screen should clear and list the following information:
AHP Pg. 5
HELP information:
F1 HELP - Display help information.
F2 DATA - Display pairwise comparison data.
F3 NEXT - Move to next level.
F4 GRAPH- Draw a bar graph of preference weights, ordered from best to worst.
F5 RUN - Calculate preference weights for the decision tree hierarchy.
F6 PRINT- Send data on screen to printer.
F7 ERASE- Erase a file.
F8 OPEN - Open a new AHP file.
F9 SAVE - Save current AHP file to disk.
F0 QUIT - Exit to DOS, (file not saved automatically).
ALT+S - Set screen colors and printer control data (stored in file AHP.CFG).
Decision tree navigation and edit keys:
ALT+I - Insert a new branch into the decision tree.
ALT+D - Delete a branch from the decision tree.
CTRL+ARROW keys - Move between levels (columns).
ARROW keys - Move within a level (column).
RETURN - Terminate input of present branch, move down to next line.
HOME - Move to the top of the next level (column).
END, PgDn - Move to the bottom of the present level (column).
PgUp - Move to the top of the present level (column).
The above help information not only indicates what each function key does,
but it also lists a set of navigation and edit keys. Play around a little
with these keys to get a better feel of the package. If you make any
changes to this file, make sure you don't push the F9 key as this will save
your changes to disk and the file CAR.AHP will be permanently altered. If
you wish to make a printout of this screen, push F6-PRINT. Use this key any
time you would like to obtain a hardcopy of the information on screen.
1.3.1 Pairwise comparisons for level 1
Position the cursor on the GOAL line (line 3) and push F2-DATA. This will
cause the pairwise comparison data to be displayed. Since the cursor was
positioned on the GOAL line, which represents level 0 in the hierarchy, the
data appearing on the screen will be the pairwise comparison matrix for
level 1 with respect to the GOAL, as follows:
┌──────────────────────────────────────────────────────────────────────────────────┐
│ FILE:> C:CAR .AHP Copyright (C) 1986-1993, ARMADA SYSTEMS │
│ Pairwise Comparison Data for level 1, with respect to: GOAL │
│ 1: Equal 3: Moderate 5: Strong 7: Very Strong 9: Extreme │
│ With respect to Goal Enter 1 to 9 (- for inverse) to indicate the │
│ relative importance or preference of: Price over Fuel econ. │
│ ════════════════════════════════════════════════════════════════════════════════ │
│ A B C D E F WEIGHTS │
│ A 3 4 4 4 2 A Price 37.6 │
│ B 2 2 2 -2 B Fuel econ. 14.8 │
│ C 1 -2 -3 C Acceleraton 7.3 │
│ D -2 -2 D Braking 7.9 │
│ E -2 E Handling 11.3 │
│ F F Styling 21.2 │
│ │
│ │
│ │
│ │
│ │
│ │
│ │
│ │
│ │
│ 1HELP 2TREE 3NEXT 4GRAPH 5RUN 6PRINT 7ERASE 8OPEN 9SAVE 10QUIT │
└──────────────────────────────────────────────────────────────────────────────────┘
AHP Pg. 6
Push the HELP key, to display the following information:
HELP information:
F1 HELP - Display help information.
F2 TREE - Display the decision tree hierarchy.
F3 NEXT - Move on to the next set of pairwise comparison data.
F4 GRAPH- Draw a bar graph of preference weights, ordered from best to worst.
F5 RUN - Calculate preference weights for this set of pairwise comparison data.
F6 PRINT- Send data on screen to printer.
F7 ERASE- Erase a file.
F8 OPEN - Open a new AHP file.
F9 SAVE - Save current AHP file to disk.
F0 QUIT - Exit to DOS, (file not saved automatically).
ALT+S - Set screen colors and printer control data (stored in file AHP.CFG).
Pairwise comparison data navigation and edit keys:
HOME - Move to the first comparison (top left).
ARROW keys - Move between comparisons.
RETURN, INS, TAB - Move to the next comparison.
DEL, BACKSPACE - Move to the previous comparison.
Now push any key, other than a function key, in order to return to the
pairwise comparison data. What we are trying to accomplish with this
matrix, is to derive a list of weights for each element in level 1, so as
to reflect quantitatively, as best as possible, our subjective importance
of these criteria with respect to our goal.
Let's have a look at the data which has been supplied. Since there are 6
elements in level 1 (Price, Fuel econ., Acceleraton, Braking, Handling, and
Styling), N(N-1)/2 or 15 comparisons are required.
The first number in the matrix is a 3, this indicates that when
contemplating a car purchase, price is moderately more important than fuel
economy . The next number is a 4 and this means that price is moderately to
strongly more important than acceleration, and so on. Notice that in the
fuel economy to styling comparison the matrix contains a -2, indicating
that styling is just slightly more important than fuel economy. A negative
just inverses the comparison. If you move the cursor around the matrix, the
elements which are being compared will be displayed on the fifth line of
your screen. Now if you push the "-" key at any spot in the matrix, you
will notice that the two elements printed on the fifth line will inverse.
An important point to remember is that if your goal is not to estimate
costs, then the first element is always preferred to the second.
Conversely, if you do wish to estimate costs, then the first element
presented on the fifth line of the pairwise comparison screen, should be
the element with the greater cost (see section 1.4.2). Therefore, to
inverse a comparison enter a negative number.
AHP Pg. 7
1.3.2 Pairwise comparisons for level 2
We have looked at level 1, now let's continue with the pairwise comparisons
for level 2 as given below. By pushing F3-NEXT, you can view this same data
on your screen. Notice that in level 2 there are 6 pairwise comparison
matrices; there is one for Price, one for Fuel econ., Acceleration,
Braking, Handling, and Styling. Whenever data is entered for this level we
must keep in mind with respect to what criteria the pairwise comparisons
are being made to. The second or fourth line on the display screen will
remind you of this.
Pairwise Comparison Data for level 2, with respect to: Price
A B C D E WEIGHTS
A -4 1 -2 -2 A Mustang GT 9.3 ▒▒
B 5 3 3 B Tempo Sport 46.0 ▒▒▒▒▒▒▒▒▒
C -3 -3 C Prelude 7.6 ▒
D 1 D Corolla GTS 18.6 ▒▒▒▒
E E VW GTI 18.6 ▒▒▒▒
Pairwise Comparison Data for level 2, with respect to: Fuel econ.
A B C D E WEIGHTS
A -3 -3 -3 -3 A Mustang GT 7.6 ▒▒
B 1 1 1 B Tempo Sport 22.7 ▒▒▒▒▒▒▒
C 2 2 C Prelude 30.4 ▒▒▒▒▒▒▒▒▒
D 1 D Corolla GTS 19.7 ▒▒▒▒▒▒
E E VW GTI 19.7 ▒▒▒▒▒▒
Pairwise Comparison Data for level 2, with respect to: Acceleraton
A B C D E WEIGHTS
A 5 5 5 4 A Mustang GT 52.3 ▒▒▒▒▒▒▒▒▒▒
B 2 -2 -3 B Tempo Sport 8.7 ▒▒
C -2 -3 C Prelude 6.6 ▒
D -2 D Corolla GTS 12.3 ▒▒
E E VW GTI 20.1 ▒▒▒
Pairwise Comparison Data for level 2, with respect to: Braking
A B C D E WEIGHTS
A 2 -3 -2 -5 A Mustang GT 8.8 ▒▒
B -4 -2 -6 B Tempo Sport 6.0 ▒
C 3 -2 C Prelude 26.6 ▒▒▒▒▒
D -5 D Corolla GTS 11.7 ▒▒
E E VW GTI 46.8 ▒▒▒▒▒▒▒▒▒
Pairwise Comparison Data for level 2, with respect to: Handling
A B C D E WEIGHTS
A 4 3 -2 2 A Mustang GT 25.1 ▒▒▒▒▒
B 1 -5 -3 B Tempo Sport 6.8 ▒
C -5 -3 C Prelude 7.2 ▒
D 4 D Corolla GTS 44.9 ▒▒▒▒▒▒▒▒▒
E E VW GTI 16.0 ▒▒▒
Pairwise Comparison Data for level 2, with respect to: Styling
A B C D E WEIGHTS
A 3 3 1 2 A Mustang GT 31.8 ▒▒▒▒▒▒▒▒▒
B 1 -3 -2 B Tempo Sport 9.9 ▒▒▒
C -3 -2 C Prelude 9.9 ▒▒▒
D 1 D Corolla GTS 27.7 ▒▒▒▒▒▒▒▒
E E VW GTI 20.6 ▒▒▒▒▒▒
AHP Pg. 8
1.3.3 Relative impact on overall goal
Study the pairwise comparisons above, when you are satisfied that you
understand how you would go about inputting this data, then push F2-TREE,
this will return you to the decision tree hierarchy. Now push F5-RUN. A set
of numbers should be generated next to each element in the decision tree,
as follows:
┌──────────────────────────────────────────────────────────────────────────────────┐
│ FILE:> C:CAR .AHP Copyright (C) 1986-1993, ARMADA SYSTEMS │
│ Decision Tree Hierarchy │
│ GOAL: To purchase the car best suited for me. │
│ ╔══════════════╤══════════════╤══════════════╤══════════════╤══════════════╗ │
│ ║ Level 1 │ Level 2 │ Level 3 │ Level 4 │ Level 5 ║ │
│ ╔═══╬══════════════╪══════════════╪══════════════╪══════════════╪══════════════╣ │
│ ║ 1 ║Price 38│Mustang GT 19│ │ │ ║ │
│ ║ 2 ║Fuel econ. 15│Tempo Sport 25│ │ │ ║ │
│ ║ 3 ║Acceleraton 7│Prelude 13│ │ │ ║ │
│ ║ 4 ║Braking 8│Corolla GTS 23│ │ │ ║ │
│ ║ 5 ║Handling 11│VW GTI 21│ │ │ ║ │
│ ║ 6 ║Styling 21│ │ │ │ ║ │
│ ║ 7 ║ │ │ │ │ ║ │
│ ║ 8 ║ │ │ │ │ ║ │
│ ║ 9 ║ │ │ │ │ ║ │
│ ║10 ║ │ │ │ │ ║ │
│ ║11 ║ │ │ │ │ ║ │
│ ║12 ║ │ │ │ │ ║ │
│ ║13 ║ │ │ │ │ ║ │
│ ║14 ║ │ │ │ │ ║ │
│ ║15 ║ │ │ │ │ ║ │
│ ║16 ║ │ │ │ │ ║ │
│ ╚═══╩══════════════╧══════════════╧══════════════╧══════════════╧══════════════╝ │
│ Overall average inconsistency= 0.18 (acceptable) │
│ 1HELP 2DATA 3NEXT 4GRAPH 5RUN 6PRINT 7ERASE 8OPEN 9SAVE 10QUIT │
└──────────────────────────────────────────────────────────────────────────────────┘
The numbers which have been generated represent preference weights
calculated from the pairwise comparison matrices given previously. These
weights have been calculated in such a way as to reflect their relative
impact on the overall goal of the hierarchy. Therefore, looking at level 2,
Mustang GT has a weight of 19, Tempo Sport has a weight of 25, Prelude 13,
Corolla GTS 23 and VW GTI 21. The alternative with the highest weight is
the one which is preferred over the rest. In this case, a Tempo Sport
should be the car purchased because it 'scores' better than the other
alternatives on the combined set of criteria which was considered. To get a
graphical representation of these scores, position the cursor anywhere in
level 2 and push F4-GRAPH.
Bar Graph of Preference Weights for level 2
Inconsistency= 0.16 (acceptable)
Tempo Sport 24.6 ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
Corolla GTS 22.6 ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
VW GTI 21.2 ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
Mustang GT 18.7 ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
Prelude 12.9 ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
AHP Pg. 9
1.4 SAMPLE PROBLEMS
1.4.1 Estimating relative lengths of lines
This example is intended to give you an idea of how to compare two elements
at a time, and to provide you with a feel for the 1-9 subjective scale used
in the AHP program. The way we will do this is we will first estimate the
relative lengths of seven straight lines. Following this, we will compare
our subjective results with actual values.
Since our goal will be to estimate relative line lengths, the hierarchy for
this problem will only consist of the seven lines being listed in level 1;
L1, L2, ..., L7. These lines are presented in figure 1.2, below:
L1 ■■■■■■■■■■■■■■■
L2 ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■
L3 ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■
L4 ■■■■■■■■■■
L5 ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■
L6 ■■■■■
L7 ■■■■■■■■■■■■■■■■■■■■
Figure 1.2. Straight lines used for pairwise comparison analysis.
The data supplied for this exercise is found on your program diskette in
file LINE.AHP, it is also listed below:
Pairwise Comparison Data for level 1, with respect to: GOAL
A B C D E F G WEIGHTS
A -3 -4 2 -2 3 -2 A L1 8.2 ▒▒
B -2 4 2 7 2 B L2 22.9 ▒▒▒▒▒▒
C 5 2 8 3 C L3 32.4 ▒▒▒▒▒▒▒▒▒
D -3 2 -2 D L4 5.5 ▒▒
E 6 2 E L5 16.6 ▒▒▒▒▒
F -4 F L6 3.0 ▒
G G L7 11.4 ▒▒▒
Several observations must be made with regard to this example. First, note
the negative pairwise comparisons. The very first element in the matrix,
for example, is a -3. This indicates that when comparing L1 and L2, L2 is
moderately longer than L1. If, on the other hand, L1 were the longer line,
then the first element in the matrix would be a positive number. This
relation holds throughout the matrix. If when entering your own data, you
enter a positive number when it really should be negative, then all is not
lost, the program will in most cases flag this error as an inconsistent
judgment. You would then go back and revise your data.
AHP Pg. 10
The second point which must be made clear is; before you start entering any
data into a pairwise comparison matrix, consider all of the alternatives in
your mind. In particular consider the worst and best, or as in this example
the shortest and longest line. This will provide you with a feel for the
relative scale you will need to use. Pairwise comparisons for elements in a
matrix must be relative to each other. Therefore, a subjective scale used
on one problem need not be the same as the scale used in another. For
example, in this problem it was decided that L2 is moderately longer than
L1 only after we looked at the longest and shortest line, L3 and L6. If the
difference between these two extremes was greater, then it is possible that
a different scale could have been used.
Briefly, the following comparisons can be made between the actual relative
lengths and those estimated with the AHP program:
ACTUAL LENGTH CALCULATED SUBJECTIVE
LINE (Units) RELATIVE LENGTH RELATIVE LENGTH
L1 15 8.6 8.2
L2 40 22.9 22.9
L3 55 31.4 32.4
L4 10 5.7 5.5
L5 30 17.1 16.6
L6 5 2.9 3.0
L7 20 11.4 11.4
As you can see, the actual values and those subjectively estimated, are
very close. Since in this example you know what the answers should be, try
to input your own data and see what kind of results you get. If you feel
your results are unsatisfactory, then revise your judgments. This way,
using trial and error, you will gain a better feeling for the subjective
scale used by this method. You may also devise your own problem where you
can compare estimated results with actual values. Some examples are:
1. Estimating relative weights of objects.
2. Estimating the relative brightness of similar objects at varying
distances from a common light source. Your results should indicate an
inverse square relationship between the brightness of an object and its
distance from the light source.
3. Estimating the relative areas of various two dimensional geometric
shapes.
AHP Pg. 11
1.4.2 Benefit/Cost analysis
This example will illustrate two key points: First it will show you how to
do a benefit to cost analysis, and second it will indicate that not all
elements in a lower level need to be connected to all the elements in the
immediately higher level.
Many decisions made in your personal or professional life require weighing
benefits against costs. Benefits of alternative courses of action may be
calculated by considering a hierarchy of objectives, attributes of
alternatives, and the alternatives themselves. This will tell us how much
each alternative contributes to the fulfillment of the objectives.
A hierarchy of costs for bringing about the alternatives may be constructed
by considering the problems which will be caused by each alternative. The
costs of the problems themselves, or the costs of solutions designed to
eliminate these problems are then analyzed in the hierarchy.
Once the two hierarchies have been constructed and the relative weights of
each alternative have been computed with respect to both costs and
benefits, then a benefit to cost ratio test may be calculated for each
alternative. The alternative with the highest ratio should be the
alternative selected. This will be the alternative which will yield the
greatest amount of benefit from a unit measure of cost.
The problem which we will model, will involve the selection of a
transportation project designed to bring people to the downtown core of a
large metropolitan city. The alternatives under study involve the
construction of an expressway, a subway, or an improvement in the present
bus service.
The benefits of the project have been grouped into economic, social and
personal benefits. Economic benefits are further subdivided into a time
savings to get to downtown, the number of jobs created by each project and
the improvement of downtown commerce due to more business. Benefits to
society are viewed as abstract quantities. They have been subdivided into
the degree of community pride generated by each alternative and the greater
number of trips to the downtown that will result. Personal benefits have
been defined by their contribution to the individual. For example the
reduction of traffic and parking problems, and the comfort and
accessibility of using each alternative. The benefit hierarchy is
illustrated in Figure 1.3.
Project costs have been grouped into economic, social, and environmental
costs. Economic costs are subdivided into both capital and operational or
maintenance costs. Social costs represent costs to society as a whole. They
are defined as the disruption of people's lifestyles, the dislocation of
people from their homes, and the general disruption to people caused by,
for example, the different levels of traffic congestion. Environmental
costs are viewed in terms of the pollution and decrease in parkland
resulting from each alternative. The cost hierarchy is illustrated in
Figure 1.4.
AHP Pg. 12
╔═════════════════════╗
Level 0 ║ BENEFITS OF PROJECT ║
╚══════════╤══════════╝
│
┌──────────────────────────┼─────────────────────────┐
│ │ │
┌───────────┴───────────┐ ┌───────────┴───────────┐ ┌──────────┴──────────┐
Level 1 │ ECONOMIC │ │ SOCIAL │ │ PERSONAL │
└─┬─────────────────────┘ └─┬─────────────────────┘ └─┬───────────────────┘
│┌────────────────────┐ │┌────────────────────┐ │┌──────────────────┐
Level 2 ├┤TIME SAVINGS │ ├┤COMMUNITY PRIDE │ ├┤TRAFFIC VOLUME │
│├────────────────────┤ │├────────────────────┤ │├──────────────────┤
├┤JOB CREATION │ └┤MORE TRIPS DOWNTOWN │ ├┤PARKING │
│├────────────────────┤ └────────┬───────────┘ │├──────────────────┤
└┤COMMERCE │ │ ├┤COMFORT │
└────────┬───────────┘ │ │├──────────────────┤
│ │ └┤ACCESSIBILITY │
│ │ └───────┬──────────┘
├──────────────────────────┼─────────────────────────┤
┌───────────┴───────────┐ ┌───────────┴───────────┐ ┌──────────┴──────────┐
Level 3 │ BUILD EXPRESSWAY │ │ BUILD SUBWAY │ │ IMPROVE BUS SERVICE │
└───────────────────────┘ └───────────────────────┘ └─────────────────────┘
Figure 1.3. Benefit hierarchy for transportation project.
╔═════════════════════╗
Level 0 ║ COSTS OF PROJECT ║
╚══════════╤══════════╝
│
┌──────────────────────────┼─────────────────────────┐
│ │ │
┌───────────┴───────────┐ ┌───────────┴───────────┐ ┌──────────┴──────────┐
Level 1 │ ECONOMIC │ │ SOCIAL │ │ ENVIRONMENTAL │
└─┬─────────────────────┘ └─┬─────────────────────┘ └─┬───────────────────┘
│┌────────────────────┐ │┌────────────────────┐ │┌──────────────────┐
Level 2 ├┤CAPITAL │ ├┤LIFESTYLE CHANGES │ ├┤POLLUTION │
│├────────────────────┤ │├────────────────────┤ │├──────────────────┤
└┤OPERATIONAL │ ├┤PEOPLE DISLOCATION │ └┤DECREASED PARKLAND│
└────────┬───────────┘ │├────────────────────┤ └───────┬──────────┘
│ └┤GENERAL DISRUPTION │ │
│ └────────┬───────────┘ │
│ │ │
├──────────────────────────┼─────────────────────────┤
│ │ │
┌───────────┴───────────┐ ┌───────────┴───────────┐ ┌──────────┴──────────┐
Level 3 │ BUILD EXPRESSWAY │ │ BUILD SUBWAY │ │ IMPROVE BUS SERVICE │
└───────────────────────┘ └───────────────────────┘ └─────────────────────┘
Figure 1.4. Cost hierarchy for transportation project.
The data and results of the analysis as generated by the program are given
on the next few pages. The results can be summarized here as follows:
┌────────────┬────────┬─────────────┐
│ EXPRESSWAY │ SUBWAY │ IMPROVE BUS │
┌────────────────────┼────────────┼────────┼─────────────┤
│ BENEFITS │ 36 │ 55 │ 9 │
├────────────────────┼────────────┼────────┼─────────────┤
│ COSTS │ 37 │ 52 │ 10 │
├────────────────────┼────────────┼────────┼─────────────┤
│ BENEFIT/COST RATIO │ 0.97 │* 1.06 *│ 0.9 │
└────────────────────┴────────────┴────────┴─────────────┘
AHP Pg. 13
In this analysis, the benefit to cost ratios of all 3 alternatives are
fairly close to each other. Nevertheless, the subway option scores slightly
better than the other two, and the expressway option scores better than the
bus option. Therefore, if enough resources and money are available then a
subway should be built. If, however, there is not enough money to build the
subway, but there is enough for an expressway, then the expressway option
should be selected. If this is the case, and the subway option is not a
feasible alternative, then it should not have been considered in the first
place.
The next few pages list the data for this problem which has been supplied
your diskette. The benefit data is found in file BENEFIT.AHP, while the
cost data is found in file COST.AHP.
If you will recall, one of the purposes of this example was to show that
not all elements in a lower level, need to be connected to all elements in
the immediately higher level. In figures 1.3 and 1.4, elements in level 2,
are not all connected to all elements in level 1. For example, it would not
help us much to make a connection between the pride generated for an
alternative to economic benefits. One can argue, that pride could reap some
economic benefits, however, its effects would be negligible when compared
with the other criteria considered, therefore no connection is made.
Looking at the data for level 2, you can see how a connection is identified
in the pairwise comparison matrix. If no connection exists for a certain
element, then no pairwise comparison is input in both the row and column of
this element. Keep in mind that, if N elements are being compared, then
N(N-1)/2 comparisons are required.
FILE:> C:BENEFIT .AHP Copyright (C) 1986-1993, ARMADA SYSTEMS
Decision Tree Hierarchy
GOAL: To determine the benefits of a transportation project to downtown core.
╔══════════════╤══════════════╤══════════════╤══════════════╤══════════════╗
║ Level 1 │ Level 2 │ Level 3 │ Level 4 │ Level 5 ║
╔═══╬══════════════╪══════════════╪══════════════╪══════════════╪══════════════╣
║ 1 ║Economic 67│Time saving 5│Expressway 36│ │ ║
║ 2 ║Social 11│Job creatin 46│Subway 55│ │ ║
║ 3 ║Personal 22│Commerce 16│Improve Bus 9│ │ ║
║ 4 ║ │Pride 3│ │ │ ║
║ 5 ║ │More trips 8│ │ │ ║
║ 6 ║ │Traffic 8│ │ │ ║
║ 7 ║ │Parking 8│ │ │ ║
║ 8 ║ │Comfort 2│ │ │ ║
║ 9 ║ │Accessible 4│ │ │ ║
║10 ║ │ │ │ │ ║
║11 ║ │ │ │ │ ║
║12 ║ │ │ │ │ ║
║13 ║ │ │ │ │ ║
║14 ║ │ │ │ │ ║
║15 ║ │ │ │ │ ║
║16 ║ │ │ │ │ ║
╚═══╩══════════════╧══════════════╧══════════════╧══════════════╧══════════════╝
Overall average inconsistency= 0.46 (acceptable)
Pairwise Comparison Data for level 1, with respect to: GOAL
A B C WEIGHTS
A 6 3 A Economic 66.7 ▒▒▒▒▒▒▒▒▒
B -2 B Social 11.1 ▒▒
C C Personal 22.2 ▒▒▒
AHP Pg. 14
Pairwise Comparison Data for level 2, with respect to: Economic
A B C D E F G H I WEIGHTS
A -7 -5 A Time saving 6.9 ▒
B 4 B Job creatin 68.7 ▒▒▒▒▒▒▒▒▒
C C Commerce 24.4 ▒▒▒
D D Pride 0.0
E E More trips 0.0
F F Traffic 0.0
G G Parking 0.0
H H Comfort 0.0
I I Accessible 0.0
Pairwise Comparison Data for level 2, with respect to: Social
A B C D E F G H I WEIGHTS
A A Time saving 0.0
B B Job creatin 0.0
C C Commerce 0.0
D -3 D Pride 25.0 ▒▒▒
E E More trips 75.0 ▒▒▒▒▒▒▒▒▒
F F Traffic 0.0
G G Parking 0.0
H H Comfort 0.0
I I Accessible 0.0
Pairwise Comparison Data for level 2, with respect to: Personal
A B C D E F G H I WEIGHTS
A A Time saving 0.0
B B Job creatin 0.0
C C Commerce 0.0
D D Pride 0.0
E E More trips 0.0
F 1 4 2 F Traffic 35.9 ▒▒▒▒▒▒▒▒▒
G 4 2 G Parking 35.9 ▒▒▒▒▒▒▒▒▒
H -3 H Comfort 8.2 ▒▒
I I Accessible 20.0 ▒▒▒▒▒
AHP Pg. 15
Pairwise Comparison Data for level 3, with respect to: Time saving
A B C WEIGHTS
A 3 9 A Expressway 66.3 ▒▒▒▒▒▒▒▒▒
B 6 B Subway 27.8 ▒▒▒▒
C C Improve Bus 5.8 ▒
Pairwise Comparison Data for level 3, with respect to: Job creatin
A B C WEIGHTS
A -4 5 A Expressway 23.7 ▒▒▒
B 8 B Subway 69.9 ▒▒▒▒▒▒▒▒▒
C C Improve Bus 6.4 ▒
Pairwise Comparison Data for level 3, with respect to: Commerce
A B C WEIGHTS
A 2 7 A Expressway 58.2 ▒▒▒▒▒▒▒▒▒
B 6 B Subway 34.8 ▒▒▒▒▒
C C Improve Bus 6.9 ▒
Pairwise Comparison Data for level 3, with respect to: Pride
A B C WEIGHTS
A -5 5 A Expressway 20.7 ▒▒▒
B 9 B Subway 73.5 ▒▒▒▒▒▒▒▒▒
C C Improve Bus 5.8 ▒
Pairwise Comparison Data for level 3, with respect to: More trips
A B C WEIGHTS
A -3 3 A Expressway 25.0 ▒▒▒
B 6 B Subway 65.5 ▒▒▒▒▒▒▒▒▒
C C Improve Bus 9.5 ▒
Pairwise Comparison Data for level 3, with respect to: Traffic
A B C WEIGHTS
A 5 9 A Expressway 73.5 ▒▒▒▒▒▒▒▒▒
B 5 B Subway 20.7 ▒▒▒
C C Improve Bus 5.8 ▒
Pairwise Comparison Data for level 3, with respect to: Parking
A B C WEIGHTS
A -9 -7 A Expressway 5.5 ▒
B 3 B Subway 65.5 ▒▒▒▒▒▒▒▒▒
C C Improve Bus 29.0 ▒▒▒▒
Pairwise Comparison Data for level 3, with respect to: Comfort
A B C WEIGHTS
A -6 -4 A Expressway 8.5 ▒
B 3 B Subway 64.4 ▒▒▒▒▒▒▒▒▒
C C Improve Bus 27.1 ▒▒▒▒
Pairwise Comparison Data for level 3, with respect to: Accessible
A B C WEIGHTS
A 6 7 A Expressway 75.8 ▒▒▒▒▒▒▒▒▒
B 2 B Subway 15.1 ▒▒
C C Improve Bus 9.1 ▒
AHP Pg. 16
FILE:> C:COST .AHP Copyright (C) 1986-1993, ARMADA SYSTEMS
Decision Tree Hierarchy
GOAL: To estimate the costs of a transportation project to the downtown core.
╔══════════════╤══════════════╤══════════════╤══════════════╤══════════════╗
║ Level 1 │ Level 2 │ Level 3 │ Level 4 │ Level 5 ║
╔═══╬══════════════╪══════════════╪══════════════╪══════════════╪══════════════╣
║ 1 ║Economic 74│Capital 65│Expressway 37│ │ ║
║ 2 ║Social 17│Operational 9│Subway 52│ │ ║
║ 3 ║Environment 9│Lifestyles 2│Improve Bus 10│ │ ║
║ 4 ║ │People Disl 11│ │ │ ║
║ 5 ║ │Disruption 4│ │ │ ║
║ 6 ║ │Pollution 7│ │ │ ║
║ 7 ║ │Parkland 2│ │ │ ║
║ 8 ║ │ │ │ │ ║
║ 9 ║ │ │ │ │ ║
║10 ║ │ │ │ │ ║
║11 ║ │ │ │ │ ║
║12 ║ │ │ │ │ ║
║13 ║ │ │ │ │ ║
║14 ║ │ │ │ │ ║
║15 ║ │ │ │ │ ║
║16 ║ │ │ │ │ ║
╚═══╩══════════════╧══════════════╧══════════════╧══════════════╧══════════════╝
Overall average inconsistency= 0.37 (acceptable)
Pairwise Comparison Data for level 1, with respect to: GOAL
A B C WEIGHTS
A 5 7 A Economic 74.0 ▒▒▒▒▒▒▒▒▒
B 2 B Social 16.7 ▒▒
C C Environment 9.4 ▒
Pairwise Comparison Data for level 2, with respect to: Economic
A B C D E F G WEIGHTS
A 7 A Capital 87.5 ▒▒▒▒▒▒▒▒▒
B B Operational 12.5 ▒
C C Lifestyles 0.0
D D People Disl 0.0
E E Disruption 0.0
F F Pollution 0.0
G G Parkland 0.0
Pairwise Comparison Data for level 2, with respect to: Social
A B C D E F G WEIGHTS
A A Capital 0.0
B B Operational 0.0
C -5 -3 C Lifestyles 10.5 ▒
D 3 D People Disl 63.7 ▒▒▒▒▒▒▒▒▒
E E Disruption 25.8 ▒▒▒▒
F F Pollution 0.0
G G Parkland 0.0
Pairwise Comparison Data for level 2, with respect to: Environment
A B C D E F G WEIGHTS
A A Capital 0.0
B B Operational 0.0
C C Lifestyles 0.0
D D People Disl 0.0
E E Disruption 0.0
F 3 F Pollution 75.0 ▒▒▒▒▒▒▒▒▒
G G Parkland 25.0 ▒▒▒
AHP Pg. 17
Pairwise Comparison Data for level 3, with respect to: Capital
A B C WEIGHTS
A -4 7 A Expressway 25.3 ▒▒▒
B 9 B Subway 69.4 ▒▒▒▒▒▒▒▒▒
C C Improve Bus 5.3 ▒
Pairwise Comparison Data for level 3, with respect to: Operational
A B C WEIGHTS
A -2 -2 A Expressway 20.0 ▒▒▒▒▒
B 1 B Subway 40.0 ▒▒▒▒▒▒▒▒▒
C C Improve Bus 40.0 ▒▒▒▒▒▒▒▒▒
Pairwise Comparison Data for level 3, with respect to: Lifestyles
A B C WEIGHTS
A 7 5 A Expressway 73.1 ▒▒▒▒▒▒▒▒▒
B -3 B Subway 8.1 ▒
C C Improve Bus 18.8 ▒▒
Pairwise Comparison Data for level 3, with respect to: People Disl
A B C WEIGHTS
A 6 8 A Expressway 76.1 ▒▒▒▒▒▒▒▒▒
B 3 B Subway 16.6 ▒▒
C C Improve Bus 7.3 ▒
Pairwise Comparison Data for level 3, with respect to: Disruption
A B C WEIGHTS
A 3 4 A Expressway 62.5 ▒▒▒▒▒▒▒▒▒
B 2 B Subway 23.8 ▒▒▒
C C Improve Bus 13.6 ▒▒
Pairwise Comparison Data for level 3, with respect to: Pollution
A B C WEIGHTS
A 8 5 A Expressway 74.2 ▒▒▒▒▒▒▒▒▒
B -3 B Subway 7.5 ▒
C C Improve Bus 18.3 ▒▒
Pairwise Comparison Data for level 3, with respect to: Parkland
A B C WEIGHTS
A 8 8 A Expressway 80.0 ▒▒▒▒▒▒▒▒▒
B 1 B Subway 10.0 ▒
C C Improve Bus 10.0 ▒
AHP Pg. 18
1.4.3 Application to psychotherapy
The hierarchical method may be used to provide insight into psychological
problem areas, in the following manner: Consider an individual's overall
well-being as the single top level entry in a hierarchy. Conceivably,
this level is primarily affected by childhood, adolescent, and adult
experiences. Factors in growth and maturity which impinge upon well-
being may be the influences of the mother and father separately, as well
as their influences together as parents, the socioeconomic background,
sibling relationships, one's peer group, schooling, religious status, and
so on.
As an example, suppose that an individual feels that his self-confidence
has been severely undermined and his social adjustments have been impaired
by a restrictive situation during childhood. The following hierarchy is
constructed, and the individual is questioned about his childhood
experiences only. He is asked to relate the elements in the hierarchy on
each level, with respect to elements in the previous level:
Goal: To determine present overall well-being
Level 1: Self-respect
Sense of security
Ability to adapt to new people and new circumstances
Level 2: Visible affection shown for subject
Ideas of strictness and ethics
Actual disciplining of child
Emphasis on personal adjustment with others
Level 3: Influence of mother
Influence of father
Influence of both mother and father
The therapy resulting from this analysis should depend on both the
judgments and any considerable inconsistency involved. This is a highly
restricted example, a more complete setting for a psychological history may
include many more elements at each level, chosen by trained individuals and
placed in such a way as to derive the maximum understanding of the subject.
AHP Pg. 19
1.4.4 Calculating expected values
Suppose that you wanted to forecast the average number of children born to
North American families in the next 10 to 20 years. The first step would be
to set up a hierarchy of factors which would influence the size of family
in the future. You may consider the following hierarchy:
Goal: To determine the average number of children born per family
Level 1: Availability of birth controls and abortion
Cost of raising children
Family income
Working mother
Older age of motherhood
Education of mother
Social pressures
Level 2: Number of children (0, 1, 2, 3, 4)
Once you have entered your pairwise comparison judgments into the model,
and the program has calculated the weights for level 2 with respect to the
goal, the expected number of children per family may be calculated as
follows:
Suppose that the following weights are obtained:
Number of children: 0 1 2 3 4
Weight for level 2: 2.8 17.4 49.5 23.9 6.4
The expected number of children per family is:
(2.8x0 + 17.4x1 + 49.5x2 + 23.9x3 + 6.4x4)/100 = 2.14
As an example of another application, this method may be used to estimate
sales increase of a corporation despite the impact of inflation, recession,
and rise of energy cost. These factors, and any others which may be
important to specific organizations may be placed in the first level in the
hierarchy. The sales increases may be divided into ranges of 0-5%, 6-10%,
11-15%, 16-20% and placed in the second level. The average rate of increase
is then calculated as in the family size problem above.
AHP Pg. 20
1.4.5 Determining optimum type of coal plant
The problem of determining the most desirable coal using energy system
technology for a given community, may be regarded as a hierarchy with
three major criteria. One is concerned with energy resource utilization
(ERU) efficiency, a second with environmental impacts, and a third one with
economics. Each of these criteria involves a number of subcriteria.
For example under ERU efficiency we have four levels. The first level is
concerned with season, topography, geography, etc. The second level is
concerned with various energy requirements of a community such as heating
and cooling, lighting etc. The third level is concerned with the method of
energy supply, and the fourth with the type of plant which generates this
energy.
Goal: Determine coal plant ERU efficiency
Level 1: Season, Topography, Geography, Climate, Form, Function, Density
Level 2: Heating and cooling, Lighting, Water heating and cooking,
Transportation, Industry, Recreation, Public services
Level 3: Electrical, Thermal, Fuel
Level 4: Stack gas cleaning with conventional boiler
Fluidized bed combustion
Low BTU gas
High BTU gas
Coal liquefaction
Solvent refined coal
For environmental impacts of the different plant types, we consider the
various pollutants produced. This hierarchy contains two levels.
Goal: Determine environmental impacts of coal plant
Level 1: Sulfur dioxide, Carbon dioxide, Carbon monoxide,
Water discharges, Solid wastes, Land use
Level 2: Stack gas cleaning with conventional boiler
Fluidized bed combustion
Low BTU gas
High BTU gas
Coal liquefaction
Solvent refined coal
The economics criterion may be further broken down into capital and
operating costs for the first level, and the coal plant alternatives in the
last level.
AHP Pg. 21
2.0 PROGRAM CONFIGURATION
Push ALT+S to customize screen colors and to configure the printer. The
following information will be displayed:
- Make necessary changes and push the RTN key to SAVE these changes to disk.
- To exit without saving changes, push the ESC key.
Screen colors: Foreground Background Border
Standard text: 7 0 0
Highlighted text: 10 0 0
Screen heading: 1 3 0
Printer control:
Printer name: HP LaserJet II
Character sequence to initialize and reset printer (base 10):
Init. Printer: 27, 38, 97, 49, 51, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0
Reset Printer: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Screen colors are specified by number. The following is a cross reference
listing of the available screen color attributes.
┌──────────┬────────────┬────────────────┐
│ COLOR │ STANDARD │ HIGH-INTENSITY │
├──────────┼────────────┼────────────────┤
│ Black │ 0 │ 8 │
│ Blue │ 1 │ 9 │
│ Green │ 2 │ 10 │
│ Cyan │ 3 │ 11 │
│ Red │ 4 │ 12 │
│ Magenta │ 5 │ 13 │
│ Brown │ 6 │ 14 │
│ White │ 7 │ 15 │
└──────────┴────────────┴────────────────┘
Printer control data must be entered in decimal (base 10) notation. If you
wish to change any printer control data, then simply consult your printer
user's manual for the control codes of functions you would like to make use
of. You may, for example want to change the character pitch and font, or
perhaps you would like to reduce the line spacing so that more lines can be
printed on one page. The possibilities are limited only by your printer.
When you have decided what functions you would like to utilize, make the
necessary changes on screen and push RTN to save these to disk.
AHP Pg. 22
3.0 ABOUT ARMADA SYSTEMS
Armada Systems was established in 1986 with the purpose of developing
unique but useful microcomputer software. Since that time, Armada Systems
has expanded it's operations, and now specializes in the following key
areas:
* Custom PC software development.
* Decision making software, seminars and consulting services.
* CA-Clipper training.
* Research and development of new software applications.
In addition to the Analytic Hierarchy Process, Armada Systems publishes the
Decision Matrix Expert (DME) and MyBASE software packages. The next several
pages are devoted to providing you with a better understanding of what
these software packages do, and how they can help you to become a more
effective decision maker.
AHP Pg. 23
3.1 THE DECISION MATRIX EXPERT (DME)
The Decision Matrix Expert (DME), is an innovative, yet remarkably easy to
use software package for decision analysis. It represents an objective,
scientific approach to replace intuition and speculation, while preserving
such qualitative factors as experience and judgment.
The DME is not a 'black box' program, it relies upon the use of popular,
well established Multiple Criteria Decision Making algorithms. Numerical
results are provided for each stage in the analysis, so that the user can
see what is happening and have confidence in the results. The use of
popular, well established algorithms, with intermediate numerical results,
is especially important to such users as educational institutions,
government agencies and consultants.
Consultants, who for example, are taxed to recommend the location for a new
garbage dump, need a tool which will evaluate possible alternatives with as
little bias as possible. Their recommendations will need to stand up to
public scrutiny, and the public hearing process which usually takes place
before a site is actually selected. This is where the use of well
established decision analysis algorithms is useful. They can be explained
and defended because quite a bit of research has gone into them.
In the DME, decisions are portrayed in a matrix which contains all of the
information required to arrive at a final decision. The columns of this
matrix represent the criteria which are important to the decision, while
the rows represent the various alternatives being considered.
In the analysis, alternatives are scanned for dominance and to ensure that
they meet the minimum cutoff constraints specified by the user. Final
ranking of alternatives is performed using the Linear Assignment Method,
Normalized Additive Weighting, ELECTRE, TOPSIS, and an aggregation and
synthesis phase. Numerical results from each of these algorithm phases are
available to the user for analysis.
3.1.1 Applications
Location planning, cost/benefit analysis, strategic planning, recruiting,
employee evaluation, resource allocation, taste testing, new product
evaluations, problem analysis, market research, and many more.
3.1.2 System requirements
The Decision Matrix Expert will work on any MS DOS compatible computer with
at least 384K RAM. A printer is recommended but not required.
AHP Pg. 24
3.2 MyBASE
MyBASE is a very powerful, easy to use, multipurpose database system. You
can use it in DOS or Windows to view, edit, sort, search, group, filter,
replace, copy/paste, merge, print, fax or export data in many ways. Both
indexing and filter methods are provided for searching, grouping, browsing
and retrieving data.
MyBASE also features a fully programmable merge utility. What is particu-
larly noteworthy is that, besides allowing you to do the standard merging
of text and data, commands may be embedded in the merge file to control how
records and data are processed, where the output is sent to, and what
external programs to call (ex. DOS functions, file viewers, word proces-
sors, spreadsheets, graphics viewers, FAX software, and so on).
For example, if you had a database of clients, you could create a merge
file to send all your clients (or just a small group of them) a personal-
ized letter. The merged letter could be sent to a printer to obtain a
hardcopy, or it could just as easily be sent directly to your client, via
FAX. If the letter was faxed, MyBASE would merge and FAX each letter
completely unattended.
A sample contact management system is included with this package. This
contact management system includes, pre-defined view screens, field edit
templates and field edit validation, default pop-up selection boxes and
sample data. Also included are sample merge programs to print envelopes,
letters, reports, and to send personalized faxes to multiple destinations.
You can easily modify this contact management system to suit your own
needs, or if you wish, you can just as easily create any number of new
databases.
3.2.1 Quick overview of features
* The program is small (less than 300K in size).
* Creates, reads and writes industry standard dBASE III files.
* Context sensitive and user customizable help system. Push F1 at any time
to display or edit the help information which relates to the current
task.
* Ability to completely define your own database structure. This includes
descriptive column headings, field edit validation, default field values,
field edit functions/templates and execute/run functions which may be
invoked by pushing Alt+E or Alt+R in the database browse table.
* Local Area Network (LAN) compatible.
* Shell to DOS or run any external program from within MyBASE with less
than 8K of memory overhead.
* Supports EMS and XMS memory for improved performance.
* Enhanced error management and error recovery.
AHP Pg. 25
* Database specific, three level password access system Can be turned
either ON or OFF).
* View data in table or record view mode (F3/TAB toggles between modes).
* Quick and simple way of defining new ways of looking at data. Unique view
windows may be defined for each database. The view windows will control
how the data will be displayed on screen and in printed reports.
* Merge print function to allow merging of text from an external text file
with data from the database. Commands may be embedded in the external
merge file to control how records and data are processed, where the
output is sent to, and what external procedures to call (ex. DOS func-
tions, word processors, graphics viewers, FAX software, label printers,
and so on).
* User configurable print drivers. Export data to printer or a DBF or ASCII
delimited file. The ability to export data to a file is extremely useful
since the exported data will be based on the current database view and
filter conditions which you have set (ie. what you see is what you get).
The exported data may then be imported into a word processor, spread-
sheet, desktop publishing package, telecommunications or fax software,
etc...
* Tag individual records for printing, merging or replacing.
* Filter database to display or print a group of selected data.
* Skip through database, searching for specific data.
* Quick, database wide, search and replacement of data.
* Memo field support for free-form notes of up to 64K in size per record.
* Copy and paste data for faster data input.
* Automatic telephone dialer.
* Calculate totals and averages for numeric data.
* Support for EGA and VGA monitors to display more data on screen.
* Allows for customization of screen colors, video size, date format, and
use of sound.
* Display or hide records marked for deletion.
* NOTE: MyBASE is continually updated and refined. The latest version
of MyBASE may have additional functionality and features not specified
here.
3.2.2 System requirements
A PC-DOS or MS-DOS compatible system with at least 640K RAM.
A hard disk with at least 1.0 MB free.
PC-DOS/MS-DOS 3.1 or higher.
AHP Pg. 26
4.0 ORDERING SOFTWARE: WHAT YOU WILL RECEIVE
When you purchase any software from Armada Systems, your satisfaction is
100% guaranteed. If for any reason you are not completely satisfied with
the product you may return it within 30 days for a refund. In addition to
this guarantee, you will receive the following:
(1) The latest version of software.
(2) Complete reference and user's guide.
(3) Free technical support.
(4) Notice of future updates and new products.
(5) Eligibility for low cost upgrades.
(6) Free shareware software, as follows:
┌────────────────────────────┬─────────────────────────────────┐
│ PROGRAM ORDERED │ FREE SHAREWARE YOU WILL RECEIVE │
├────────────────────────────┼─────────────────────────────────┤
│ Analytic Hierarchy Process │ MyBASE │
│ Decision Matrix Expert │ MyBASE │
│ MyBASE │ Analytic Hierarchy Process │
└────────────────────────────┴─────────────────────────────────┘
To place your order, fill out the order form on the following page and mail
it to Armada Systems, along with a company purchase order, cheque or money
order payment, made out to "B. BORZIC". Payment must be in the quoted U.S.
or Canadian funds. Site licensing and volume discounts (QTY. >= 5) are
available, please write for details.
ARMADA SYSTEMS SOFTWARE REGISTRATION AND ORDER FORM
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To order software, please fill out this order form and mail it to the
address given below, along with a company purchase order, cheque or money
order payment, made out to "B. BORZIC". Payment must be in the quoted U.S.
or Canadian funds. Site licensing and volume discounts (QTY. >= 5) are
available, please write for details.
When you purchase software from Armada Systems, your satisfaction is 100%
guaranteed. If for any reason you are not completely satisfied with the
product you may return it within 30 days for a refund.
Boris Borzic, Armada Systems
P.O. Box 637, Station A
Downsview, Ontario
M3M 3A9 CANADA
Tel. (416) 889-2617 or (905) 889-2617 after October 4, 1993
NAME ____________________________ TITLE __________________________________
COMPANY _________________________ DEPARTMENT _____________________________
ADDRESS ___________________________________________________________________
CITY ____________________________ STATE/PROVINCE _________________________
ZIP/POSTAL CODE _________________ COUNTRY ________________________________
PHONE ___________________________ FAX ____________________________________
Would you like the program supplied on 5.25" or 3.5" disks? _______________
Where did you obtain the AHP software? ____________________________________
AHP 3.01 - 9312400
+-------------------------------------------------------------------------+
| DESCRIPTION | U.S. $ | CDN $ | QTY | TOTAL $ |
|-------------------------------------|--------|--------|-----|-----------|
| Analytic Hierarchy Process (AHP) | 99.00 | 119.00 | | |
|-------------------------------------|--------|--------|-----|-----------|
| Decision Matrix Expert (DME) | 99.00 | 119.00 | | |
|-------------------------------------|--------|--------|-----|-----------|
| MyBASE | 124.00 | 149.00 | | |
|-------------------------------------|--------|--------|-----|-----------|
| AHP + DME ordered together | 149.00 | 179.00 | | |
|-------------------------------------|--------|--------|-----|-----------|
| AHP + DME + MyBASE ordered together | 249.00 | 299.00 | | |
+-------------------------------------------------------------|-----------|
Purchase order processing charge | 15.00 |
(cross out if payment is enclosed) | |
|-----------|
Shipping & handling | 8.00 |
|-----------|
Applicable taxes | |
|-----------|
TOTAL | |
+-----------+
Signature ______________________________ Date ____________________________
Use the back of this sheet to add any comments or suggestions you may have.
REFERENCES
Alexander M. Joyce, Saaty L. Thomas: "Thinking With Models,"
Pergamon Press
Chryssolouris G, Chan S., Cobb W.: "Decision Making in the
Factory Floor," COMMLINE, May-June 1986
Green P.E., Wind Y.: "Multiattribute Decisions in Marketing:
A Measurement Approach," Dryden Press, 1973
Ho K. James: "Analytic Hierarchies and Holistic Preferences,"
College of Business Administration
The University of Tennessee, Knoxville, TN 37996
Hwang C.L., Yoon K.: "Multiple Attribute Decision Making,
Methods and Applications," Springer-Verlang, 1981
Raiffa Howard: "Decision Analysis, Introductory Lectures on
Choices Under Uncertainty," Addison-Wesley, 1968
Saaty L. Thomas: "The Analytic Hierarchy Process,"
McGraw-Hill, 1980
Szonyi A.J., Fenton R.G., White J.A., Agee M.H., Case K.E.:
"Principles of Engineering Economic Analysis,"
John Wiley and Sons, 1982
Wagner M. Harvey: "Principles of Operations Research,"
Prentice-Hall, 1975
NOTES
