







             __                         ___                          _
      ____   ~7@e                       \@@                           '+,
      @@@@@>,  `7@.                      @@\                      ..    `@.
      @@|  `?,   @@,                     \@@                    %@@@+.  /@@.
      @@|    ?;   @@,                     @@\                  %@@"    +@@+
      @@|     `'  `@@                     \@@                  @@%       ~
      @@|          )@L                 A.  @@\                 +@@
      @@|          )@@                /@L  \@@               .   \\
      @@|          ;@@,              .@@@   @@\              \      `. 
      @@|          ;@@;              @@@'   \@@               +,.     \\
      @@|          ;@@;             /@@P     @@\                 ++.    @\
      @@|          ;@@;            ,@@@      \@@                    \    @+
      @@|          I@@;            ---'       @@\                    +   @@,
      @@|          @@@'                       \@@                    '   @@)
      @@|         %@@;            __________   @@\            __         @@@
      @@|        %@@P            j@@@@@@@@@@L  \@@         .  @@;        @@%
      --'      .%@@P            ,@@@            @@\        :   +j       j@@)
              .@@@'             @@@'            \@@        `\    ~     ,@@)
   ________.+@@@P'          ___@@@/            __@@\        \\._______j@@)
   @@@@@@@@@@@P'            @@@@@P             @@@@@.        `+@@@@@@@@%'



             D E C I S I O N    A N A L Y S I S    S Y S T E M

                     The Modern Art of Decision Making













                     USER'S GUIDE AND REFERENCE MANUAL

                            Shareware Edition
                               Release 2.50


___________________________________________________________________________

   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.
___________________________________________________________________________





DAS - Decision Analysis System
The Modern Art of Decision Making
Program Serial No. 9334300, Release 2.50





A Product Comment Form is provided at the front of this publication. If 
this form has been removed, you can mail your comments to the address
below:


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

Tel. (905) 889-2617

















DAS, DME, AHP 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 _____________________________
OBTAINED FROM ___________________  DATE ___________________________________



                             TABLE OF CONTENTS






                                                                       PAGE
                                                                    
  ARMADA SYSTEMS LICENSE AGREEMENT ...................................   i
  PRODUCT COMMENT FORM ...............................................  ii
                                                                    
  GETTING STARTED .................................................... iii
  CREATING A WORKING COPY OF DAS                                       iii
  DISK CONTENTS                                                         iv
                                                                    
                                                                    
  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 EXPERT ........................................   5
       2.1  INTRODUCTION                                                 5
       2.2  THEORY OF OPERATION                                          5
       2.3  USING THE DME                                                7
                                                                    
  3.0  ANALYTIC HIERARCHY PROCESS ....................................  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 THE AHP                                               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

  4.0  ABOUT ARMADA SYSTEMS ..........................................  31
       4.1  MyBASE                                                      32

  5.0  ORDERING SOFTWARE .............................................  34

  ARMADA SYSTEMS SOFTWARE REGISTRATION AND ORDER FORM ................  35

  REFERENCES .........................................................  36
        
                                     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.

                                    ii   

2.50 - 9334300

PRODUCT COMMENT FORM


Use this form if you have any comments, or suggestions regarding the DAS 
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__________________________
WHERE DID YOU OBTAIN THIS SOFTWARE?________________________________________

COMMENTS/SUGGESTIONS:

                                    iii



GETTING STARTED

Before doing anything, it is suggested 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 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
           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

                                    iv



DISK CONTENTS

DAS.EXE - This  is  the  main  program  which  is  used  to initialize  and 
transfer control to the  DME and  AHP 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.
 
DME.EXE - Decision Matrix Expert 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.

AHP.EXE - Analytic Hierarchy Process 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.

SETUP.DAS - Program setup file defining screen colors  and  printer control
codes.

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

DAYCARE.DME - This sample file demonstrates  how a study  to  determine the
prime location for a  new office may  be  performed using DME.  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.AHP - File contains pairwise comparison data for  the same car purchase
problem as in CAR.DME, except that this data is subjective. See section 3.3.

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

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 3.5.

XYZCOMP.AHP - This sample file shows how  a  comparative performance evalu-
ation  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. 
                                     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 Expert (DME), and  the  Analytic
Hierarchy Process (AHP). Detailed descriptions of these are found, respect-
fully,  in  section  2  and section 3 of  this  manual.  Briefly,  the  DME
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 AHP 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:

Ŀ
 Decision Analysis System  2.50          Copyright (C) 1986-1993, ARMADA SYSTEMS  
 FOR NON-COMMERCIAL, EDUCATIONAL AND EVALUATION USE ONLY!     Serial No. 9334300  
                                                                                  
 Boris Borzic, Armada Systems                                                     
 P.O. Box 637, Station 'A'                                                        
 Downsview, Ontario, Canada  M3M 3A9                                              
  
 Push a FUNCTION KEY to enter a command.                                          
                                                                                  
 This is a shareware product which may be freely copied and distributed to        
 others. The programs, data files and documentation which constitute this         
 package, however, are a complete entity which must not be sold, separated,       
 altered, or reverse engineered in any way shape or form. Furthermore, use of     
 this shareware software is limited to 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.                               
                                                                                  
 When you register, you will be eligible for telephone support, and will receive  
 the latest version of DAS (with no scrolling message) which will allow you to    
 save your own files to disk.                                                     
                                                                                  
 Push F3 to print a DAS registration and order form....                           
                                                                                  
 1-DME   2-AHP   3-DAS ORDER FORM 5-FILES 6-SETUP 7-RNAME 8-ERASE 9-HELP 10-QUIT  

                                     2



The program 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  information
should appear on the screen:


HELP information:

F1 DME  - Run Decision Matrix Expert.
          This program makes use of primarily quantitative, tangeable data.
          It is less demanding than the AHP and it can be used with data
          provided by several independent sources.
F2 AHP  - Run Analytic Hierarchy Process.
          This program is designed to be used with highly subjective and
          qualitative data. It requires more data input than the DME but,
          it can be used with intangeable criteria.
F3 ORDER- Print a DAS registration and order form.
F5 FILES- Display disk file directory.
F6 SETUP- Set screen colors and printer control data (stored in file SETUP.DAS).
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. To print a DAS registration and order form, push F3.

The  other keys F5 to F10, 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
   Standard text:                7          0          0
   Highlighted text:            10          0          0
   Screen heading:               0          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: 


                   Ŀ
                    COLOR      STANDARD   HIGH-INTENSITY 
                   Ĵ
                    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 DME 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 DME application program, then you need not worry about these  two
variables.
                                     5


2.0                       DECISION MATRIX EXPERT


2.1  INTRODUCTION

The Decision Matrix Expert 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  impor-
tant to the decision, while the rows depict the various alternatives  being 
considered. This program can handle up to 48 criteria and 60  alternatives. 
It  is  extremely  easy  to use. By  discarding  dominated  or  substandard 
alternatives, it enables you to quickly narrow down the set of alternatives 
you need to consider.

This application program will be most useful when much of the data you have 
is easily quantifiable, rather than being of the qualitative or  subjective 
nature. For those occasions when your data cannot be easily quantified, you 
should consider using the Analytic Hierarchy Process described in section 3
of this manual.

The  next  section will provide an explanation of the method used  in  this 
program  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.


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. 

This  program  uses  a number of different methods 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 of  alterna-
tives 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.  The Hwang and Yoon
book, "Multiple Attribute Decision Making" is especially informative.

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.

As the program proceeds through each algorithm phase, intermediate  results 
are  written  to  a file called OUTPUT.DME. You can see  these  results  by
loading this file into the DME program. A sample printout of the OUTPUT.DME
file is provided in section 2.3.

One major point to keep in mind about the DME application program, is  that
DME  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  Analytic Hierarchy Process
(AHP) should be used (see section 3).
                                     7


2.3  USING THE DME

Let's  have a look at a practical application of the DME program. In  order
to  get  familiarized  with  the system, we will be  going  through  a  car 
purchase problem which is supplied on your diskette. 

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.DME is to be found) followed
by  RTN. This will trigger the DME application program to be loaded and  to
open  file CAR.DME in drive x. Once the file has been loaded, the  computer
display screen will look something like this:


Ŀ 
 Decision Matrix Expert    File 'A:CAR     .DME'   (C) 1986-1993, ARMADA SYSTEMS  
 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            
 Ĵ 
 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  - Evaluate alternatives, (results are written to a file OUTPUT.DME).
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 Expert, (file is not saved automatically).


As indicated on screen, this is page 1 of the help screen, push HELP  again 
to view page 2:
                                     8




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.DME is  to  be
found)  followed  by  RTN to load file CAR.DME  into  the  DME  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 Analytic Hierarchy Process. 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  AHP 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
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.
                                     9 



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 so that we can see how the program will rank all five 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  AHP  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 selected over the others. 

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 DME program assumes a linear  relationship  between
elements  in  a  criteria column. If strong  personal  feelings  exist  for 
certain  criteria then results produced with the AHP 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:
                                    10



                        ACTUAL     CALCULATED WEIGHT    AHP 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



As  the DME program evaluates alternatives, intermediate results from  each
algorithm phase are written to a file called OUTPUT.DME. If you would  like
to  see  these  results then push F10 to QUIT DME, then push  F1  and  type
OUTPUT  followed  by  RTN.  The  following is  a  sample  printout  of  the 
OUTPUT.DME file for the above car selection problem:


   Decision Matrix Expert           File 'OUTPUT  .DME'

    Algorithm outputs from file: CAR     .DME
       Ranking phase:  LAM (rank), NAW (weight), ELECTRE (rank), TOPSIS (weight)   
       Aggregation phase:  AVG. RANK, # OF WINS, # WIN-LOSS                        

   =============|===  1 ===|===  2 ===|===  3 ===|===  4 ===|===  5 ===|===  6 ===|===  7 ===|===  8 ===|
   ALGORITHM    |   LAM    |   NAW    | ELECTRE  |  TOPSIS  |AVG. RANK |# OF WINS |# WIN-LOSS|FINAL RANK|
   PHASE        |          |          |          |          |          |          |          |          |
                |          |          |          |          |          |          |          |          |
   -------------|----------|----------|----------|----------|----------|----------|----------|----------|
   ALTERNATIVES |          |          |          |          |          |          |          |          |
    1 Mustang GT|      4.0 |   -273.2 |      2.0 |     44.1 |      3.5 |      1.0 |     -2.0 |      4.0 |
    2 Tempo GL-S|      1.0 |   -167.1 |      1.0 |     57.3 |      1.3 |      4.0 |      4.0 |      1.0 |
    3 Prelude   |      5.0 |   -620.9 |      5.0 |     25.3 |      5.0 |          |     -4.0 |      5.0 |
    4 CorollaGTS|      3.0 |   -102.0 |      1.0 |     56.3 |      1.8 |      3.0 |      2.0 |      2.0 |
    5 VW GTI    |      2.0 |   -191.5 |      2.0 |     49.1 |      2.5 |      2.0 |          |      3.0 |


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 7. This number is arbitrary,  however 
it really shouldn't be much smaller than 7 since some good alternatives may 
be  thrown away. On the other hand, if it is much larger than 7,  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                     ANALYTIC HIERARCHY PROCESS


3.1  INTRODUCTION

The Analytic Hierarchy Process (AHP) 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 AHP 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 AHP to be  an  indispensable
tool.

The  next section will deal with the method used by this program  to  model
problems. We will then move on to the actual hands-on use of this  program,
and  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 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.

                                    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 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.


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 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  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




                                     ͻ
Level 0                                GOAL  
                                     ͼ 
                                          
                 Ŀ
             Ŀ    Ŀ   Ŀ   Ŀ
Level 1       PRICE      FUEL ECONOMY     STYLING     RELIABILITY 
                       
                                                               
                 Ĵ
                                                               
             Ŀ       Ŀ        Ŀ       Ŀ
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 AHP 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 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.

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.AHP is to be found) followed
by  RTN. This will trigger the AHP application program to be loaded and  to
open  file CAR.AHP in drive x. Once the file has been loaded, the  computer
display screen will look something like this:

                                    14




Ŀ
 Analytic Hierarchy Process  File 'A:CAR     .AHP' (C) 1986-1993, ARMADA SYSTEMS  
 Decision Tree Hierarchy                                                          
 GOAL: To purchase a car.                                                         
     ͻ 
        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                                                                        
 ͼ 
                                                                                  
 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 Analytic Hierarchy Process, (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.AHP is to be found) followed by  RTN
to re-load file CAR.AHP.


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:


Ŀ
 Analytic Hierarchy Process  File 'A:CAR     .AHP' (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                                         
                                                                                  
                                                                                  
                                                                                  
                                                                                  
                                                                                  
                                                                                  
                                                                                  
                                                                                  
                                                                                  
                                                                                  
                                                                                  
 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 Analytic Hierarchy Process, (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:


Ŀ
 Analytic Hierarchy Process  File 'A:CAR     .AHP' (C) 1986-1993, ARMADA SYSTEMS  
 Decision Tree Hierarchy                                                          
 GOAL: To purchase the car best suited for me.                                    
     ͻ 
        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                                                                         
 ͼ 
 Overall average inconsistency= 0.18 (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= 0.16 (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 AHP 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.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 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 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 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



                                      ͻ
Level 0                                BENEFITS OF PROJECT 
                                      ͼ
                                                 
                      Ŀ
                                                                         
          Ŀ  Ŀ  Ŀ
Level 1    ECONOMIC                 SOCIAL                   PERSONAL            
              
            Ŀ    Ŀ    Ŀ
Level 2     ôTIME SAVINGS            ôCOMMUNITY PRIDE         ôTRAFFIC VOLUME    
            Ĵ    Ĵ    Ĵ
            ôJOB CREATION            MORE TRIPS DOWNTOWN     ôPARKING           
            Ĵ         Ĵ
            COMMERCE                                          ôCOMFORT           
                                           Ĵ
                                                                ACCESSIBILITY     
                                                                 
                      Ĵ
          Ŀ  Ŀ  Ŀ
Level 3    BUILD EXPRESSWAY         BUILD SUBWAY             IMPROVE BUS SERVICE 
              

         Figure 3.4. Benefit hierarchy for transportation project.



                                      ͻ
Level 0                                  COSTS OF PROJECT  
                                      ͼ
                                                 
                      Ŀ
                                                                         
          Ŀ  Ŀ  Ŀ
Level 1    ECONOMIC                 SOCIAL                   ENVIRONMENTAL       
              
            Ŀ    Ŀ    Ŀ
Level 2     ôCAPITAL                 ôLIFESTYLE CHANGES       ôPOLLUTION         
            Ĵ    Ĵ    Ĵ
            OPERATIONAL             ôPEOPLE DISLOCATION      DECREASED PARKLAND
                 Ĵ     
                                      GENERAL DISRUPTION               
                                                    
                                                                         
                      Ĵ
                                                                         
          Ŀ  Ŀ  Ŀ
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:

                             Ŀ
                              EXPRESSWAY  SUBWAY  IMPROVE BUS 
        Ĵ
         BENEFITS                36        55         9      
        Ĵ
         COSTS                   37        52        10      
        Ĵ
         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.AHP
file, while the cost hierarchy is found in the COST.AHP 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.


Analytic Hierarchy Process  File 'A:benefit .AHP' (C) 1986-1993, ARMADA SYSTEMS
Decision Tree Hierarchy
GOAL: To determine the benefits of a transportation project to downtown core.
    ͻ
       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                                                                       
ͼ  
Overall average inconsistency= 0.46 (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




Analytic Hierarchy Process  File 'A:cost    .AHP' (C) 1986-1993, ARMADA SYSTEMS
Decision Tree Hierarchy
GOAL: To estimate the costs of a transportation project to the downtown core.
    ͻ
       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                                                                       
ͼ  
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 

                                    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


4.0  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 DAS,  Armada Systems publishes the MyBASE  software package.
The next several pages are devoted to  providing  you with a  better under-
standing of  what MyBASE is,  and how it  can help you  to manage data more
effectively.

                                    32


4.1  MyBASE

MyBASE  is a very powerful, easy to use, multipurpose database system.  You
can  use  MyBASE  in DOS or Windows to; view, edit,  sort,  search,  group, 
filter,  replace, copy/paste, merge, print, fax, import and 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.  This  important 
utility  will not only allow you do the standard merging of text and  data, 
but will also allow you to add macros to the merge file to control how data 
is  processed, where the output is sent to, and what external  programs  to 
call  (ex.  DOS  functions, file viewers,  word  processors,  spreadsheets, 
graphics viewers, FAX software, and so on).

For example, if you had a database of clients, you can create a merge  file 
to  send  all your clients (or just a small group of them)  a  personalized 
letter. The merged letter may be sent to a printer to obtain a hardcopy, or 
it  can  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.


Key features:

   * The program is small and fast.
   * Creates, reads and writes industry standard dBASE III files.
   * Memo field support for free-form notes of up to 64K in size each.
   * Context sensitive and user customizable help.
   * Password access.
   * Quick and simple database index and view setup.
   * View data in table or record view mode.
   * User configurable print drivers.
   * Tag individual records for printing, merging or replacing.
   * Filter database to display, print or merge a group of selected data.
   * Skip through database, searching for specific data.
   * Copy and paste data for faster input.
   * Templates and functions for data entry validation.
   * Define pop-up selection boxes for easier data entry.
   * Automatic telephone dialer.
   * Merge text, data and run external programs automatically.
   * Swap to DOS or run and pass data to any external program.
   * Support for EGA and VGA monitors to display more data on screen.
   * Supports EMS and XMS memory for improved performance.
   * Enhanced error management and error recovery.
   * Local Area Network (LAN) compatible.

                                    33


Contact management system:

A  sample  contact management system is included with  this  package.  This
contact  management  system includes, predefined 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. 

This  contact  management system can be easily modified to  suit  your  own 
needs. If you wish, you can also create any number of new databases.


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.

                                    34


5.0 ORDERING SOFTWARE

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:

     * The latest version of software.
     * Complete reference and user's guide.
     * Free technical support.
     * Notice of future updates and new products.
     * Eligibility for low cost upgrades.
     * Free shareware software, as follows:

     Ŀ
      PROGRAM ORDERED             FREE SHAREWARE YOU WILL RECEIVE  
     Ĵ
      DAS, DME, or AHP            MyBASE                          
      MyBASE                      Decision Analysis System        
     

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 "BORIS BORZIC". Payment must be in  the  quoted 
U.S. or Canadian funds. Site licensing and volume discounts (for quantities 
of 7 or more) 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 "BORIS BORZIC". Payment must be in the quoted
U.S. or Canadian funds. Site licensing and volume discounts (QTY. >= 7) are
available, please write for details.

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

Tel. (905) 889-2617


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 DAS software? ____________________________________

DAS 2.50 - 9334300
Ŀ
           DESCRIPTION                U.S. $   CDN $  QTY   TOTAL $  
͵
 Complete DAS package (DME + AHP)     149.00  179.00                 
Ĵ
 DME program only                      99.00  119.00                 
Ĵ
 AHP program only                      99.00  119.00                 
Ĵ
 MyBASE (single user version)         130.00  156.00                 
Ĵ
 MyBASE (multi-user/LAN version)      270.00  324.00                 
Ĵ
 DME + AHP + MyBASE (single user)     259.00  310.00                 
Ĵ
 DME + AHP + MyBASE (multi-user)      399.00  479.00                 
Ĵ
                             Purchase order processing charge    15.00   
                           (cross out if payment is enclosed)            
                                                              Ĵ
                                          Shipping & handling     8.00   
                                                              Ĵ
                                             Applicable taxes            
                                                              Ĵ
                                                        TOTAL            
                                                              

Signature ______________________________  Date ____________________________

Use the back of this sheet to add your comments or suggestions.








                                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


