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__ ___ _ ____ ~7@e \@@ '+, @@@@@>, `7@. @@\ .. `@. @@| `?, @@, \@@ %@@@+. /@@. @@| ?; @@, @@\ %@@" +@@+ @@| `' `@@ \@@ @@% ~ @@| )@L A. @@\ +@@ @@| )@@ /@L \@@ . \\ @@| ;@@, .@@@ @@\ \ `. @@| ;@@; @@@' \@@ +,. \\ @@| ;@@; /@@P @@\ ++. @\ @@| ;@@; ,@@@ \@@ \ @+ @@| I@@; ---' @@\ + @@, @@| @@@' \@@ ' @@) @@| %@@; __________ @@\ __ @@@ @@| %@@P j@@@@@@@@@@L \@@ . @@; @@% --' .%@@P ,@@@ @@\ : +j j@@) .@@@' @@@' \@@ `\ ~ ,@@) ________.+@@@P' ___@@@/ __@@\ \\._______j@@) @@@@@@@@@@@P' @@@@@P @@@@@. `+@@@@@@@@%' Decision Analysis System The Modern Art of Decision Making USER'S GUIDE AND REFERENCE MANUAL Shareware Edition Release 2.45 ___________________________________________________________________________ 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 Shareware Edition Program Serial No. 9317190, Release 2.45 Changes are periodically made to the information herein; these changes will be incorporated in new editions of this publication. A Product Comment Form is provided at the front of this publication. If this form has been removed, you can mail any comments to the address below: Armada Systems P.O. Box 637, Station A Downsview, Ontario M3M 3A9 Canada Tel. (416) 889-2617 or (905) 889-2617 after October 4, 1993 DAS, DMM, PCM and MyBASE are Trademarks of Armada Systems. Copyright (C) 1986-1993, Armada Systems All Rights Reserved. Written in Canada. For your records: NAME ____________________________ TITLE __________________________________ COMPANY _________________________ DEPARTMENT _____________________________ DATE PROGRAM RECEIVED ___________ OBTAINED FROM __________________________ TABLE OF CONTENTS PAGE ARMADA SYSTEMS LICENSE AGREEMENT ................................... i 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 METHOD ........................................ 5 2.1 INTRODUCTION 5 2.2 THEORY OF OPERATION 5 2.3 USING DMM 7 3.0 PAIRWISE COMPARISON METHOD .................................... 11 3.1 INTRODUCTION 11 3.2 THEORY OF OPERATION 11 3.2.1 Pairwise comparisons and inconsistency 12 3.2.2 Example 12 3.3 USING PCM 13 3.3.1 Pairwise comparisons for level 1 15 3.3.2 Pairwise comparisons for level 2 16 3.3.3 Relative impact on overall goal 18 3.4 SAMPLE PROBLEMS 19 3.4.1 Estimating relative lengths of lines 19 3.4.2 Benefit/Cost analysis 21 3.4.3 Application to psychotherapy 28 3.4.4 Calculating expected values 29 3.4.5 Determining optimum type of coal plant 30 4.0 ABOUT ARMADA SYSTEMS .......................................... 31 4.1 MyBASE 32 4.1.1 Quick overview of features 32 4.1.2 System requirements 33 5.0 ORDERING SOFTWARE: WHAT YOU WILL RECEIVE ...................... 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 2.45 - 9317190 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 _________________ PHONE (_______)_________________________ COMPUTER BRAND __________________ MODEL __________________________________ DATE PROGRAM RECEIVED ___________ OBTAINED FROM __________________________ COMMENTS/SUGGESTIONS: iii GETTING STARTED Before doing anything, we suggest that you make a working copy of the disk supplied to you. You should then keep the original disk as a back-up copy, in a safe place where it will not come in contact with any heat, dust, or magnetic radiation. In the event that your working copy is ever damaged or destroyed, you can always make a new copy from the original disk. CREATING A WORKING COPY OF DAS To make a working copy of DAS, simply follow one of the procedures below corresponding to your computer system: Hard disk system: 1. Boot-up PC DOS or MS DOS operating system (you should see the C> prompt appear on screen). 2. Insert DAS floppy disk into drive A. 3. Type the following: md\das cd\das copy a:*.* c: 4. To start using DAS, type the following: cd\das das Floppy disk system: 1. Insert the PC DOS or MS DOS diskette supplied with your computer into drive A. 2. Boot-up DOS operating system by either turning computer on, or if already on, push the CTRL, ALT and DEL keys simultaneously (you should see the A> prompt on screen). 3. Insert a blank diskette into drive B 4. Type the following: format b:/s 5. When finished, replace the DOS disk in drive A with the DAS diskette 6. Type the following: copy a:*.* b: 7. To start using DAS, do the following: insert the working copy of DAS into drive A, boot-up computer and type das iv DISK CONTENTS DAS.EXE - This is the main program which is used to initialize and transfer control to the DMM and PCM application programs. It is also used to create or edit the SETUP.DAS file which contains the user defined screen colors and control code sequences to send to the printer at the start and completion of printing. See section 1. DMM.EXE - Decision Matrix Method program. This program will provide the user with an unbiased ranking of alternatives considered. It is primarily designed to be used with tangible and easily quantifiable data. See section 2. PCM.EXE - Pairwise Comparison Method 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.DMM - File contains the data required in determining which car to purchase from a set of alternatives. See section 2.3. DAYCARE.DMM - This sample file demonstrates how a study to determine the prime location for a new office may be performed using DMM. The problem presented is concerned with determining an ideal location for a day-care facility in a large metropolitan area. The data presented, was actually obtained from government statistical publications. CAR.PCM - File contains pairwise comparison data for the same car purchase problem as in CAR.DMM, except that this data is subjective. See section 3.3. LINE.PCM - File contains subjective pairwise comparisons of various lines in order that their relative lengths may be estimated. See section 3.4. BENEFIT.PCM & COST.PCM - These two files contain the hierarchical structure and subjective pairwise comparisons of the benefits and costs associated with three large scale transportation projects. Results are used in a benefit/cost analysis of these projects. See section 3.5. XYZCOMP.PCM - This sample file shows how a comparative performance evalu- ation of a company's branch-plant offices may be conducted using PCM. The hierarchy for this problem consists of braking the company down into major departments (engineering, sales, manufacturing, etc...), considering performance factors (productivity, quality, profitability, etc...), and finally the various branch-plant offices. 1 1.0 DECISION ANALYSIS SYSTEM 1.1 INTRODUCTION More often than not, the decisions you make in your personal or profes- sional life can be made without a lot of fuss. Either your best choice is clear to you without much analysis, or the decision is not important enough to warrant any great amount of attention. Occasionally, however, you probably find yourself in a situation where you feel it is worth your time and effort to think systematically and hard about the different courses of action you might pursue. It is in these cases that the Decision Analysis System (DAS) will be of most help to you. DAS will aid an individual who is faced with a problem of choice in selecting an alternative that is consistent with his personal basic judgments and preferences. It consists of two separate and independent application programs: the Decision Matrix Method (DMM), and the Pairwise Comparison Method (PCM). Detailed descriptions of these are found, respect- fully, in section 2 and section 3 of this manual. Briefly, the DMM application program is designed to be used primarily with tangible and easily quantifiable data. It will provide the user with an unbiased ranking of alternatives considered. The PCM application program on the other hand, is designed to deal specifically with subjective assessments and evaluations of alternatives and criteria. It requires the user to develop a hierarchical structure of the problem, and enables him to quantify the impact of each element in this hierarchy on the overall goal of the study. 1.2 USING DAS To get started using DAS simply "boot-up" your computer's PC DOS or MS DOS operating system and then load DAS as prescribed in the GETTING STARTED section at the front of this manual. When this program has been loaded into memory, your computer screen will look similar to the following: ┌──────────────────────────────────────────────────────────────────────────────────┐ │ Decision Analysis System 2.45 Copyright (C) 1986-1993, ARMADA SYSTEMS │ │ Shareware Edition ░▒▓ FOR EDUCATIONAL AND TRIAL USE ONLY ▓▒░ Serial No. 9317190 │ │ │ │ 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-DMM 2-PCM 3-DAS ORDER FORM 5-FILES 6-SETUP 7-RNAME 8-ERASE 9-HELP 10-QUIT │ └──────────────────────────────────────────────────────────────────────────────────┘ 2 The computer is now waiting for you to issue a command. If this is the first time you are using this program, you are probably unsure of what that might be. In that case, push the HELP key F9. The following help infor- mation should appear on the screen: HELP information: F1 DMM - Execute Decision Matrix Method. This method makes use of primarily quantitative, tangible data. It is less demanding than the PCM method and it can be used with data provided by several independent sources. F2 PCM - Execute Pairwise Comparison Method. This method is designed to be used with highly subjective and qualitative data. It requires more data input than the DMM method, but it can be used with intangible criteria. 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 F0, you could say, perform a support function. This function should be quite clear from the information presented on the help screen, except perhaps for key F6, SETUP. As indicated by the help information, pushing this key will enable you to create a file SETUP.DAS, which will contain the screen color definitions and control sequences to send to the printer each time something is printed. It will also allow you to specify the control sequences for resetting the printer when printing is completed. Refer to the next section for more on this. 1.3 SCREEN COLORS AND PRINTER CONTROL Push key F6. You will hear the disk drives activate as the program tries to locate the SETUP.DAS file. If this file is not found in any drive, then the following message will flash on the display screen: Can't find file 'SETUP.DAS', using default values. 3 The bottom two-thirds of the display screen will then fill with the fol- lowing information: Editing printer and screen control data: - Make necessary changes and push the RTN key to SAVE these changes to disk. - To exit without changing anything, push a FUNCTION key or the ESC key. Screen colors: Foreground Background Border Normal characters: 7 0 0 Highlighted characters: 10 0 0 Screen heading: 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: ┌──────────┬────────────┬────────────────┐ │ COLOR │ STANDARD │ HIGH-INTENSITY │ ├──────────┼────────────┼────────────────┤ │ Black │ 0 │ 8 │ │ Blue │ 1 │ 9 │ │ Green │ 2 │ 10 │ │ Cyan │ 3 │ 11 │ │ Red │ 4 │ 12 │ │ Magenta │ 5 │ 13 │ │ Brown │ 6 │ 14 │ │ White │ 7 │ 15 │ └──────────┴────────────┴────────────────┘ Figure 1.1. Screen color attributes As indicated in the printer control section, default control characters which will be transmitted to the printer prior to printing are: (13)+(15) in base 10. The first character (13), denotes the ASCII value for a carriage return. This code causes the print head to advance to the leftmost column of the page. If you have an Epson compatible dot matrix printer, the second character (15), tells your printer to start printing in the compressed mode. While in this mode, the printer can put 136 characters on a standard eight inch line. The sequence for resetting the printer is left blank, which means that when printing is completed, the printer will remain in the compressed mode. You may of course change this character sequence if you wish, or you can reset your printer when finished by turning it OFF then ON. 4 If you wish to change any of the printer control data above, then simply consult your printer's applications manual for the control codes of funct- ions you would like to make use of. You may, for example want to change the character pitch, or perhaps you would like to reduce the line spacing so that more lines can be printed on one page. The possibilities are limited only by your printer. When you have decided what functions you would like to utilize, make the necessary changes on screen and push RTN to save these to disk. It should be noted that, data for the number of columns per line (136), and number of lines per page (66) are not printer control characters. They are used only by the DMM applications program in calculating how to best print- out large decision matrix spreadsheets. If you were to change the printer line spacing, for example, then you would also have to calculate the number of lines per page that the printer will be able to print, and consequently change this variable in the SETUP.DAS file. Similarly, if you change the horizontal print spacing, then you will also be required to update the number of columns per line variable. If you will not be printing anything from the DMM application program, then you need not worry about these two variables. 5 2.0 DECISION MATRIX METHOD 2.1 INTRODUCTION The Decision Matrix Method models decisions by representing 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 Pairwise Comparison Method 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. In this application program, a number of different methods are used to arrive at a final preference ordering of alternatives. By using several different methods, a variety of viewpoints can be taken into account when rankings for all alternatives are finally formulated. The decision matrix is first scanned for dominated alternatives. An alternative is said to be dominated, if there exists another alternative in the matrix which excels it in one or more criteria and equals it in the remainder. If any dominated alternatives are found, they are flagged to the user and he may elect to erase these from the matrix. 6 The next step is to check each alternative to see if they satisfy the minimum requirements specified by each criteria. For example, if you wish to buy a car and you only have $10,000 to spend, it's no use considering a brand new Porshe. Alternatives which do not satisfy these cutoff criteria are flagged and the user again has the option of erasing these from the decision matrix, revising the cutoff constraints, or continuing with no change. After all undesirable alternatives have been flagged or eliminated, those alternatives remaining in the matrix are preference ordered by using four different and independent analytical techniques. These techniques are: The Linear Assignment Method, Normalized Additive Weighting, ELECTRE, and TOPSIS methods. We will not dwell on the theory of each of these methods as they are fairly complicated. You may however, consult the list of refer- ences at the end of this manual for more information. 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.DMM. You can see these results by loading this file into the DMM program. A sample printout of the OUTPUT.DMM file is provided in section 2.3. One major point to keep in mind about the DMM application program, is that DMM assumes a linear relationship between elements within a criteria column. For example, the method assumes that the relative difference between $10 and $11 is the same as the difference between $10,000 and $11,000. The ratio between these two sets of values is the same (ie. 10%), but most people would be much more reluctant to spend the extra $1,000 as opposed to spending the extra $1. The problem is that people's subjective feelings are not linear, and these feelings are affected by such factors as how rich or how poor a person is. Answers produced with this program how- ever, will be unbiased, but they may not always be in complete agreement with the decision maker. It is therefore suggested that, for problems where certain attributes are not considered to be linear (as explained above), or where much of the data is subjective, then the Pairwise Comparison Method (PCM) should be used (see section 3). 7 2.3 USING DMM Let's have a look at using the DMM application program on the computer. In order to get familiarized with the system, we will be going through a car purchase problem which is provided on the file CAR.DMM. If you have not yet loaded the DAS control program, then please do so in the manner prescribed in the GETTING STARTED section at the front of this manual. Once DAS has been loaded, push function key F1 and type x:CAR (x is the drive letter indicating where the file CAR.DMM is to be found) followed by RTN. This will trigger the DMM application program to be loaded and to open file CAR.DMM in drive x. Once the file has been loaded, the computer display screen will look something like this: ┌──────────────────────────────────────────────────────────────────────────────────┐ │ Decision Matrix Method File 'A:CAR .DMM' (C) 1986-1992, ARMADA SYSTEMS │ │ Push a FUNCTION KEY to enter a command. │ │ ═════════════╦═══ 1 ═══╤═══ 2 ═══╤═══ 3 ═══╤═══ 4 ═══╤═══ 5 ═══╤═══ 6 ═══╕ │ │ CRITERIA ║Price ($) │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 │ │ │ │ ─────────────╫──────────┼──────────┼──────────┼──────────┼──────────┼──────────┤ │ │ 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.DMM). F6 PRINT- Printout the decision matrix or results from a RUN. F7 SAVE - Save to disk any changes made to the decision matrix. F8 ERASE- Erase a file. F9 HELP - Display the help screen, (push again for more information). F0 QUIT - Exit the Decision Matrix Method, (file is not saved automatically). 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.DMM is to be found) followed by RTN to load file CAR.DMM into the DMM application program. Once the file has been loaded, take a closer look at the decision matrix. This same car purchase problem is used in section 3.3 of this manual to explain how to use the Pairwise Comparison Method. It is strongly suggested that after going through this exercise, you take a look at section 3 and compare the two different methods used to tackle the same problem. Consider the subjective weights assigned to each criteria, these were deve- loped with the PCM application program and rounded off to the nearest decimal. A higher numerical value indicates that the corresponding criteria is regarded as being more important than another criteria assigned a lower value. For example, in this problem, price is voted as the most important criteria and it is given 38% of the total weight. The scale used in assign- ing these weights is not important, a 1 to 10 scale may have been used just as well. The crucial factor is that values should be assigned in such a way that they are all relative to each other. If it is felt that each criteria should be assigned an equal weight, then this row may be left blank. Next, let's consider the cutoffs associated with each criteria. As before, if you do not wish to enter any cutoffs then you may leave this row blank. In our example, price has a cutoff of $11,000, since this is the maximum amount that we would like to spend on a car. We would also like to get a 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 PCM application program in section 3, you will find that they are in agreement. The Tempo GL-S is rated as the best choice, based on the information supplied and the criteria considered. This car should therefore be 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 DMM program assumes a linear relationship between elements in a criteria column. If strong personal feelings exist for certain criteria then results produced with the PCM program will reflect this bias, and the decision analysis will be in closer agreement with the decision maker. An example of this non-linear personal bias can be seen in this example by considering the car prices: 10 ACTUAL CALCULATED WEIGHT PCM WEIGHT ALTERNATIVE PRICE ($) (ACTUAL) (SUBJECTIVE) Mustang GT 10,700 17.9 9.3 Tempo GL-S 8,000 24.0 46.0 Prelude 11,000 17.4 7.6 Corolla GTS 9,500 20.2 18.6 VW GTI 9,400 20.4 18.6 As the DMM program evaluates alternatives, intermediate results from each algorithm phase are written to a file called OUTPUT.DMM. If you would like to see these results then push F10 to QUIT DMM, then push F1 and type OUTPUT followed by RTN. The following is a sample printout of the OUTPUT.DMM file for the above car selection problem: Decision Matrix Method File 'OUTPUT .DMM' Algorithm outputs from file: CAR .DMM 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 PAIRWISE COMPARISON METHOD 3.1 INTRODUCTION The Pairwise Comparison Method (PCM) will be most beneficial when you wish to model complex problems, and the only data available to solve these problems is your own subjective judgments or those of a group. Please note that the PCM is not only useful in decision making problems, but also in any other area where you find it necessary to quantify a number of subject- ive criteria but otherwise find it difficult to do so. Once you have learned to use this method, you will find the PCM to be an indispensable tool. The next section will deal with the method used by this application program to model problems. We will then move on to the actual hands-on use of this program on a computer. Finally, several examples will be presented to clarify the method somewhat more and to suggest some areas of application. It is strongly suggested that you look at these examples, as they are a source of much information. 3.2 THEORY OF OPERATION The technique used by the PCM application program is referred to as the Analytic Hierarchy Process (AHP). It is a proven scientific method, originally developed by Thomas L. Saaty at the Wharton School and described in his book "The Analytic Hierarchy Process" published by McGraw-Hill, 1980. We will not go into the actual theory and mathematical formulations of the method, because it is fairly involved. The interested reader can however consult the book "The Analytic Hierarchy Process" for much greater detail and more examples. Here, we shall be primarily concerned with the application of the method. The AHP requires that a problem be decomposed into a hierarchical model, structured so as to capture it's basic elements. Hierarchical decomposition involves setting up levels, where each level contains a set of elements. These elements are grouped in such a way that those of a lower level directly influence the elements in the immediately higher level, these in turn must influence elements in the next level and so on up to the goal of the hierarchy. The objective is to derive a set of quantitative weights for elements in the last level which reflect as best as possible their relative impact on the goal of the hierarchy. The way we accomplish this, is to compare in pairs, elements in each level with respect to those elements in the immediately higher level. The advantage of setting up a problem in a hierarchical structure is that it helps you in focusing your attention on each part of the problem separately. However, it is important to remember that results obtained with the use of this program are only as good as the model you have constructed and the data you have entered into it. 12 3.2.1 Pairwise comparisons and inconsistency Pairwise comparisons are made using a 1 to 9 numerical scale. For example, if elements A and B are being compared, a 1 would indicate that they are both equal and a 9 would indicate that A is extremely better than B. Inter- mediate values are used to arrive at a compromise between these two extreme points. When we compare N elements in a level with respect to an element in the immediately higher level, we would require N(N-1)/2 comparisons. That is, if 4 elements are being compared with each other, then a total of 6 pairwise comparisons are needed. These pairwise comparisons are entered into what is called a pairwise comparison matrix. As well as being able to calculate subjective weights based on your pairwise comparisons, the system can also provide you with an indication of your judgment consistency, or inconsistency as it is referred to in the program. Inconsistency in pairwise comparison judgments can best be described with the following example: If you were to say that stone A is heavier than stone B which is heavier than C, and then say that stone C is heavier than A, then your judgments would be inconsistent. In real life situations, one can not escape the fact that many things are in fact inconsistent. For example, in a game of sport team A can beat team B, team B can beat team C, but team C can nevertheless beat team A. In general, a pairwise comparison matrix with an inconsistency index of 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 PCM. The first question you must ask yourself is, what factors will influence your goal. Thinking a little bit about this, you would probably come up with things such as price, fuel economy, styling, reliability and so on. These would form the elements of the first level. You would then ask yourself a similar question as before; what factors would influence the price, fuel economy, styling and relia- bility. The answer is obvious that a particular car will influence the factors of level 1. Therefore the second level in your decision hierarchy will be comprised of the different types of cars which you are considering, ie. your alternatives. Figure 3.1 illustrates this hierarchy in graphical form: 13 ╔════════╗ Level 0 ║ GOAL ║ ╚════╤═══╝ │ ┌───────────────┬────────┴───────┬───────────────┐ ┌───┴───┐ ┌──────┴───────┐ ┌────┴────┐ ┌──────┴──────┐ Level 1 │ PRICE │ │ FUEL ECONOMY │ │ STYLING │ │ RELIABILITY │ └───┬───┘ └──────┬───────┘ └────┬────┘ └──────┬──────┘ │ │ │ │ ├───────────────┼────────────────┼───────────────┤ │ │ │ │ ┌───┴───┐ ┌───┴───┐ ┌───┴───┐ ┌───┴───┐ Level 2 │ CAR A │ │ CAR B │ │ CAR C │ │ CAR D │ └───────┘ └───────┘ └───────┘ └───────┘ Figure 3.1. Hierarchy for a car purchase problem. This particular problem requires only 2 levels in the model to describe. Highly complex models can however be created with up to 5 levels and 16 elements per level using the PCM application program. The technique used in creating a complex model would be the same as the one explained above. Once the hierarchical model has been created, pairwise comparison data must be entered into the computer. Elements in level 1 are first compared (in pairs) with respect to the overall goal (level 0). For example, with respect to a goal of purchasing a car, you would need to compare the elements; price, fuel economy, styling and reliability with each other, in pairs. The program will use these pairwise comparisons to arrive at a quantitative weight for each element in level 1, in such a way that subjec- tive preferences are reflected with respect to level 0 (overall goal). The next step involves performing a pairwise comparison of elements in level 2 (alternatives) with respect to elements in level 1 (price, fuel economy, styling, etc...). Again this data will be used by the program to arrive at a set of quantitative weights for each alternative with respect to each criteria in level 1. When you have finished inputting all pairwise comparison data, the program can calculate preference weights for the alternatives (level 2) with respect to the overall goal (level 0). The alternative with the highest score should be the alternative selected. 3.3 USING PCM This section is intended to be used as a tutorial in learning to apply PCM on a computer. A car purchase problem which is supplied on the file CAR.PCM will be analyzed. If you have not yet loaded the DAS control program, then please do so in the manner prescribed in the GETTING STARTED section at the front of this manual. Once DAS has been loaded, push function key F2 and type x:CAR (x is the drive letter indicating where the file CAR.PCM is to be found) followed by RTN. This will trigger the PCM application program to be loaded and to open file CAR.PCM in drive x. Once the file has been loaded, the computer display screen will look something like this: 14 ┌──────────────────────────────────────────────────────────────────────────────────┐ │ Pairwise Comparison Method File 'A:CAR .PCM' (C) 1986-1992, ARMADA SYSTEMS │ │ Decision Tree Hierarchy │ │ GOAL: To purchase a car. │ │ ╔══════════════╤══════════════╤══════════════╤══════════════╤══════════════╗ │ │ ║ Level 1 │ Level 2 │ Level 3 │ Level 4 │ Level 5 ║ │ │ ╔═══╬══════════════╪══════════════╪══════════════╪══════════════╪══════════════╣ │ │ ║ 1 ║Price │Mustang GT │ │ │ ║ │ │ ║ 2 ║Fuel econ. │Tempo Sport │ │ │ ║ │ │ ║ 3 ║Acceleraton │Prelude │ │ │ ║ │ │ ║ 4 ║Braking │Corolla GTS │ │ │ ║ │ │ ║ 5 ║Handling │VW GTI │ │ │ ║ │ │ ║ 6 ║Styling │ │ │ │ ║ │ │ ║ 7 ║ │ │ │ │ ║ │ │ ║ 8 ║ │ │ │ │ ║ │ │ ║ 9 ║ │ │ │ │ ║ │ │ ║10 ║ │ │ │ │ ║ │ │ ║11 ║ │ │ │ │ ║ │ │ ║12 ║ │ │ │ │ ║ │ │ ║13 ║ │ │ │ │ ║ │ │ ║14 ║ │ │ │ │ ║ │ │ ║15 ║ │ │ │ │ ║ │ │ ║16 ║ │ │ │ │ ║ │ │ ╚═══╩══════════════╧══════════════╧══════════════╧══════════════╧══════════════╝ │ │ │ │ 1-DATA 2-FILES 3-GRAPH 4-ORDER 5-RUN 6-PRINT 7-SAVE 8-ERASE 9-HELP 10-QUIT │ └──────────────────────────────────────────────────────────────────────────────────┘ As indicated on the second line of the screen, this represents the decision tree hierarchy. Compare the method used to represent this hierarchy on screen, with the method presented in Figure 3.1. The bottom line lists the active function keys. To get a little more information on what each key does push F9, the HELP key. Your computer display screen should clear and list the following information: HELP information: F1 DATA - Display pairwise comparison data. F2 FILES- Display disk file directory. F3 GRAPH- Draw a bar graph of preference weights. F4 ORDER- Draw a bar graph of preference weights, ordered from best to worst. F5 RUN - Calculate preference weights for the decision tree hierarchy. F6 PRINT- Send data on screen to printer. F7 SAVE - Save to disk any changes made to the file. F8 ERASE- Erase a file. F9 HELP - Display help information. F0 QUIT - Exit the Pairwise Comparison Method, (file not saved automatically). Special keys to help in editing the decision tree hierarchy: ALT+I - Insert a new branch into the decision tree. ALT+D - Delete a branch from the decision tree. CTRL+ARROW keys - Move between levels (columns). ARROW keys - Move within a level (column). RETURN - Terminate input of present branch, move down to next line. HOME - Move to the top of the next level (column). END, PgDn - Move to the bottom of the present level (column). PgUp - Move to the top of the present level (column). Note that the HELP screen reveals what each function key does. It also lists a set of editing keys which will be useful in editing the hierarchy. Play around a little with these keys to get a better feel for what each one does. If in the process of experimenting, you have inadvertently changed 15 some of the data, then push the QUIT key F10 to go back the DAS control program. Now push function key F1, and, as before type x:CAR (x is the drive letter indicating where file CAR.PCM is to be found) followed by RTN to re-load file CAR.PCM. 3.3.1 Pairwise comparisons for level 1 Position the cursor on the GOAL line (line 3) and push F1, the DATA key. As indicated by the HELP screen information, this will cause the pairwise comparison data to be displayed. Since the cursor was positioned on the GOAL line, which represents level 0 in the hierarchy, the data appearing on the screen will be the pairwise comparison matrix for level 1 with respect to the GOAL, as follows: ┌──────────────────────────────────────────────────────────────────────────────────┐ │ Pairwise Comparison Method File 'A:CAR .PCM' (C) 1986-1992, 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 Pairwise Comparison Method, (file not saved automatically). Special keys to help in editing the pairwise comparison data: HOME - Move to the first comparison (top left). ARROW keys - Move between comparisons. RETURN, INS, TAB - Move to the next comparison. DEL, BACKSPACE - Move to the previous comparison. Now push any key, other than a function key, in order to return to the pairwise comparison data. What we are trying to accomplish with this matrix, is to derive a list of weights for each element in level 1, so as to reflect quantitatively as best as possible, our subjective importance of these criteria with respect to our goal. Let's have a look at the data which has been supplied. Since there are 6 elements in level 1 (Price, Fuel econ., Acceleraton, Braking, Handling, and Styling), N(N-1)/2 or 15 comparisons are required. The first number in the matrix is a 3, this indicates that when contem- plating a car purchase, price is moderately more important than fuel economy . The next number is a 4 and this means that price is moderately to strongly more important than acceleration, and so on. Notice that in the fuel economy to styling comparison the matrix contains a -2, indicating that styling is just slightly more important than fuel economy. A negative just inverses the comparison. If you move the cursor around the matrix, the elements which are being compared will be displayed on the fifth line of your screen. Now if you push the "-" key at any spot in the matrix, you will notice that the two elements printed on the fifth line will inverse. An important note to remember is that if your goal is not to estimate costs, then the first element is always preferred to the second. Conver- sely, if you do wish to estimate costs, then the first element presented on the fifth line of the pairwise comparison screen, should be the element with the greater cost (see section 3.4.2). Therefore, to inverse a compari- son enter a negative number. 3.3.2 Pairwise comparisons for level 2 We have looked at level 1, now let's continue with the pairwise comparisons for level 2 as given below. By pushing F2, the key labeled NEXT, you can view this same data on your screen. Notice that in level 2 there are 6 pairwise comparison matrices; there is one for Price, one for Fuel econ., 17 Acceleration, Braking, Handling, and Styling. Whenever data is entered for this level we must keep in mind with respect to what criteria the pairwise comparisons are being made to. The second or fourth line on the display screen will remind you of this. Pairwise Comparison Data for level 2, with respect to: Price A B C D E WEIGHTS A -4 1 -2 -2 A Mustang GT 9.3 ▒▒ B 5 3 3 B Tempo Sport 46.0 ▒▒▒▒▒▒▒▒▒ C -3 -3 C Prelude 7.6 ▒ D 1 D Corolla GTS 18.6 ▒▒▒▒ E E VW GTI 18.6 ▒▒▒▒ Pairwise Comparison Data for level 2, with respect to: Fuel econ. A B C D E WEIGHTS A -3 -3 -3 -3 A Mustang GT 7.6 ▒▒ B 1 1 1 B Tempo Sport 22.7 ▒▒▒▒▒▒▒ C 2 2 C Prelude 30.4 ▒▒▒▒▒▒▒▒▒ D 1 D Corolla GTS 19.7 ▒▒▒▒▒▒ E E VW GTI 19.7 ▒▒▒▒▒▒ Pairwise Comparison Data for level 2, with respect to: Acceleraton A B C D E WEIGHTS A 5 5 5 4 A Mustang GT 52.3 ▒▒▒▒▒▒▒▒▒▒ B 2 -2 -3 B Tempo Sport 8.7 ▒▒ C -2 -3 C Prelude 6.6 ▒ D -2 D Corolla GTS 12.3 ▒▒ E E VW GTI 20.1 ▒▒▒ Pairwise Comparison Data for level 2, with respect to: Braking A B C D E WEIGHTS A 2 -3 -2 -5 A Mustang GT 8.8 ▒▒ B -4 -2 -6 B Tempo Sport 6.0 ▒ C 3 -2 C Prelude 26.6 ▒▒▒▒▒ D -5 D Corolla GTS 11.7 ▒▒ E E VW GTI 46.8 ▒▒▒▒▒▒▒▒▒ Pairwise Comparison Data for level 2, with respect to: Handling A B C D E WEIGHTS A 4 3 -2 2 A Mustang GT 25.1 ▒▒▒▒▒ B 1 -5 -3 B Tempo Sport 6.8 ▒ C -5 -3 C Prelude 7.2 ▒ D 4 D Corolla GTS 44.9 ▒▒▒▒▒▒▒▒▒ E E VW GTI 16.0 ▒▒▒ Pairwise Comparison Data for level 2, with respect to: Styling A B C D E WEIGHTS A 3 3 1 2 A Mustang GT 31.8 ▒▒▒▒▒▒▒▒▒ B 1 -3 -2 B Tempo Sport 9.9 ▒▒▒ C -3 -2 C Prelude 9.9 ▒▒▒ D 1 D Corolla GTS 27.7 ▒▒▒▒▒▒▒▒ E E VW GTI 20.6 ▒▒▒▒▒▒ 18 3.3.3 Relative impact on overall goal Study the pairwise comparisons above, when you are satisfied that you understand how you would go about inputting this data, then push F1, the key labeled TREE, this will return you to the decision tree hierarchy. Now push the RUN key, F5. A set of numbers should be generated next to each element in the decision tree, similar to the following: ┌──────────────────────────────────────────────────────────────────────────────────┐ │ Pairwise Comparison Method File 'A:CAR .PCM' (C) 1986-1992, ARMADA SYSTEMS │ │ Decision Tree Hierarchy │ │ GOAL: To purchase the car best suited for me. │ │ ╔══════════════╤══════════════╤══════════════╤══════════════╤══════════════╗ │ │ ║ Level 1 │ Level 2 │ Level 3 │ Level 4 │ Level 5 ║ │ │ ╔═══╬══════════════╪══════════════╪══════════════╪══════════════╪══════════════╣ │ │ ║ 1 ║Price 38│Mustang GT 19│ │ │ ║ │ │ ║ 2 ║Fuel econ. 15│Tempo Sport 25│ │ │ ║ │ │ ║ 3 ║Acceleraton 7│Prelude 13│ │ │ ║ │ │ ║ 4 ║Braking 8│Corolla GTS 23│ │ │ ║ │ │ ║ 5 ║Handling 11│VW GTI 21│ │ │ ║ │ │ ║ 6 ║Styling 21│ │ │ │ ║ │ │ ║ 7 ║ │ │ │ │ ║ │ │ ║ 8 ║ │ │ │ │ ║ │ │ ║ 9 ║ │ │ │ │ ║ │ │ ║10 ║ │ │ │ │ ║ │ │ ║11 ║ │ │ │ │ ║ │ │ ║12 ║ │ │ │ │ ║ │ │ ║13 ║ │ │ │ │ ║ │ │ ║14 ║ │ │ │ │ ║ │ │ ║15 ║ │ │ │ │ ║ │ │ ║16 ║ │ │ │ │ ║ │ │ ╚═══╩══════════════╧══════════════╧══════════════╧══════════════╧══════════════╝ │ │ Overall average inconsistency= 0.18 (acceptable) │ │ 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 PCM program. The way we will do this, is to estimate the relative lengths of seven straight lines, and then compare these subjective results with actual values. Since our goal will be to estimate relative line lengths, the hierarchy for this problem will only consist of the seven lines being listed in level 1; L1, L2, ..., L7. These lines are drawn in figure 3.3, below: L1 ■■■■■■■■■■■■■■■ L2 ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ L3 ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ L4 ■■■■■■■■■■ L5 ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ L6 ■■■■■ L7 ■■■■■■■■■■■■■■■■■■■■ Figure 3.3. Straight lines used for pairwise comparison analysis. The data which we have supplied for this exercise is found on your program diskette in the file LINE.PCM, it is also listed below: Pairwise Comparison Data for level 1, with respect to: GOAL A B C D E F G WEIGHTS A -3 -4 2 -2 3 -2 A L1 8.2 ▒▒ B -2 4 2 7 2 B L2 22.9 ▒▒▒▒▒▒ C 5 2 8 3 C L3 32.4 ▒▒▒▒▒▒▒▒▒ D -3 2 -2 D L4 5.5 ▒▒ E 6 2 E L5 16.6 ▒▒▒▒▒ F -4 F L6 3.0 ▒ G G L7 11.4 ▒▒▒ Several observations must be made with regard to this example. First, note the negative pairwise comparisons. The very first element in the matrix, for example, is a -3. This indicates that when comparing L1 and L2, L2 is moderately longer than L1. If, on the other hand, L1 were the longer line, then the first element in the matrix would be a positive number. This relation holds throughout the matrix. If when inputting your own data, you enter a positive number when it really should be negative, then all is not lost, the computer will in most cases flag this error as an inconsistent judgment. You would then go back and revise your data. 20 The second point which must be made clear is, before you start inputting any data into a pairwise comparison matrix, consider all of the alterna- tives in your mind. In particular consider the worst and best, or as in this example the shortest and longest line. This will provide you with a feel for the relative scale you will need to use. Pairwise comparisons for elements in a matrix must be relative to each other. Therefore, a subjec- tive scale used on one problem need not be the same as in an other. For example, in this problem it was decided that L2 is moderately longer than L1 only after we looked at the longest and shortest line, L3 and L6. If the difference between these two extremes was greater, then it is possible that a different scale could have been used. Briefly, the following comparisons can be made between the actual relative lengths and those estimated with the PCM program: ACTUAL LENGTH CALCULATED SUBJECTIVE LINE (Units) RELATIVE LENGTH RELATIVE LENGTH L1 15 8.6 8.2 L2 40 22.9 22.9 L3 55 31.4 32.4 L4 10 5.7 5.5 L5 30 17.1 16.6 L6 5 2.9 3.0 L7 20 11.4 11.4 As you can see, the actual values and those estimated through subjective means are very close. Since in this example you know what the answers should be, try to input your own data and see what kind of results you get. If you feel your results are unsatisfactory, then revise your judgments. This way, using trial and error, you will gain a sense for the subjective scale used by this method. You may also devise your own problem where you can compare estimated results with actual values. Some examples are: 1. Estimating relative weights of objects. 2. Estimating the relative brightness of similar objects at varying distances from a common light source. Your results should indicate an inverse square relationship between the brightness of an object and its distance from the light source. 3. Estimating the relative areas of various two dimensional geometric shapes. 21 3.4.2 Benefit/Cost analysis This example will illustrate two key points: First it will show you how to do a benefit to cost analysis, and second it will indicate that not all elements in a lower level need to be connected to all the elements in the immediately higher level. Many decisions made in your personal or professional life require weighing benefits against costs. Benefits of alternative courses of action may be calculated by considering a hierarchy of objectives, attributes of alterna- tives, and the alternatives themselves. This will tell us how much each alternative contributes to the fulfillment of the objectives. A hierarchy of costs for bringing about the alternatives may be constructed by considering the problems which will be caused by each alternative. The costs of the problems themselves, or the costs of solutions designed to eliminate these problems are then analyzed in the hierarchy. Once the two hierarchies have been constructed and the relative weights of each alternative have been computed with respect to both costs and benefits, then we can perform a benefit to cost ratio test for each alter- native. The alternative with the highest ratio should be the alternative selected. This will be the alternative which will yield the greatest amount of benefit from a unit measure of cost. The problem which we will model, will involve the selection of a transpor- tation project designed to bring people to the downtown core of a large metropolitan city. The alternatives under study involve the construction of an expressway, a subway, or an improvement in the present bus service. The benefits of the project have been grouped into economic, social and personal benefits. Economic benefits are further subdivided into a time savings to get to downtown, the number of jobs created by each project and the improvement of downtown commerce due to more business. Benefits to society are viewed as abstract quantities. They have been subdivided into the degree of community pride generated by each alternative and the greater number of trips to the downtown that will result. Personal benefits have been defined by their contribution to the individual. For example the reduction of traffic and parking problems, and the comfort and accessi- bility of using each alternative. The benefit hierarchy is illustrated in Figure 3.4. Project costs have been grouped into economic, social, and environmental costs. Economic costs are subdivided into both capital and operational or maintenance costs. Social costs represent costs to society as a whole. They are defined as the disruption of people's lifestyles, the dislocation of people from their homes, and the general disruption to people caused by, for example, the different levels of traffic congestion. Environmental costs are viewed in terms of the pollution and decrease in parkland result- ing from each alternative. The cost hierarchy is illustrated in Figure 3.5. 22 ╔═════════════════════╗ Level 0 ║ BENEFITS OF PROJECT ║ ╚══════════╤══════════╝ │ ┌──────────────────────────┼─────────────────────────┐ │ │ │ ┌───────────┴───────────┐ ┌───────────┴───────────┐ ┌──────────┴──────────┐ Level 1 │ ECONOMIC │ │ SOCIAL │ │ PERSONAL │ └─┬─────────────────────┘ └─┬─────────────────────┘ └─┬───────────────────┘ │┌────────────────────┐ │┌────────────────────┐ │┌──────────────────┐ Level 2 ├┤TIME SAVINGS │ ├┤COMMUNITY PRIDE │ ├┤TRAFFIC VOLUME │ │├────────────────────┤ │├────────────────────┤ │├──────────────────┤ ├┤JOB CREATION │ └┤MORE TRIPS DOWNTOWN │ ├┤PARKING │ │├────────────────────┤ └────────┬───────────┘ │├──────────────────┤ └┤COMMERCE │ │ ├┤COMFORT │ └────────┬───────────┘ │ │├──────────────────┤ │ │ └┤ACCESSIBILITY │ │ │ └───────┬──────────┘ ├──────────────────────────┼─────────────────────────┤ ┌───────────┴───────────┐ ┌───────────┴───────────┐ ┌──────────┴──────────┐ Level 3 │ BUILD EXPRESSWAY │ │ BUILD SUBWAY │ │ IMPROVE BUS SERVICE │ └───────────────────────┘ └───────────────────────┘ └─────────────────────┘ Figure 3.4. Benefit hierarchy for transportation project. ╔═════════════════════╗ Level 0 ║ COSTS OF PROJECT ║ ╚══════════╤══════════╝ │ ┌──────────────────────────┼─────────────────────────┐ │ │ │ ┌───────────┴───────────┐ ┌───────────┴───────────┐ ┌──────────┴──────────┐ Level 1 │ ECONOMIC │ │ SOCIAL │ │ ENVIRONMENTAL │ └─┬─────────────────────┘ └─┬─────────────────────┘ └─┬───────────────────┘ │┌────────────────────┐ │┌────────────────────┐ │┌──────────────────┐ Level 2 ├┤CAPITAL │ ├┤LIFESTYLE CHANGES │ ├┤POLLUTION │ │├────────────────────┤ │├────────────────────┤ │├──────────────────┤ └┤OPERATIONAL │ ├┤PEOPLE DISLOCATION │ └┤DECREASED PARKLAND│ └────────┬───────────┘ │├────────────────────┤ └───────┬──────────┘ │ └┤GENERAL DISRUPTION │ │ │ └────────┬───────────┘ │ │ │ │ ├──────────────────────────┼─────────────────────────┤ │ │ │ ┌───────────┴───────────┐ ┌───────────┴───────────┐ ┌──────────┴──────────┐ Level 3 │ BUILD EXPRESSWAY │ │ BUILD SUBWAY │ │ IMPROVE BUS SERVICE │ └───────────────────────┘ └───────────────────────┘ └─────────────────────┘ Figure 3.5. Cost hierarchy for transportation project. The data and results of the analysis as generated by the program are given on the next few pages. The results can be summarized here as follows: ┌────────────┬────────┬─────────────┐ │ EXPRESSWAY │ SUBWAY │ IMPROVE BUS │ ┌────────────────────┼────────────┼────────┼─────────────┤ │ BENEFITS │ 36 │ 55 │ 9 │ ├────────────────────┼────────────┼────────┼─────────────┤ │ COSTS │ 37 │ 52 │ 10 │ ├────────────────────┼────────────┼────────┼─────────────┤ │ BENEFIT/COST RATIO │ 0.97 │* 1.06 *│ 0.9 │ └────────────────────┴────────────┴────────┴─────────────┘ 23 In this analysis, the benefit to cost ratios of all 3 alternatives are fairly close to each other. Nevertheless, the subway option scores slightly better than the other two, and the expressway option scores better than the bus option. Therefore, if enough resources and money are available then a subway should be built. If, however, there is not enough money to build the subway, but there is enough for an expressway, then the expressway option should be selected. If this is the case, and the subway option is not a feasible alternative, then it should not have been considered in the first place. The next few pages list the data for this problem as supplied on the DAS distribution diskette. The benefit hierarchy is found in the BENEFIT.PCM file, while the cost hierarchy is found in the COST.PCM file. If you think back, you will recall that one of the purposes of this example was to show that not all elements in a lower level, need to be connected to all elements in the immediately higher level. In figures 3.4 and 3.5, elements in level 2, are not all connected to all elements in level 1. For example, it would not help us much to make a connection between the pride generated for an alternative to economic benefits. One can argue, that pride could reap some economic benefits, however, its effects would be negligible when compared with the other criteria considered, therefore no connection is made. Looking at the data for level 2, you can see how a connection is identified in the pairwise comparison matrix. If no connect- ion exists for a certain element, then no pairwise comparison is input in both the row and column of this element. Keep in mind that, if N elements are being compared, then N(N-1)/2 comparisons are required. Pairwise Comparison Method File 'A:benefit .PCM' (C) 1986-1992, ARMADA SYSTEMS Decision Tree Hierarchy GOAL: To determine the benefits of a transportation project to downtown core. ╔══════════════╤══════════════╤══════════════╤══════════════╤══════════════╗ ║ Level 1 │ Level 2 │ Level 3 │ Level 4 │ Level 5 ║ ╔═══╬══════════════╪══════════════╪══════════════╪══════════════╪══════════════╣ ║ 1 ║Economic 67│Time saving 5│Expressway 36│ │ ║ ║ 2 ║Social 11│Job creatin 46│Subway 55│ │ ║ ║ 3 ║Personal 22│Commerce 16│Improve Bus 9│ │ ║ ║ 4 ║ │Pride 3│ │ │ ║ ║ 5 ║ │More trips 8│ │ │ ║ ║ 6 ║ │Traffic 8│ │ │ ║ ║ 7 ║ │Parking 8│ │ │ ║ ║ 8 ║ │Comfort 2│ │ │ ║ ║ 9 ║ │Accessible 4│ │ │ ║ ║10 ║ │ │ │ │ ║ ║11 ║ │ │ │ │ ║ ║12 ║ │ │ │ │ ║ ║13 ║ │ │ │ │ ║ ║14 ║ │ │ │ │ ║ ║15 ║ │ │ │ │ ║ ║16 ║ │ │ │ │ ║ ╚═══╩══════════════╧══════════════╧══════════════╧══════════════╧══════════════╝ Overall average inconsistency= 0.46 (acceptable) 24 Pairwise Comparison Data for level 1, with respect to: GOAL A B C WEIGHTS A 6 3 A Economic 66.7 ▒▒▒▒▒▒▒▒▒ B -2 B Social 11.1 ▒▒ C C Personal 22.2 ▒▒▒ Pairwise Comparison Data for level 2, with respect to: Economic A B C D E F G H I WEIGHTS A -7 -5 A Time saving 6.9 ▒ B 4 B Job creatin 68.7 ▒▒▒▒▒▒▒▒▒ C C Commerce 24.4 ▒▒▒ D D Pride 0.0 E E More trips 0.0 F F Traffic 0.0 G G Parking 0.0 H H Comfort 0.0 I I Accessible 0.0 Pairwise Comparison Data for level 2, with respect to: Social A B C D E F G H I WEIGHTS A A Time saving 0.0 B B Job creatin 0.0 C C Commerce 0.0 D -3 D Pride 25.0 ▒▒▒ E E More trips 75.0 ▒▒▒▒▒▒▒▒▒ F F Traffic 0.0 G G Parking 0.0 H H Comfort 0.0 I I Accessible 0.0 Pairwise Comparison Data for level 2, with respect to: Personal A B C D E F G H I WEIGHTS A A Time saving 0.0 B B Job creatin 0.0 C C Commerce 0.0 D D Pride 0.0 E E More trips 0.0 F 1 4 2 F Traffic 35.9 ▒▒▒▒▒▒▒▒▒ G 4 2 G Parking 35.9 ▒▒▒▒▒▒▒▒▒ H -3 H Comfort 8.2 ▒▒ I I Accessible 20.0 ▒▒▒▒▒ Pairwise Comparison Data for level 3, with respect to: Time saving A B C WEIGHTS A 3 9 A Expressway 66.3 ▒▒▒▒▒▒▒▒▒ B 6 B Subway 27.8 ▒▒▒▒ C C Improve Bus 5.8 ▒ Pairwise Comparison Data for level 3, with respect to: Job creatin A B C WEIGHTS A -4 5 A Expressway 23.7 ▒▒▒ B 8 B Subway 69.9 ▒▒▒▒▒▒▒▒▒ C C Improve Bus 6.4 ▒ 25 Pairwise Comparison Data for level 3, with respect to: Commerce A B C WEIGHTS A 2 7 A Expressway 58.2 ▒▒▒▒▒▒▒▒▒ B 6 B Subway 34.8 ▒▒▒▒▒ C C Improve Bus 6.9 ▒ Pairwise Comparison Data for level 3, with respect to: Pride A B C WEIGHTS A -5 5 A Expressway 20.7 ▒▒▒ B 9 B Subway 73.5 ▒▒▒▒▒▒▒▒▒ C C Improve Bus 5.8 ▒ Pairwise Comparison Data for level 3, with respect to: More trips A B C WEIGHTS A -3 3 A Expressway 25.0 ▒▒▒ B 6 B Subway 65.5 ▒▒▒▒▒▒▒▒▒ C C Improve Bus 9.5 ▒ Pairwise Comparison Data for level 3, with respect to: Traffic A B C WEIGHTS A 5 9 A Expressway 73.5 ▒▒▒▒▒▒▒▒▒ B 5 B Subway 20.7 ▒▒▒ C C Improve Bus 5.8 ▒ Pairwise Comparison Data for level 3, with respect to: Parking A B C WEIGHTS A -9 -7 A Expressway 5.5 ▒ B 3 B Subway 65.5 ▒▒▒▒▒▒▒▒▒ C C Improve Bus 29.0 ▒▒▒▒ Pairwise Comparison Data for level 3, with respect to: Comfort A B C WEIGHTS A -6 -4 A Expressway 8.5 ▒ B 3 B Subway 64.4 ▒▒▒▒▒▒▒▒▒ C C Improve Bus 27.1 ▒▒▒▒ Pairwise Comparison Data for level 3, with respect to: Accessible A B C WEIGHTS A 6 7 A Expressway 75.8 ▒▒▒▒▒▒▒▒▒ B 2 B Subway 15.1 ▒▒ C C Improve Bus 9.1 ▒ 26 Pairwise Comparison Method File 'A:cost .PCM' (C) 1986-1992, ARMADA SYSTEMS Decision Tree Hierarchy GOAL: To estimate the costs of a transportation project to the downtown core. ╔══════════════╤══════════════╤══════════════╤══════════════╤══════════════╗ ║ Level 1 │ Level 2 │ Level 3 │ Level 4 │ Level 5 ║ ╔═══╬══════════════╪══════════════╪══════════════╪══════════════╪══════════════╣ ║ 1 ║Economic 74│Capital 65│Expressway 37│ │ ║ ║ 2 ║Social 17│Operational 9│Subway 52│ │ ║ ║ 3 ║Environment 9│Lifestyles 2│Improve Bus 10│ │ ║ ║ 4 ║ │People Disl 11│ │ │ ║ ║ 5 ║ │Disruption 4│ │ │ ║ ║ 6 ║ │Pollution 7│ │ │ ║ ║ 7 ║ │Parkland 2│ │ │ ║ ║ 8 ║ │ │ │ │ ║ ║ 9 ║ │ │ │ │ ║ ║10 ║ │ │ │ │ ║ ║11 ║ │ │ │ │ ║ ║12 ║ │ │ │ │ ║ ║13 ║ │ │ │ │ ║ ║14 ║ │ │ │ │ ║ ║15 ║ │ │ │ │ ║ ║16 ║ │ │ │ │ ║ ╚═══╩══════════════╧══════════════╧══════════════╧══════════════╧══════════════╝ Overall average inconsistency= 0.37 (acceptable) Pairwise Comparison Data for level 1, with respect to: GOAL A B C WEIGHTS A 5 7 A Economic 74.0 ▒▒▒▒▒▒▒▒▒ B 2 B Social 16.7 ▒▒ C C Environment 9.4 ▒ Pairwise Comparison Data for level 2, with respect to: Economic A B C D E F G WEIGHTS A 7 A Capital 87.5 ▒▒▒▒▒▒▒▒▒ B B Operational 12.5 ▒ C C Lifestyles 0.0 D D People Disl 0.0 E E Disruption 0.0 F F Pollution 0.0 G G Parkland 0.0 Pairwise Comparison Data for level 2, with respect to: Social A B C D E F G WEIGHTS A A Capital 0.0 B B Operational 0.0 C -5 -3 C Lifestyles 10.5 ▒ D 3 D People Disl 63.7 ▒▒▒▒▒▒▒▒▒ E E Disruption 25.8 ▒▒▒▒ F F Pollution 0.0 G G Parkland 0.0 Pairwise Comparison Data for level 2, with respect to: Environment A B C D E F G WEIGHTS A A Capital 0.0 B B Operational 0.0 C C Lifestyles 0.0 D D People Disl 0.0 E E Disruption 0.0 F 3 F Pollution 75.0 ▒▒▒▒▒▒▒▒▒ G G Parkland 25.0 ▒▒▒ 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 it in DOS or Windows to view, edit, sort, search, group, filter, replace, copy/paste, merge, print, fax or export data in many ways. Both indexing and filter methods are provided for searching, grouping, browsing and retrieving data. MyBASE also features a fully programmable merge utility. What is particu- larly noteworthy is that, besides allowing you to do the standard merging of text and data, commands may be embedded in the merge file to control how records and data are processed, where the output is sent to, and what external programs to call (ex. DOS functions, file viewers, word proces- sors, spreadsheets, graphics viewers, FAX software, and so on). For example, if you had a database of clients, you could create a merge file to send all your clients (or just a small group of them) a personal- ized letter. The merged letter could be sent to a printer to obtain a hardcopy, or it could just as easily be sent directly to your client, via FAX. If the letter was faxed, MyBASE would merge and FAX each letter completely unattended. A sample contact management system is included with this package. This contact management system includes, pre-defined view screens, field edit templates and field edit validation, default pop-up selection boxes and sample data. Also included are sample merge programs to print envelopes, letters, reports, and to send personalized faxes to multiple destinations. You can easily modify this contact management system to suit your own needs, or if you wish, you can just as easily create any number of new databases. 4.1.1 Quick overview of features * The program is small and fast (less than 300K in size). * Creates, reads and writes industry standard dBASE III files. * Context sensitive and user customizable help system. Push F1 at any time to display or edit the help information which relates to the current task. * Ability to completely define your own database structure. This includes descriptive column headings, field edit validation, default field values, field edit functions/templates and execute/run functions which may be invoked by pushing Alt+E or Alt+R in the database browse table. * Local Area Network (LAN) compatible. * Shell to DOS or run any external program from within MyBASE with less than 8K of memory overhead. * Supports EMS and XMS memory for improved performance. * Enhanced error management and error recovery. 33 * Database specific, three level password access system Can be turned either ON or OFF). * View data in table or record view mode (F3/TAB toggles between modes). * Quick and simple way of defining new ways of looking at data. Unique view windows may be defined for each database. The view windows will control how the data will be displayed on screen and in printed reports. * Merge print function to allow merging of text from an external text file with data from the database. Commands may be embedded in the external merge file to control how records and data are processed, where the output is sent to, and what external procedures to call (ex. DOS func- tions, word processors, graphics viewers, FAX software, label printers, and so on). * User configurable print drivers. Export data to printer or a DBF or ASCII delimited file. The ability to export data to a file is extremely useful since the exported data will be based on the current database view and filter conditions which you have set (ie. what you see is what you get). The exported data may then be imported into a word processor, spread- sheet, desktop publishing package, telecommunications or fax software, etc... * Tag individual records for printing, merging or replacing. * Filter database to display or print a group of selected data. * Skip through database, searching for specific data. * Quick, database wide, search and replacement of data. * Memo field support for free-form notes of up to 64K in size per record. * Copy and paste data for faster data input. * Automatic telephone dialer. * Calculate totals and averages for numeric data. * Support for EGA and VGA monitors to display more data on screen. * Allows for customization of screen colors, video size, date format, and use of sound. * Display or hide records marked for deletion. * NOTE: MyBASE is continually updated and refined. The latest version of MyBASE may have additional functionality and features not specified here. 4.1.2 System requirements A PC-DOS or MS-DOS compatible system with at least 640K RAM. A hard disk with at least 1.0 MB free. PC-DOS/MS-DOS 3.1 or higher. 34 5.0 ORDERING SOFTWARE: WHAT YOU WILL RECEIVE When you purchase any software from Armada Systems, your satisfaction is 100% guaranteed. If for any reason you are not completely satisfied with the product you may return it within 30 days for a refund. In addition to this guarantee, you will receive the following: (1) The latest version of software. (2) Complete reference and user's guide. (3) Free technical support. (4) Notice of future updates and new products. (5) Eligibility for low cost upgrades. (6) Free shareware software, as follows: ┌────────────────────────────┬─────────────────────────────────┐ │ PROGRAM ORDERED │ FREE SHAREWARE YOU WILL RECEIVE │ ├────────────────────────────┼─────────────────────────────────┤ │ DAS, DMM, or PCM │ 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 "B. BORZIC". Payment must be in the quoted U.S. or Canadian funds. Site licensing and volume discounts (QTY. >= 5) are available, please write for details. ARMADA SYSTEMS SOFTWARE REGISTRATION AND ORDER FORM ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ To order software, please fill out this order form and mail it to the address given below, along with a company purchase order, cheque or money order payment, made out to "B. BORZIC". Payment must be in the quoted U.S. or Canadian funds. Site licensing and volume discounts (QTY. >= 5) are available, please write for details. When you purchase software from Armada Systems, your satisfaction is 100% guaranteed. If for any reason you are not completely satisfied with the product you may return it within 30 days for a refund. Boris Borzic, Armada Systems P.O. Box 637, Station A Downsview, Ontario M3M 3A9 CANADA Tel. (416) 889-2617 or (905) 889-2617 after October 4, 1993 NAME ____________________________ TITLE __________________________________ COMPANY _________________________ DEPARTMENT _____________________________ ADDRESS ___________________________________________________________________ CITY ____________________________ STATE/PROVINCE _________________________ ZIP/POSTAL CODE _________________ COUNTRY ________________________________ PHONE ___________________________ FAX ____________________________________ Would you like the program supplied on 5.25" or 3.5" disks? _______________ Where did you obtain the DAS software? ____________________________________ DAS 2.45 - 9317190 +-------------------------------------------------------------------------+ | DESCRIPTION | U.S. $ | CDN $ | QTY | TOTAL $ | |-------------------------------------|--------|--------|-----|-----------| | Complete DAS package (DMM + PCM) | 149.00 | 179.00 | | | |-------------------------------------|--------|--------|-----|-----------| | DMM program only | 99.00 | 119.00 | | | |-------------------------------------|--------|--------|-----|-----------| | PCM program only | 99.00 | 119.00 | | | |-------------------------------------|--------|--------|-----|-----------| | MyBASE | 124.00 | 149.00 | | | |-------------------------------------|--------|--------|-----|-----------| | DMM + PCM + MyBASE ordered together | 249.00 | 299.00 | | | +-------------------------------------------------------------|-----------| Purchase order processing charge | 15.00 | (cross out if payment is enclosed) | | |-----------| Shipping & handling | 8.00 | |-----------| Applicable taxes | | |-----------| TOTAL | | +-----------+ Signature ______________________________ Date ____________________________ Use the back of this sheet to add any comments or suggestions you may have. REFERENCES Alexander M. Joyce, Saaty L. Thomas: "Thinking With Models," Pergamon Press Chryssolouris G, Chan S., Cobb W.: "Decision Making in the Factory Floor," COMMLINE, May-June 1986 Green P.E., Wind Y.: "Multiattribute Decisions in Marketing: A Measurement Approach," Dryden Press, 1973 Ho K. James: "Analytic Hierarchies and Holistic Preferences," College of Business Administration The University of Tennessee, Knoxville, TN 37996 Hwang C.L., Yoon K.: "Multiple Attribute Decision Making, Methods and Applications," Springer-Verlang, 1981 Raiffa Howard: "Decision Analysis, Introductory Lectures on Choices Under Uncertainty," Addison-Wesley, 1968 Saaty L. Thomas: "The Analytic Hierarchy Process," McGraw-Hill, 1980 Szonyi A.J., Fenton R.G., White J.A., Agee M.H., Case K.E.: "Principles of Engineering Economic Analysis," John Wiley and Sons, 1982 Wagner M. Harvey: "Principles of Operations Research," Prentice-Hall, 1975 NOTES