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Decision Analysis System V2.05. Evaluate alternatives, cost/benefit analysis, sales forecasting, etc.
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Decision Analysis System V2.05. Evaluate alternatives, cost/benefit analysis, sales forecasting, etc.
File Name File Size Zip Size Zip Type
BENEFIT.PCM 1408 576 deflated
CAR.DMM 640 325 deflated
CAR.PCM 1152 477 deflated
COST.PCM 1024 472 deflated
DAS.EXE 37679 23069 deflated
DAS.TXT 106752 27870 deflated
DAYCARE.DMM 5120 1879 deflated
DMM.EXE 59871 32314 deflated
LINE.PCM 384 190 deflated
MANUAL.EXE 44594 29611 deflated
PCM.EXE 54847 29109 deflated
XYZCOMP.PCM 2432 970 deflated

Download File DAS.ZIP Here

Contents of the DAS.TXT file














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Decision Analysis System
The Modern Art of Decision Making

















USERS MANUAL

Shareware Edition
Release 2.05



___________________________________________________________________________





DAS - Decision Analysis System
The Modern Art of Decision Making
Shareware Edition
Third Printing (May 1989)
Program Serial No. 8928900, Release 2.05




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 may use or distribute any of the information you supply, in
any way it believes appropriate, without incurring any obligations whatso-
ever.


Armada Systems
Product Feedback
P.O. Box 637, Station A
Downsview, Ontario
Canada M3M 3A9





DAS, DMM, and PCM are Trademarks of Armada Systems.

Copyright (C) 1986, 1989 Armada Systems
All Rights Reserved.
Written in Canada.









For your records:

NAME ____________________________ TITLE __________________________________
COMPANY _________________________ DEPARTMENT _____________________________
DATE PROGRAM RECEIVED ___________ OBTAINED FROM __________________________





TABLE OF CONTENTS






PAGE

ARMADA SYSTEMS LICENSE AGREEMENT - - - - - - - - - - - - - - - - - - i
DAS ORDER FORM - - - - - - - - - - - - - - - - - - - - - - - - - - - ii
PRODUCT COMMENT FORM - - - - - - - - - - - - - - - - - - - - - - - - iii

GETTING STARTED - - - - - - - - - - - - - - - - - - - - - - - - - - iv
CREATING A WORKING COPY OF DAS iv
SHAREWARE DISK CONTENTS v


1.0 DECISION ANALYSIS SYSTEM - - - - - - - - - - - - - - - - - - - 1
1.1 INTRODUCTION 1
1.2 USING DAS 1
1.3 SCREEN COLORS AND PRINTER CONTROL 2

2.0 DECISION MATRIX METHOD - - - - - - - - - - - - - - - - - - - - 5
2.1 INTRODUCTION 5
2.2 THEORY OF OPERATION 5
2.3 USING DMM 7

3.0 PAIRWISE COMPARISON METHOD - - - - - - - - - - - - - - - - - - 11
3.1 INTRODUCTION 11
3.2 THEORY OF OPERATION 11
3.2.1 Pairwise comparisons and inconsistency 12
3.2.2 Example 12
3.3 USING PCM 13
3.3.1 Pairwise comparisons for level 1 15
3.3.2 Pairwise comparisons for level 2 16
3.3.3 Relative impact on overall goal 18
3.4 SAMPLE PROBLEMS 19
3.4.1 Estimating relative lengths of lines 19
3.4.2 Benefit/Cost analysis 21
3.4.3 Application to psychotherapy 28
3.4.4 Calculating expected values 29
3.4.5 Determining optimum type of coal plant 30

REFERENCES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 31

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, or reduced to any electronic medium or machine
readable form, in whole or in part, except as specifically authorized,
without the prior written consent of Armada Systems.

Armada Systems specifically authorizes individuals and organizations to
make copies of its shareware software for the purpose of free distribution
to other individuals or organizations. The software and documentation may
not be sold, there must be no fee involved in distributing the software,
other than for a small reasonable fee to cover the cost of any distribution
media and service charges. Such copying is limited to making complete
unaltered copies of the shareware software. The 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.

Copying or distribution of non-shareware and commercial software is not
permitted. Registered users may however make back-up copies of the non-
shareware software provided to them. The non-shareware programs may be used
on any machine as long as a copy of these programs is not being used on
another machine or terminal at the same time.

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 below:

Armada Systems
P.O. Box 637, Station A
Downsview, Ontario
Canada M3M 3A9
ii

2.05 - 8928900

DECISION ANALYSIS SYSTEM ORDER FORM

A commercial version of the DAS software and user manual, is available as
follows: Application programs, DMM and PCM, may be purchased separately for
$65.00 U.S. funds, or they may be purchased together, as a complete DAS
package for $95.00 U.S. funds.

To order, fill out this order form and mail it to the address given below
along with a cheque or money order payment made out to Boris Borzic.
Payment must be in the quoted U.S. or equivalent Canadian funds.

Boris Borzic, President
Armada Systems
P.O. Box 637, Station A
Downsview, Ontario
Canada M3M 3A9


NAME ____________________________ TITLE __________________________________
COMPANY _________________________ DEPARTMENT _____________________________
ADDRESS ___________________________________________________________________
CITY ____________________________ STATE/PROVINCE _________________________
ZIP/POSTAL CODE _________________ PHONE (_______)_________________________

What type of computer are you going to use this package on? _______________
Would you like the program supplied on 5.25" or 3.5" floppies? ____________
Where did you obtain the shareware package? _______________________________
How did you learn about this product? _____________________________________
What will be your primary application for the DAS program? ________________
___________________________________________________________________________
___________________________________________________________________________
Comments:
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________


DESCRIPTION PRICE $ QTY TOTAL $

Complete DAS package (DMM + PCM) 95.00

DMM program only 65.00

PCM program only 65.00

Applicable sales tax

TOTAL (U.S. funds)



Signature ______________________________ Date ____________________________
iii

2.05 - 8928900

PRODUCT COMMENT FORM


Use this form if you have any comments, or suggestions regarding the DAS
program or this manual. Armada Systems may use or distribute any of the
information you supply, in any way it believes appropriate, without incur-
ring any obligations whatsoever. Mail your comments to:

Armada Systems
Product Feedback
P.O. Box 637, Station A
Downsview, Ontario
Canada M3M 3A9


NAME ____________________________ TITLE __________________________________
COMPANY _________________________ DEPARTMENT _____________________________
ADDRESS ___________________________________________________________________
CITY ____________________________ STATE/PROVINCE _________________________
ZIP/POSTAL CODE _________________ PHONE (_______)_________________________
COMPUTER BRAND __________________ MODEL __________________________________
DATE PROGRAM RECEIVED ___________ OBTAINED FROM __________________________

COMMENTS:

iv



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 DAS

To make a working copy of DAS, simply follow one of the procedures below
corresponding to your computer system:

Hard disk system:
1. Boot-up PC DOS or MS DOS operating system
(you should see the C> prompt appear on screen).
2. Insert DAS floppy disk into drive A.
3. Type the following:
md\das
cd\das
copy a:*.* c:
4. To start using DAS, type the following:
cd\das
das

Floppy disk system:
1. Insert the PC DOS or MS DOS diskette supplied with your
computer 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
DAS diskette
6. Type the following:
copy a:*.* b:
7. To start using DAS, do the following:
insert the working copy of DAS into drive A, boot-up
computer and type das

v



SHAREWARE DISK CONTENTS

DAS.EXE - This is the main program which is used to initialize and
transfer control to the DMM and PCM application programs. It is also used
to create or edit the SETUP.DAS file which contains the user defined
screen colors and control code sequences to send to the printer at the
start and completion of printing. See section 1.

DMM.EXE - Decision Matrix Method application program. This program will
provide the user with an unbiased ranking of alternatives considered. It is
primarily designed to be used with tangible and easily quantifiable data.
See section 2.

PCM.EXE - Pairwise Comparison Method application program. This program is
based on the premise that it is easier to compare two objects then it is
to compare several objects. It will enable a user to easily quantify
subjective criteria, and thus develop effective decision strategies,
consistent with personal preferences. See section 3.

MANUAL.EXE - Program for printing this manual.

DAS.TXT - This manual.

CAR.DMM - File contains the data required in determining which car to
purchase from a set of alternatives. See section 2.3.

DAYCARE.DMM - This sample file demonstrates how a study to determine the
prime location for a new office may be performed using DMM. The problem
presented is concerned with determining an ideal location for a day-care
facility in a large metropolitan area. The data presented, was actually
obtained from government statistical publications.

CAR.PCM - File contains pairwise comparison data for the same car purchase
problem as in CAR.DMM, except that this data is subjective. See section 3.3.

LINE.PCM - File contains subjective pairwise comparisons of various lines
in order that their relative lengths may be estimated. See section 3.4.

BENEFIT.PCM & COST.PCM - 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 3.5.

XYZCOMP.PCM - This sample file shows how a comparative performance evalu-
ation of a company's branch-plant offices may be conducted using PCM.
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.
1


1.0 DECISION ANALYSIS SYSTEM


1.1 INTRODUCTION

More often than not, the decisions you make in your personal or profes-
sional 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 Decision Analysis
System (DAS) will be of most help to you.

DAS will aid an individual who is faced with a problem of choice in
selecting an alternative that is consistent with his personal basic
judgments and preferences. It consists of two separate and independent
application programs: the Decision Matrix Method (DMM), and the Pairwise
Comparison Method (PCM). Detailed descriptions of these are found, respect-
fully, in section 2 and section 3 of this manual. Briefly, the DMM
application program is designed to be used primarily with tangible and
easily quantifiable data. It will provide the user with an unbiased ranking
of alternatives considered. The PCM application program on the other hand,
is designed to deal specifically with subjective assessments and
evaluations of alternatives and criteria. It requires the user to develop a
hierarchical structure of the problem, and enables him to quantify the
impact of each element in this hierarchy on the overall goal of the study.


1.2 USING DAS

To get started using DAS simply "boot-up" your computer's PC DOS or MS DOS
operating system and then load DAS as prescribed in the GETTING STARTED
section at the front of this manual. When this program has been loaded into
memory, your computer screen will look similar to the following:


Decision Analysis System 2.05 Copyright (C) ARMADA SYSTEMS 1986, 1989
Shareware Edition Serial No. 8928900

Boris Borzic, Armada Systems
P.O. Box 637, Station 'A'
Downsview, Ontario, Canada M3M 3A9

Push a FUNCTION KEY to enter a command.

This software package may be freely copied and distributed. The programs, data
files and documentation however, must not be sold, separated or altered.

The complete shareware edition of DAS consists of the following files:
DAS.EXE, DMM.EXE, PCM.EXE, MANUAL.EXE, DAS.TXT, CAR.DMM, DAYCARE.DMM,
CAR.PCM, LINE.PCM, BENEFIT.PCM, COST.PCM, XYZCOMP.PCM

Commercial versions of DAS may be obtained as follows:
Application programs DMM and PCM may be purchased individually for $65.00 U.S.
or they may be purchased together as a complete package for $95.00 U.S.
To order, please specify which package you would like and send a cheque or
money order payable to Boris Borzic at the above address. Payment must include
any applicable sales taxes and be made in U.S. or equivalent Canadian funds.

1-DMM 2-PCM 3 4 5-FILES 6-SETUP 7-RNAME 8-ERASE 9-HELP 10-QUIT


2



The computer is now waiting for you to issue a command. If this is the
first time you are using this program, you are probably unsure of what that
might be. In that case, push the HELP key F9. The following help infor-
mation should appear on the screen:


HELP information:

F1 DMM - Execute Decision Matrix Method.
This method makes use of primarily quantitative, tangible data.
It is less demanding than the PCM method and it can be used with data
provided by several independent sources.
F2 PCM - Execute Pairwise Comparison Method.
This method is designed to be used with highly subjective and
qualitative data. It requires more data input than the DMM method,
but it can be used with intangible criteria.
F5 FILES- Display disk file directory.
F6 PRSET- Enter data to store in file 'SETUP.DAS'. This data will be used to
specify screen colors and to control the printer at print time.
F7 RNAME- Rename a file.
F8 ERASE- Erase a file.
F9 HELP - Display help information.
F0 QUIT - Exit to DOS.


As you can probably guess, function keys F1 and F2 are the most important
commands at this stage. Pushing one of these two keys will transfer control
to a specific application program. If you would like to start using one of
these programs, refer to either section 2 or section 3 of this manual for
further information.

The other keys F5 to F0, you could say, perform a support function. This
function should be quite clear from the information presented on the help
screen, except perhaps for key F6, SETUP. As indicated by the help
information, pushing this key will enable you to create a file SETUP.DAS,
which will contain the screen color definitions and control sequences to
send to the printer each time something is printed. It will also allow you
to specify the control sequences for resetting the printer when printing is
completed. Refer to the next section for more on this.


1.3 SCREEN COLORS AND PRINTER CONTROL

Push key F6. You will hear the disk drives activate as the program tries to
locate the SETUP.DAS file. If this file is not found in any drive, then the
following message will flash on the display screen:


Can't find file 'SETUP.DAS', using default values.

3



The bottom two-thirds of the display screen will then fill with the fol-
lowing information:


Editing printer and screen control data:

- Make necessary changes and push the RTN key to SAVE these changes to disk.
- To exit without changing anything, push a FUNCTION key or the ESC key.

Screen colors: Foreground Background Border
Normal characters: 7 0 0
Highlighted characters: 10 0 0
Screen heading: 4 7 0

Printer control:
Number of columns per line: 136 (min 80, max 255)
Number of lines per page: 66 (min 40)
Character sequence to initialize and reset printer (base 10):
Init. Printer: 13, 15, 0, 0, 0, 0, 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


The screen and printer control data displayed, are default values which
will be used by the program if a SETUP.DAS file is not present. A listing
of available screen colors is presented in figure 1.1, below:



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



Figure 1.1. Screen color attributes


As indicated in the printer control section, default control characters
which will be transmitted to the printer prior to printing are: (13)+(15)
in base 10. The first character (13), denotes the ASCII value for a
carriage return. This code causes the print head to advance to the leftmost
column of the page. If you have an Epson compatible dot matrix printer, the
second character (15), tells your printer to start printing in the
compressed mode. While in this mode, the printer can put 136 characters on
a standard eight inch line. The sequence for resetting the printer is left
blank, which means that when printing is completed, the printer will remain
in the compressed mode. You may of course change this character sequence if
you wish, or you can reset your printer when finished by turning it OFF
then ON.

4



If you wish to change any of the printer control data above, then simply
consult your printer's applications manual for the control codes of funct-
ions you would like to make use of. You may, for example want to change the
character pitch, 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.

It should be noted that, data for the number of columns per line (136), and
number of lines per page (66) are not printer control characters. They are
used only by the DMM applications program in calculating how to best print-
out large decision matrix spreadsheets. If you were to change the printer
line spacing, for example, then you would also have to calculate the number
of lines per page that the printer will be able to print, and consequently
change this variable in the SETUP.DAS file. Similarly, if you change the
horizontal print spacing, then you will also be required to update the
number of columns per line variable. If you will not be printing anything
from the DMM application program, then you need not worry about these two
variables.

5


2.0 DECISION MATRIX METHOD


2.1 INTRODUCTION

The Decision Matrix Method models decisions by representing them in a
matrix containing all of the information required to arrive at a final
decision. The columns of this matrix contain the criteria which are impor-
tant to the decision, while the rows contain the various alternatives being
considered. This program can handle up to 50 criteria and 60 alternatives.
It is an extremely easy method to use, enabling one to quickly narrow down
the set of alternatives to consider, by discarding dominated or substandard
alternatives.

This application program will be most useful when much of the data one has
is easily quantifiable, rather than being of the qualitative or subjective
nature. However, when data can not be easily quantified, one should
consider using the Pairwise Comparison Method described in section 3 of
this manual.

An explanation of the method used in this application program to model
problems will be presented in the next section. We will then proceed to the
hands-on application of this program on a computer, where an example will
be illustrated to clarify the method somewhat more.


2.2 THEORY OF OPERATION

As stated earlier, this method models problems using a decision matrix. The
columns of this matrix represent the criteria while the rows represent the
alternatives. Much scientific work has been done in the past in order to
arrive at a method which will take this decision matrix and prioritize the
alternatives from best to worst. Unfortunately, no universal method has yet
been developed which will preference order the alternatives in complete
agreement with all decision makers. There are methods which assume that the
decision maker is an extreme pessimist (ex. the maximin method which
selects an alternative to minimize losses), while some others assume that
he is an extreme optimist (ex. the maximax method which selects an alterna-
tive to maximize profits). Most methods try to achieve a balance between
these two extreme cases.

In this application program, a number of different methods are used to
arrive at a final preference ordering of alternatives. By using several
different methods, a variety of viewpoints can be taken into account when
rankings for all alternatives are finally formulated.

The decision matrix is first scanned for dominated alternatives. An
alternative is said to be dominated, if there exists another alternative in
the matrix which excels it in one or more criteria and equals it in the
remainder. If any dominated alternatives are found, they are flagged to the
user and he may elect to erase these from the matrix.

6



The next step is to check each alternative to see if they satisfy the
minimum requirements specified by each criteria. For example, if you wish
to buy a car and you only have $10,000 to spend, it's no use considering a
brand new Porshe. Alternatives which do not satisfy these cutoff criteria
are flagged and the user again has the option of erasing these from the
decision matrix, revising the cutoff constraints, or continuing with no
change.

After all undesirable alternatives have been flagged or eliminated, those
alternatives remaining in the matrix are preference ordered by using four
different and independent analytical techniques. These techniques are: The
Linear Assignment Method, Normalized Additive Weighting, ELECTRE, and
TOPSIS methods. We will not dwell on the theory of each of these methods as
they are fairly complicated. You may however, consult the list of refer-
ences at the end of this manual for more information.

An aggregation phase follows, which applies three different ordering tech-
niques to aggregate the four sets of alternative preferences generated
above. The first technique ranks alternatives according to their mean rank-
ings. The second calculates a score for each alternative based upon the
number of times that alternative is preferred to the other alternatives. In
effect this method counts the number of 'wins'. The last procedure is
similar to the second in that it takes into account the number of 'wins',
but to arrive at a final ranking, this procedure also subtracts the number
of 'losses'.

Finally, having produced three sets of aggregate rankings, a synthesis
phase is reached which tries to arrive at a consensus among these three
different aggregation strategies. The consensus is made by a partial
ordering technique which synthesizes the differing viewpoints. This means
that when the final ranking of alternatives is presented on screen, two or
more alternatives can be ranked equally if no substantial difference is
found between them. It would be up to the user to make the final distinc-
tion, if it is required.

One major point to keep in mind about the DMM application program, is that
DMM assumes a linear relationship between elements within a criteria
column. For example, the method assumes that the relative difference
between $10 and $11 is the same as the difference between $10,000 and
$11,000. The ratio between these two sets of values is the same (ie. 10%),
but most people would be much more reluctant to spend the extra $1,000 as
opposed to spending the extra $1. The problem is that people's subjective
feelings are not linear, and these feelings are affected by such factors as
how rich or how poor a person is. Answers produced with this program how-
ever, will be unbiased, but they may not always be in complete agreement
with the decision maker. It is therefore suggested that, for problems where
certain attributes are not considered to be linear (as explained above), or
where much of the data is subjective, then the Pairwise Comparison Method
(PCM) should be used (see section 3).
7


2.3 USING DMM

Let's have a look at using the DMM application program on the computer. In
order to get familiarized with the system, we will be going through a car
purchase problem which is provided on the file CAR.DMM.

If you have not yet loaded the DAS control program, then please do so in
the manner prescribed in the GETTING STARTED section at the front of this
manual. Once DAS has been loaded, push function key F1 and type x:CAR (x is
the drive letter indicating where the file CAR.DMM is to be found) followed
by RTN. This will trigger the DMM application program to be loaded and to
open file CAR.DMM in drive x. Once the file has been loaded, the computer
display screen will look something like this:



Decision Matrix Method File 'A:CAR .DMM' (C) ARMADA SYSTEMS 1986, 1989
Push a FUNCTION KEY to enter a command.
1 2 3 4 5 6
CRITERIA Price ($) EPA (mpg) 0-60 (Sec)Brake (ft)Lateral(g)Styling
WEIGHTS 38.0 15.0 7.0 8.0 11.0 21.0
CUTOFFS -11000.0 25.0 -12.0 -155.0 77.0

ALTERNATIVES
1 Mustang GT -10700.0 21.0 -7.0 -146.0 83.0 9.0
2 Tempo GL-S -8000.0 29.0 -10.9 -152.0 77.0 6.0
3 Prelude -11000.0 30.0 -11.1 -135.0 78.0 6.0
4 CorollaGTS -9500.0 28.0 -10.6 -143.0 87.0 8.0
5 VW GTI -9400.0 28.0 -10.2 -125.0 81.0 7.0


Information on this Decision Matrix:

This decision matrix contains the relevant data required in determining which
car to purchase (1985 model year).






1-CRITR 2-ALTRN 3-INFO 4-FILES 5-RUN 6-PRINT 7-SAVE 8-ERASE 9-HELP 10-QUIT



You will note that the bottom line of the screen lists the active function
keys. To get a little more information on what each key does push F9, the
HELP key. The bottom half of your screen should fill with the following
text:

HELP information: page 1, (Push HELP again for page 2).

F1 CRITR- Enter criteria data; including titles, subjective weights and cutoffs.
F2 ALTRN- Enter data for alternatives.
F3 INFO - Enter or display a 3 line summary of the present decision matrix.
F4 FILES- Display disk file directory.
F5 RUN - Compute the best alternatives from the present decision matrix.
F6 PRINT- Printout the decision matrix or results from a RUN.
F7 SAVE - Save to disk any changes made to the decision matrix.
F8 ERASE- Erase a file.
F9 HELP - Display the help screen, (push again for more information).
F0 QUIT - Exit the Decision Matrix Method, (file is not saved automatically).

8



As indicated on screen, this is page 1 of the help screen, push HELP again
to view page 2:


HELP information: page 2, (Push HELP again for page 1).

DEL, BACKSPACE - Move LEFT within a cell.
INS, TAB - Move RIGHT within a cell.
RETURN - Terminate input of current data.
ARROW keys - Move between cells.
Pg Up/Pg Dn - Display previous/next page.
HOME/END - Move to beginning/end of line.
ESC - Cancel command.
CTRL+ARROW key - Move to far end of current line or column.
ALT+I - Insert a new criteria or alternative at the present position.
ALT+D - Delete the current criteria (column) or alternative (row).


This help screen lists the editing keys which will be useful in editing the
matrix. The best way to get a feel for what each key does is to try them
out, however, since the matrix we are looking at presently is very small,
you will not be able to experience the full advantage of many of the keys.
Therefore, we suggest that you build your own matrix large enough to be
able to experiment with all of the keys. If you are building a matrix of
useful information, be careful in using the ALT+D key as this key will
erase a complete row or column of data.

If the "car" matrix has been changed, then push the QUIT key F10. This will
re-load the DAS control program. Now push function key F1, and, as before
type x:CAR (x is the drive letter indicating where file CAR.DMM is to be
found) followed by RTN to load file CAR.DMM into the DMM application
program. Once the file has been loaded, take a closer look at the decision
matrix. This same car purchase problem is used in section 3.3 of this
manual to explain how to use the Pairwise Comparison Method. It is strongly
suggested that after going through this exercise, you take a look at
section 3 and compare the two different methods used to tackle the same
problem.

Consider the subjective weights assigned to each criteria, these were deve-
loped with the PCM application program and rounded off to the nearest
decimal. A higher numerical value indicates that the corresponding criteria
is regarded as being more important than another criteria assigned a lower
value. For example, in this problem, price is voted as the most important
criteria and it is given 38% of the total weight. The scale used in assign-
ing these weights is not important, a 1 to 10 scale may have been used just
as well. The crucial factor is that values should be assigned in such a way
that they are all relative to each other. If it is felt that each criteria
should be assigned an equal weight, then this row may be left blank.

Next, let's consider the cutoffs associated with each criteria. As before,
if you do not wish to enter any cutoffs then you may leave this row blank.
In our example, price has a cutoff of $11,000, since this is the maximum
amount that we would like to spend on a car. We would also like to get a

9



car with a combined EPA rating better than 25 mpg, Having a 0 to 60 mph
acceleration of at least 12 seconds, a maximum stopping distance of 155
feet from 60 mph, and being able to attain a minimum 0.77g lateral acceler-
ation on a 150 foot circular track. Alternatives not satisfying these
minimum requirements will be flagged by the computer.

The data for each alternative is listed in the ALTERNATIVES section of the
decision matrix. Notice that in the price, acceleration and braking dist-
ance columns, all numerical entries are negative. This is because we
consider all of these criteria to be costs, that is, higher values in these
columns are less desirable than lower values. Making all entries negative
reverses this relationship, therefore, -146 is greater than -152 (ie. a
braking distance of 146 feet is better than one of 152 feet). In the
styling column, each alternative is subjectively rated on a scale of 1 to
10. The scale used is arbitrary, you may use any scale you wish, as long as
it is meaningful and each alternative is rated comparatively.

Now that we have studied the data presented in the matrix, lets see how the
computer will rate each alternative. To do this, push function key F5,
labeled RUN. If you would like a printout of the results, then push the
PRINT key after pushing RUN, otherwise push RUN again. The bottom half of
the screen will clear and you should see the following message appear:


The following alternatives do not satisfy the cutoff constraints:
You can delete these alternatives or go back and change the cutoff constraints.

Mustang GT


The reason that the Mustang was flagged as not satisfying the cutoff cons-
traints, is because we specified that we would like to get a car which has
a combined EPA rating of 25 mpg or better. Since the Mustang is rated at 21
mpg, it does not satisfy our requirements, therefore it should really be
erased from the decision matrix by pushing ALT+D, but for this example lets
keep it, in order to see how the computer will rank all alternatives. Push
RUN to continue. The bottom half of the screen will again clear and the
following alternative preference order rankings will be presented:


RANK ALTERNATIVES
1 - - Tempo GL-S
2 - - CorollaGTS
3 - - VW GTI
4 - - Mustang GT
5 - - Prelude


Compare these results with results obtained using the PCM application
program in section 3, you will find that they are in agreement. The Tempo
GL-S is rated as the best choice, based on the information supplied and the
criteria considered. This car should therefore be the one selected over the
others.

10



It would be worth-while to note here that, answers produced by the two
different systems will not always yield similar results. This is because,
as stated earlier, the DMM program assumes a linear relationship between
elements in a criteria column. If strong personal feelings exist for
certain criteria then results produced with the PCM program will reflect
this bias, and the decision analysis will be in closer agreement with the
decision maker. An example of this non-linear personal bias can be seen in
this example by considering the car prices:


ACTUAL CALCULATED WEIGHT PCM WEIGHT
ALTERNATIVE PRICE ($) (ACTUAL) (SUBJECTIVE)

Mustang GT 10,700 17.9 9.3
Tempo GL-S 8,000 24.0 46.0
Prelude 11,000 17.4 7.6
Corolla GTS 9,500 20.2 18.6
VW GTI 9,400 20.4 18.6


If this were a much larger problem, with many more alternatives and crite-
ria, a sensitivity analysis of the results should be conducted as follows:
After obtaining rankings for all alternatives in the matrix, delete those
alternatives (by locating the cursor in the proper row and pushing ALT+D)
having a ranking of say greater than 5. This number is arbitrary, however
it really shouldn't be much smaller than 5 since some good alternatives may
be thrown away. On the other hand, if it is much larger than 5, then not
much information may be gained, and the process may have to be repeated.
After the worst ranked alternatives have been eliminated from the decision
matrix, push RUN to obtain preference order rankings for the alternatives
remaining. Compare these results with results obtained previously using the
original set of alternatives. They should be similar, although they may
not always be exactly the same. If any major discrepancies do exist, then
you may again delete some of the worst ranked alternatives and generate a
still smaller set of rankings. The reason for this sensitivity analysis of
results is that more accurate rankings can be obtained when less
alternatives are being evaluated, especially when there are a large number
of conflicting criteria.
11


3.0 PAIRWISE COMPARISON METHOD


3.1 INTRODUCTION

The Pairwise Comparison Method (PCM) 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. Please note
that the PCM is not only useful in decision making problems, but also in
any other area where you find it necessary to quantify a number of subject-
ive criteria but otherwise find it difficult to do so. Once you have
learned to use this method, you will find the PCM to be an indispensable
tool.

The next section will deal with the method used by this application program
to model problems. We will then move on to the actual hands-on use of this
program on a computer. Finally, several examples will be presented to
clarify the method somewhat more and to suggest some areas of application.
It is strongly suggested that you look at these examples, as they are a
source of much information.


3.2 THEORY OF OPERATION

The technique used by the PCM application program is referred to as the
Analytic Hierarchy Process (AHP). It 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. However, it is important to remember that results obtained with
the use of this program are only as good as the model you have constructed
and the data you have entered into it.

12



3.2.1 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. Inter-
mediate 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 system can 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 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 an inconsistency index of 10% or less is
acceptable, and up to 15% 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.


3.2.2 Example

Let's look at an example. Suppose your goal is to purchase a car and you
wish to model this decision using PCM. 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 relia-
bility. The answer is obvious that a particular car will influence the
factors of level 1. 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 3.1 illustrates this hierarchy in graphical
form:
13





Level 0 GOAL




Level 1 PRICE FUEL ECONOMY STYLING RELIABILITY





Level 2 CAR A CAR B CAR C CAR D



Figure 3.1. 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 PCM application 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, in such a way that subjec-
tive preferences are reflected with respect to level 0 (overall goal).

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.


3.3 USING PCM

This section is intended to be used as a tutorial in learning to apply PCM
on a computer. A car purchase problem which is supplied on the file CAR.PCM
will be analyzed.

If you have not yet loaded the DAS control program, then please do so in
the manner prescribed in the GETTING STARTED section at the front of this
manual. Once DAS has been loaded, push function key F2 and type x:CAR (x is
the drive letter indicating where the file CAR.PCM is to be found) followed
by RTN. This will trigger the PCM application program to be loaded and to
open file CAR.PCM in drive x. Once the file has been loaded, the computer
display screen will look something like this:

14





Pairwise Comparison Method File 'A:CAR .PCM' (C) ARMADA SYSTEMS 1986, 1989
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


1-DATA 2-FILES 3-GRAPH 4-ORDER 5-RUN 6-PRINT 7-SAVE 8-ERASE 9-HELP 10-QUIT



As indicated on the second line of the screen, this represents the decision
tree hierarchy. Compare the method used to represent this hierarchy on
screen, with the method presented in Figure 3.1.

The bottom line lists the active function keys. To get a little more
information on what each key does push F9, the HELP key. Your computer
display screen should clear and list the following information:

HELP information:

F1 DATA - Display pairwise comparison data.
F2 FILES- Display disk file directory.
F3 GRAPH- Draw a bar graph of preference weights.
F4 ORDER- 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 SAVE - Save to disk any changes made to the file.
F8 ERASE- Erase a file.
F9 HELP - Display help information.
F0 QUIT - Exit the Pairwise Comparison Method, (file not saved automatically).

Special keys to help in editing the decision tree hierarchy:
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).


Note that the HELP screen reveals what each function key does. It also
lists a set of editing keys which will be useful in editing the hierarchy.
Play around a little with these keys to get a better feel for what each one
does. If in the process of experimenting, you have inadvertently changed

15



some of the data, then push the QUIT key F10 to go back the DAS control
program. Now push function key F1, and, as before type x:CAR (x is the
drive letter indicating where file CAR.PCM is to be found) followed by RTN
to re-load file CAR.PCM.


3.3.1 Pairwise comparisons for level 1

Position the cursor on the GOAL line (line 3) and push F1, the DATA key. As
indicated by the HELP screen information, 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:




Pairwise Comparison Method File 'A:CAR .PCM' (C) ARMADA SYSTEMS 1986, 1989
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











1-TREE 2-NEXT 3-GRAPH 4-ORDER 5-RUN 6-PRINT 7-SAVE 8-ERASE 9-HELP 10-QUIT



Note that the function key line here is slightly different, F1 and F2 have
changed. Push the HELP key in order to get an explanation of these new
function keys as well as a listing of the active editing keys used on this
screen. The following will be the HELP information displayed:

16




HELP information:

F1 TREE - Display the decision tree hierarchy.
F2 NEXT - Move on to the next set of pairwise comparison data.
F3 GRAPH- Draw a bar graph of preference weights.
F4 ORDER- 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 SAVE - Save to disk any changes made to the file.
F8 ERASE- Erase a file.
F9 HELP - Display help information.
F0 QUIT - Exit the Pairwise Comparison Method, (file not saved automatically).

Special keys to help in editing the pairwise comparison data:
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 contem-
plating 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 note to remember is that if your goal is not to estimate
costs, then the first element is always preferred to the second. Conver-
sely, 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 3.4.2). Therefore, to inverse a compari-
son enter a negative number.


3.3.2 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 F2, the key labeled 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.,

17



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

18



3.3.3 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 F1, the
key labeled TREE, this will return you to the decision tree hierarchy. Now
push the RUN key, F5. A set of numbers should be generated next to each
element in the decision tree, similar to the following:



Pairwise Comparison Method File 'A:CAR .PCM' (C) ARMADA SYSTEMS 1986, 1989
Decision Tree Hierarchy
GOAL: To purchase the car best suited for me.

Level 1 Level 2 Level 3 Level 4 Level 5

1 Price 38Mustang GT 19
2 Fuel econ. 15Tempo Sport 25
3 Acceleraton 7Prelude 13
4 Braking 8Corolla GTS 23
5 Handling 11VW GTI 21
6 Styling 21
7
8
9
10
11
12
13
14
15
16

Overall average inconsistency= 1.8% (acceptable)
1-DATA 2-FILES 3-GRAPH 4-ORDER 5-RUN 6-PRINT 7-SAVE 8-ERASE 9-HELP 10-QUIT



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 F3 or F4. Pushing F4, ORDER, should produce a screen
output similar to the one below:


Bar Graph of Preference Weights for level 2
Inconsistency= 1.6% (acceptable)

Tempo Sport 24.6
Corolla GTS 22.6
VW GTI 21.2
Mustang GT 18.7
Prelude 12.9


Pushing F3, GRAPH, will also produce a bar graph, except that it will
not be ordered from highest to lowest score.
19


3.4 SAMPLE PROBLEMS


3.4.1 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 endow you with a feel for the 1-9 subjective scale used
in the PCM program. The way we will do this, is to estimate the relative
lengths of seven straight lines, and then compare these 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 drawn in figure 3.3, below:


L1
L2
L3
L4
L5
L6
L7

Figure 3.3. Straight lines used for pairwise comparison analysis.


The data which we have supplied for this exercise is found on your program
diskette in the file LINE.PCM, 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 inputting your own data, you
enter a positive number when it really should be negative, then all is not
lost, the computer will in most cases flag this error as an inconsistent
judgment. You would then go back and revise your data.
20



The second point which must be made clear is, before you start inputting
any data into a pairwise comparison matrix, consider all of the alterna-
tives 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 subjec-
tive scale used on one problem need not be the same as in an other. 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 PCM 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 estimated through subjective
means 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 sense 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.

21


3.4.2 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 alterna-
tives, 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 we can perform a benefit to cost ratio test for each alter-
native. 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 transpor-
tation 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 accessi-
bility of using each alternative. The benefit hierarchy is illustrated in
Figure 3.4.

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 result-
ing from each alternative. The cost hierarchy is illustrated in Figure 3.5.

22




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 3.4. 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 3.5. 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


23



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 as supplied on the DAS
distribution diskette. The benefit hierarchy is found in the BENEFIT.PCM
file, while the cost hierarchy is found in the COST.PCM file.

If you think back, you will recall that 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 3.4 and 3.5,
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 connect-
ion 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.


Pairwise Comparison Method File 'A:benefit .PCM' (C) ARMADA SYSTEMS 1986, 1989
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 67Time saving 5Expressway 36
2 Social 11Job creatin 46Subway 55
3 Personal 22Commerce 16Improve 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= 4.6% (acceptable)

24




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



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



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

25




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

26




Pairwise Comparison Method File 'A:cost .PCM' (C) ARMADA SYSTEMS 1986, 1989
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 74Capital 65Expressway 37
2 Social 17Operational 9Subway 52
3 Environment 9Lifestyles 2Improve 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= 3.7% (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

27




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

28


3.4.3 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 experien-
ces 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 judgmen-
ts 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.

29


3.4.4 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 impor-
tant 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.

30


3.4.5 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 opera-
ting costs for the first level, and the coal plant alternatives in the last
level.

31







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




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