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With your registration you will not only receive technical support and the latest version of software, but you will also be sponsoring the continued support and future enhancements of this product. ___________________________________________________________________________ AHP - Analytic Hierarchy Process, Release 3.01 The Modern Art of Decision Making Program Serial No. 9317420 Changes are periodically made to the information herein; these changes will be incorporated in new editions of this publication. A Product Comment Form is provided at the front of this publication. If this form has been removed, you can mail any comments to the address below: Armada Systems P.O. Box 637, Station A Downsview, Ontario M3M 3A9 Canada DAS, DMM, PCM, DME and MyBASE are Trademarks of Armada Systems. Copyright (C) 1986-1993, Armada Systems All Rights Reserved Made in Canada For your records: NAME ____________________________ TITLE __________________________________ COMPANY _________________________ DEPARTMENT _____________________________ DATE PROGRAM RECEIVED ___________ OBTAINED FROM __________________________ TABLE OF CONTENTS PAGE ARMADA SYSTEMS LICENSE AGREEMENT ....................... i PRODUCT COMMENT FORM ................................... ii GETTING STARTED ........................................ iii CREATING A WORKING COPY OF AHP iii DISK CONTENTS iv 1.0 THE ANALYTIC HIERARCHY PROCESS .................... 1 1.1 INTRODUCTION 1 1.2 THEORY OF OPERATION 2 1.2.1 Pairwise comparisons and inconsistency 2 1.2.2 Example 2 1.3 USING THE AHP 4 1.3.1 Pairwise comparisons for level 1 5 1.3.2 Pairwise comparisons for level 2 7 1.3.3 Relative impact on overall goal 8 1.4 SAMPLE PROBLEMS 9 1.4.1 Estimating relative lengths of lines 9 1.4.2 Benefit/Cost analysis 11 1.4.3 Application to psychotherapy 18 1.4.4 Calculating expected values 19 1.4.5 Determining optimum type of coal plant 20 2.0 PROGRAM CONFIGURATION ............................. 21 3.0 ABOUT ARMADA SYSTEMS .............................. 22 3.1 THE DECISION MATRIX EXPERT (DME) 23 3.1.1 Applications 23 3.1.2 System requirements 23 3.2 MyBASE 24 3.2.1 Quick overview of features 24 3.2.2 System requirements 25 4.0 ORDERING SOFTWARE: WHAT YOU WILL RECEIVE ........... 26 ARMADA SYSTEMS SOFTWARE REGISTRATION AND ORDER FORM .... 27 REFERENCES ............................................. 28 AHP i ARMADA SYSTEMS LICENSE AGREEMENT Read this agreement carefully. Use or distribution of this product consti- tutes your acceptance of the terms and conditions of this agreement! GENERAL LICENSE TERMS This documentation and the software described in it are copyrighted with all rights reserved worldwide by Armada Systems. Under the copyright laws, neither the documentation nor the software may be copied, photocopied, reproduced, translated, modified, reverse engineered, or reduced to any electronic medium or machine readable form, in whole or in part, except as specifically authorized below, without the prior written consent of Armada Systems. Armada Systems specifically authorizes individuals and organizations to make complete unaltered copies of this software, for the purpose of free distribution to other individuals or organizations. This software and documentation may not be sold, no fee must be involved in the distribution of this software except, for a small reasonable fee to cover the cost of any distribution media and service charges. This software which consists of application programs, data files and documentation, are a complete entity which must not be separated or altered in any way shape or form. Individuals or organizations who wish to distribute or market this software for the purpose of financial or other material gain, must first receive the authorization to do so by contacting Armada Systems. Armada Systems authorizes the use of this software for non-commercial, educational, and evaluation purposes only. If you are using or intend to use this software for any other purposes, then you must register with Armada Systems by purchasing the commercial version of the software. Copying (except for back-up purposes) and distribution of software provided to registered users is not permitted. DISCLAIMER This documentation and the software described in it are provided "as is," without any warranty as to their performance, accuracy, or freedom from error, or as to any results generated through their use. Armada Systems excludes without limitation any and all implied warranties, including warranties of merchantability and fitness for a particular purpose. You assume the entire risk as to the results and performance of the software and documentation. Armada Systems will under no circumstances be liable for any direct, indirect, special, incidental, or consequential damages arising out of the use or inability to use the software or documentation, even if advised of the possibility of such damages. GENERAL Should you have any questions concerning this Agreement, you may contact Armada Systems by writing to the address given at the front of this manual. 3.01 - 9317420 AHP ii PRODUCT COMMENT FORM Use this form if you have any comments or suggestions regarding the AHP program or this manual. Mail your comments to: Armada Systems P.O. Box 637, Station A Downsview, Ontario M3M 3A9 Canada NAME_________________________________ TITLE________________________________ COMPANY______________________________ DEPARTMENT___________________________ ADDRESS____________________________________________________________________ CITY_________________________________ STATE/PROVINCE_______________________ ZIP/POSTAL CODE______________________ COUNTRY______________________________ PHONE________________________________ FAX__________________________________ COMPUTER TYPE________________________ DOS VERSION__________________________ DATE PROGRAM RECEIVED________________ OBTAINED FROM________________________ COMMENTS/SUGGESTIONS: AHP iii GETTING STARTED Before doing anything, we suggest that you make a working copy of the disk supplied to you. You should then keep the original disk as a back-up copy, in a safe place where it will not come in contact with any heat, dust, or magnetic radiation. In the event that your working copy is ever damaged or destroyed, you can always make a new copy from the original disk. CREATING A WORKING COPY OF AHP To make a working copy of AHP, simply follow one of the procedures below corresponding to your computer system: Hard disk system: 1. Boot-up DOS operating system (you should see the C> prompt appear on screen). 2. Insert AHP floppy disk into drive A. 3. Type the following: MD\AHP CD\AHP COPY A:*.* C: 4. To start using AHP, type the following: CD\AHP AHP Floppy disk system: 1. Insert your DOS diskette into drive A. 2. Boot-up DOS operating system by either turning computer on, or if already on, push the CTRL, ALT and DEL keys simultaneously (you should see the A> prompt on screen). 3. Insert a blank diskette into drive B 4. Type the following: FORMAT B:/S 5. When finished, replace the DOS disk in drive A with the AHP diskette 6. Type the following: COPY A:*.* B: 7. To start using AHP, do the following: insert the working copy of AHP into drive A, boot-up computer and type AHP AHP iv DISK CONTENTS AHP.EXE Analytic Hierarchy Process program. MANUAL.EXE Program for printing this manual. AHP.TXT This manual. AHP.CFG Program configuration file defining screen colors and printer control codes. CAR.AHP Sample file illustrating the use of the AHP in a car purchase problem. LINE.AHP File contains subjective pairwise comparisons of various lines in order that their relative lengths may be estimated. See section 1.4. BENEFIT.AHP & COST.AHP These two files contain the hierarchical structure and subjective pairwise comparisons of the benefits and costs associated with three large scale transportation projects. Results are used in a benefit/cost analysis of these projects. See section 1.4. XYZCOMP.AHP This sample file shows how a comparative performance evaluation of a company's branch-plant offices may be conducted using AHP. The hierarchy for this problem consists of braking the company down into major departments (engineering, sales, manufacturing, etc...), considering performance factors (productivity, quality, profitability, etc...), and finally the various branch-plant offices. AHP Pg. 1 1.0 ANALYTIC HIERARCHY PROCESS 1.1 INTRODUCTION More often than not, the decisions you make in your personal or professional life can be made without a lot of fuss. Either your best choice is clear to you without much analysis, or the decision is not important enough to warrant any great amount of attention. Occasionally, however, you probably find yourself in a situation where you feel it is worth your time and effort to think systematically and hard about the different courses of action you might pursue. It is in these cases that the Analytic Hierarchy Process (AHP) will be of most help to you. When faced with a problem of choice, the AHP will help you in selecting an alternative that is consistent with your personal basic judgments and preferences. The AHP is designed to deal specifically with subjective assessments and evaluations of alternatives and criteria. This package will be most beneficial when you wish to model complex problems, and the only data available to solve these problems is your own subjective judgments or those of a group. The AHP is not only useful in decision making problems, but also in any other area where you find it difficult to quantify subjective data. In addition to the AHP, a companion decision analysis program, the Decision Matrix Expert (DME), is available separately from Armada Systems. Designed to be used with primarily tangible and easily quantifiable data, the DME models decisions by representing the problem in a matrix containing all the information required to arrive at a final decision. The columns of this matrix portray the criteria which are important to the decision, while the rows depict the various alternatives being considered. Through its analysis of the decision matrix, the DME will provide you with an unbiased ranking of alternatives. In addition, by discarding dominated or substandard alternatives, the DME will enable you to quickly narrow down the set of alternatives you need to consider. See section 3.1 in this manual for more details on this package and how to order it. The AHP program will be most useful when data is not readily available or when data is highly qualitative or subjective in nature. For those occasions where you would like to be as objective as possible in a decision problem, or where physical data is readily available, you should consider obtaining the Decision Matrix Expert software package from Armada Systems. The next section will provide an explanation of the method used by the AHP to model problems. We will then proceed to a hands-on application of the program, illustrating a practical example to clarify the method in greater detail. Finally, a number of additional examples will be presented to illustrate how the AHP may be used in many different applications. It is strongly recommended that you look at these examples, as they are a source of much information. AHP Pg. 2 1.2 THEORY OF OPERATION The technique used by the AHP is a proven scientific method, originally developed by Thomas L. Saaty at the Wharton School and described in his book "The Analytic Hierarchy Process" published by McGraw-Hill, 1980. We will not go into the actual theory and mathematical formulations of the method, because it is fairly involved. The interested reader can however consult the book "The Analytic Hierarchy Process" for much greater detail and more examples. Here, we shall be primarily concerned with the application of the method. The AHP requires that a problem be decomposed into a hierarchical model, structured so as to capture it's basic elements. Hierarchical decomposition involves setting up levels, where each level contains a set of elements. These elements are grouped in such a way that those of a lower level directly influence the elements in the immediately higher level, these in turn must influence elements in the next level and so on up to the goal of the hierarchy. The objective is to derive a set of quantitative weights for elements in the last level which reflect, as best as possible, their relative impact on the goal of the hierarchy. The way we accomplish this, is to compare, in pairs, elements in each level, with respect to those elements in the immediately higher level. The advantage of setting up a problem in a hierarchical structure is that it helps you in focusing your attention on each part of the problem separately. Keep in mind however, that results obtained with the use of this program will only be as good as the model you have constructed and the data you have entered into it. 1.2.1 Pairwise comparisons and inconsistency Pairwise comparisons are made using a 1 to 9 numerical scale. For example, if elements A and B are being compared, a 1 would indicate that they are both equal and a 9 would indicate that A is extremely better than B. Intermediate values are used to arrive at a compromise between these two extreme points. When we compare N elements in a level with respect to an element in the immediately higher level, we would require N(N-1)/2 comparisons. That is, if 4 elements are being compared with each other, then a total of 6 pairwise comparisons are needed. These pairwise comparisons are entered into what is called a pairwise comparison matrix. As well as being able to calculate subjective weights based on your pairwise comparisons, the software will also provide you with an indication of your judgment consistency, or inconsistency as it is referred to in the program. Inconsistency in pairwise comparison judgments can best be described with the following example: If you were comparing the weight of three stones, and were to say that; stone A is heavier than stone B which is heavier than C, and then say that stone C is heavier than A, then your judgments would be inconsistent. In real life situations, one can not escape the fact that many things are in fact inconsistent. For example, in a game of sport team A can beat team B, team B can beat team C, but team C can nevertheless beat team A. In general, a pairwise comparison matrix with AHP Pg. 3 an inconsistency index of 1.0 or less is acceptable, and up to 1.5 can be tolerated in some cases, but any more than this should result in a review of the judgments. If the judgments are found to be a true representation of the actual system, then the matrix should be left as is, though you should remember the consequent higher margin of error when analyzing the results. 1.2.2 Example Let's look at an example. Suppose your goal is to purchase a car and you wish to model this decision using AHP. The first question you must ask yourself is, what factors will influence your goal. Thinking a little bit about this, you would probably come up with things such as price, fuel economy, styling, reliability and so on. These would form the elements of the first level. You would then ask yourself a similar question as before; what factors would influence the price, fuel economy, styling and reliability. The answer is obvious that a particular car will influence the factors of level1. Therefore the second level in your decision hierarchy will be comprised of the different types of cars which you are considering, ie. your alternatives. Figure 1.1 illustrates this hierarchy in graphical form: ╔════════╗ Level 0 ║ GOAL ║ ╚════╤═══╝ │ ┌───────────────┬────────┴───────┬───────────────┐ ┌───┴───┐ ┌──────┴───────┐ ┌────┴────┐ ┌──────┴──────┐ Level 1 │ PRICE │ │ FUEL ECONOMY │ │ STYLING │ │ RELIABILITY │ └───┬───┘ └──────┬───────┘ └────┬────┘ └──────┬──────┘ │ │ │ │ ├───────────────┼────────────────┼───────────────┤ │ │ │ │ ┌───┴───┐ ┌───┴───┐ ┌───┴───┐ ┌───┴───┐ Level 2 │ CAR A │ │ CAR B │ │ CAR C │ │ CAR D │ └───────┘ └───────┘ └───────┘ └───────┘ Figure 1.1. Hierarchy for a car purchase problem. This particular problem requires only 2 levels in the model to describe. Highly complex models can however be created with up to 5 levels and 16 elements per level using the AHP program. The technique used in creating a complex model would be the same as the one explained above. Once the hierarchical model has been created, pairwise comparison data must be entered into the computer. Elements in level 1 are first compared (in pairs) with respect to the overall goal (level 0). For example, with respect to a goal of purchasing a car, you would need to compare the elements; price, fuel economy, styling and reliability with each other, in pairs. The program will use these pairwise comparisons to arrive at a quantitative weight for each element in level 1, which will depict that element's subjective preference with respect to level 0. AHP Pg. 4 The next step involves performing a pairwise comparison of elements in level 2 (alternatives) with respect to elements in level 1 (price, fuel economy, styling, etc...). Again this data will be used by the program to arrive at a set of quantitative weights for each alternative with respect to each criteria in level 1. When you have finished inputting all pairwise comparison data, the program can calculate preference weights for the alternatives (level 2) with respect to the overall goal (level 0). The alternative with the highest score should be the alternative selected. 1.3 USING THE AHP This section is intended to be used as a tutorial in learning how to use the AHP program. A car purchase problem which is supplied on your diskette, will be analyzed. Once you have loaded the AHP, push F8, and type x followed by CAR (x is the drive letter indicating where the file CAR.AHP is to be found) followed by RTN. Once the file has been loaded, the computer display screen will look something like this: ┌──────────────────────────────────────────────────────────────────────────────────┐ │ FILE:> C:CAR .AHP Copyright (C) 1986-1993, ARMADA SYSTEMS │ │ Decision Tree Hierarchy │ │ GOAL: To purchase a car. │ │ ╔══════════════╤══════════════╤══════════════╤══════════════╤══════════════╗ │ │ ║ Level 1 │ Level 2 │ Level 3 │ Level 4 │ Level 5 ║ │ │ ╔═══╬══════════════╪══════════════╪══════════════╪══════════════╪══════════════╣ │ │ ║ 1 ║Price │Mustang GT │ │ │ ║ │ │ ║ 2 ║Fuel econ. │Tempo Sport │ │ │ ║ │ │ ║ 3 ║Acceleraton │Prelude │ │ │ ║ │ │ ║ 4 ║Braking │Corolla GTS │ │ │ ║ │ │ ║ 5 ║Handling │VW GTI │ │ │ ║ │ │ ║ 6 ║Styling │ │ │ │ ║ │ │ ║ 7 ║ │ │ │ │ ║ │ │ ║ 8 ║ │ │ │ │ ║ │ │ ║ 9 ║ │ │ │ │ ║ │ │ ║10 ║ │ │ │ │ ║ │ │ ║11 ║ │ │ │ │ ║ │ │ ║12 ║ │ │ │ │ ║ │ │ ║13 ║ │ │ │ │ ║ │ │ ║14 ║ │ │ │ │ ║ │ │ ║15 ║ │ │ │ │ ║ │ │ ║16 ║ │ │ │ │ ║ │ │ ╚═══╩══════════════╧══════════════╧══════════════╧══════════════╧══════════════╝ │ │ │ │ 1HELP 2DATA 3NEXT 4GRAPH 5RUN 6PRINT 7ERASE 8OPEN 9SAVE 10QUIT │ └──────────────────────────────────────────────────────────────────────────────────┘ As indicated on the second line of the screen, this represents the decision tree hierarchy. Compare the method used to express this hierarchy on screen, with the method presented in Figure 1.1. The bottom line lists the active function keys. To get a little more information on what each key does push F1-HELP. Your computer display screen should clear and list the following information: AHP Pg. 5 HELP information: F1 HELP - Display help information. F2 DATA - Display pairwise comparison data. F3 NEXT - Move to next level. F4 GRAPH- Draw a bar graph of preference weights, ordered from best to worst. F5 RUN - Calculate preference weights for the decision tree hierarchy. F6 PRINT- Send data on screen to printer. F7 ERASE- Erase a file. F8 OPEN - Open a new AHP file. F9 SAVE - Save current AHP file to disk. F0 QUIT - Exit to DOS, (file not saved automatically). ALT+S - Set screen colors and printer control data (stored in file AHP.CFG). Decision tree navigation and edit keys: ALT+I - Insert a new branch into the decision tree. ALT+D - Delete a branch from the decision tree. CTRL+ARROW keys - Move between levels (columns). ARROW keys - Move within a level (column). RETURN - Terminate input of present branch, move down to next line. HOME - Move to the top of the next level (column). END, PgDn - Move to the bottom of the present level (column). PgUp - Move to the top of the present level (column). The above help information not only indicates what each function key does, but it also lists a set of navigation and edit keys. Play around a little with these keys to get a better feel of the package. If you make any changes to this file, make sure you don't push the F9 key as this will save your changes to disk and the file CAR.AHP will be permanently altered. If you wish to make a printout of this screen, push F6-PRINT. Use this key any time you would like to obtain a hardcopy of the information on screen. 1.3.1 Pairwise comparisons for level 1 Position the cursor on the GOAL line (line 3) and push F2-DATA. This will cause the pairwise comparison data to be displayed. Since the cursor was positioned on the GOAL line, which represents level 0 in the hierarchy, the data appearing on the screen will be the pairwise comparison matrix for level 1 with respect to the GOAL, as follows: ┌──────────────────────────────────────────────────────────────────────────────────┐ │ FILE:> C:CAR .AHP Copyright (C) 1986-1993, ARMADA SYSTEMS │ │ Pairwise Comparison Data for level 1, with respect to: GOAL │ │ 1: Equal 3: Moderate 5: Strong 7: Very Strong 9: Extreme │ │ With respect to Goal Enter 1 to 9 (- for inverse) to indicate the │ │ relative importance or preference of: Price over Fuel econ. │ │ ════════════════════════════════════════════════════════════════════════════════ │ │ A B C D E F WEIGHTS │ │ A 3 4 4 4 2 A Price 37.6 │ │ B 2 2 2 -2 B Fuel econ. 14.8 │ │ C 1 -2 -3 C Acceleraton 7.3 │ │ D -2 -2 D Braking 7.9 │ │ E -2 E Handling 11.3 │ │ F F Styling 21.2 │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ 1HELP 2TREE 3NEXT 4GRAPH 5RUN 6PRINT 7ERASE 8OPEN 9SAVE 10QUIT │ └──────────────────────────────────────────────────────────────────────────────────┘ AHP Pg. 6 Push the HELP key, to display the following information: HELP information: F1 HELP - Display help information. F2 TREE - Display the decision tree hierarchy. F3 NEXT - Move on to the next set of pairwise comparison data. F4 GRAPH- Draw a bar graph of preference weights, ordered from best to worst. F5 RUN - Calculate preference weights for this set of pairwise comparison data. F6 PRINT- Send data on screen to printer. F7 ERASE- Erase a file. F8 OPEN - Open a new AHP file. F9 SAVE - Save current AHP file to disk. F0 QUIT - Exit to DOS, (file not saved automatically). ALT+S - Set screen colors and printer control data (stored in file AHP.CFG). Pairwise comparison data navigation and edit keys: HOME - Move to the first comparison (top left). ARROW keys - Move between comparisons. RETURN, INS, TAB - Move to the next comparison. DEL, BACKSPACE - Move to the previous comparison. Now push any key, other than a function key, in order to return to the pairwise comparison data. What we are trying to accomplish with this matrix, is to derive a list of weights for each element in level 1, so as to reflect quantitatively, as best as possible, our subjective importance of these criteria with respect to our goal. Let's have a look at the data which has been supplied. Since there are 6 elements in level 1 (Price, Fuel econ., Acceleraton, Braking, Handling, and Styling), N(N-1)/2 or 15 comparisons are required. The first number in the matrix is a 3, this indicates that when contemplating a car purchase, price is moderately more important than fuel economy . The next number is a 4 and this means that price is moderately to strongly more important than acceleration, and so on. Notice that in the fuel economy to styling comparison the matrix contains a -2, indicating that styling is just slightly more important than fuel economy. A negative just inverses the comparison. If you move the cursor around the matrix, the elements which are being compared will be displayed on the fifth line of your screen. Now if you push the "-" key at any spot in the matrix, you will notice that the two elements printed on the fifth line will inverse. An important point to remember is that if your goal is not to estimate costs, then the first element is always preferred to the second. Conversely, if you do wish to estimate costs, then the first element presented on the fifth line of the pairwise comparison screen, should be the element with the greater cost (see section 1.4.2). Therefore, to inverse a comparison enter a negative number. AHP Pg. 7 1.3.2 Pairwise comparisons for level 2 We have looked at level 1, now let's continue with the pairwise comparisons for level 2 as given below. By pushing F3-NEXT, you can view this same data on your screen. Notice that in level 2 there are 6 pairwise comparison matrices; there is one for Price, one for Fuel econ., Acceleration, Braking, Handling, and Styling. Whenever data is entered for this level we must keep in mind with respect to what criteria the pairwise comparisons are being made to. The second or fourth line on the display screen will remind you of this. Pairwise Comparison Data for level 2, with respect to: Price A B C D E WEIGHTS A -4 1 -2 -2 A Mustang GT 9.3 ▒▒ B 5 3 3 B Tempo Sport 46.0 ▒▒▒▒▒▒▒▒▒ C -3 -3 C Prelude 7.6 ▒ D 1 D Corolla GTS 18.6 ▒▒▒▒ E E VW GTI 18.6 ▒▒▒▒ Pairwise Comparison Data for level 2, with respect to: Fuel econ. A B C D E WEIGHTS A -3 -3 -3 -3 A Mustang GT 7.6 ▒▒ B 1 1 1 B Tempo Sport 22.7 ▒▒▒▒▒▒▒ C 2 2 C Prelude 30.4 ▒▒▒▒▒▒▒▒▒ D 1 D Corolla GTS 19.7 ▒▒▒▒▒▒ E E VW GTI 19.7 ▒▒▒▒▒▒ Pairwise Comparison Data for level 2, with respect to: Acceleraton A B C D E WEIGHTS A 5 5 5 4 A Mustang GT 52.3 ▒▒▒▒▒▒▒▒▒▒ B 2 -2 -3 B Tempo Sport 8.7 ▒▒ C -2 -3 C Prelude 6.6 ▒ D -2 D Corolla GTS 12.3 ▒▒ E E VW GTI 20.1 ▒▒▒ Pairwise Comparison Data for level 2, with respect to: Braking A B C D E WEIGHTS A 2 -3 -2 -5 A Mustang GT 8.8 ▒▒ B -4 -2 -6 B Tempo Sport 6.0 ▒ C 3 -2 C Prelude 26.6 ▒▒▒▒▒ D -5 D Corolla GTS 11.7 ▒▒ E E VW GTI 46.8 ▒▒▒▒▒▒▒▒▒ Pairwise Comparison Data for level 2, with respect to: Handling A B C D E WEIGHTS A 4 3 -2 2 A Mustang GT 25.1 ▒▒▒▒▒ B 1 -5 -3 B Tempo Sport 6.8 ▒ C -5 -3 C Prelude 7.2 ▒ D 4 D Corolla GTS 44.9 ▒▒▒▒▒▒▒▒▒ E E VW GTI 16.0 ▒▒▒ Pairwise Comparison Data for level 2, with respect to: Styling A B C D E WEIGHTS A 3 3 1 2 A Mustang GT 31.8 ▒▒▒▒▒▒▒▒▒ B 1 -3 -2 B Tempo Sport 9.9 ▒▒▒ C -3 -2 C Prelude 9.9 ▒▒▒ D 1 D Corolla GTS 27.7 ▒▒▒▒▒▒▒▒ E E VW GTI 20.6 ▒▒▒▒▒▒ AHP Pg. 8 1.3.3 Relative impact on overall goal Study the pairwise comparisons above, when you are satisfied that you understand how you would go about inputting this data, then push F2-TREE, this will return you to the decision tree hierarchy. Now push F5-RUN. A set of numbers should be generated next to each element in the decision tree, as follows: ┌──────────────────────────────────────────────────────────────────────────────────┐ │ FILE:> C:CAR .AHP Copyright (C) 1986-1993, ARMADA SYSTEMS │ │ Decision Tree Hierarchy │ │ GOAL: To purchase the car best suited for me. │ │ ╔══════════════╤══════════════╤══════════════╤══════════════╤══════════════╗ │ │ ║ Level 1 │ Level 2 │ Level 3 │ Level 4 │ Level 5 ║ │ │ ╔═══╬══════════════╪══════════════╪══════════════╪══════════════╪══════════════╣ │ │ ║ 1 ║Price 38│Mustang GT 19│ │ │ ║ │ │ ║ 2 ║Fuel econ. 15│Tempo Sport 25│ │ │ ║ │ │ ║ 3 ║Acceleraton 7│Prelude 13│ │ │ ║ │ │ ║ 4 ║Braking 8│Corolla GTS 23│ │ │ ║ │ │ ║ 5 ║Handling 11│VW GTI 21│ │ │ ║ │ │ ║ 6 ║Styling 21│ │ │ │ ║ │ │ ║ 7 ║ │ │ │ │ ║ │ │ ║ 8 ║ │ │ │ │ ║ │ │ ║ 9 ║ │ │ │ │ ║ │ │ ║10 ║ │ │ │ │ ║ │ │ ║11 ║ │ │ │ │ ║ │ │ ║12 ║ │ │ │ │ ║ │ │ ║13 ║ │ │ │ │ ║ │ │ ║14 ║ │ │ │ │ ║ │ │ ║15 ║ │ │ │ │ ║ │ │ ║16 ║ │ │ │ │ ║ │ │ ╚═══╩══════════════╧══════════════╧══════════════╧══════════════╧══════════════╝ │ │ Overall average inconsistency= 0.18 (acceptable) │ │ 1HELP 2DATA 3NEXT 4GRAPH 5RUN 6PRINT 7ERASE 8OPEN 9SAVE 10QUIT │ └──────────────────────────────────────────────────────────────────────────────────┘ The numbers which have been generated represent preference weights calculated from the pairwise comparison matrices given previously. These weights have been calculated in such a way as to reflect their relative impact on the overall goal of the hierarchy. Therefore, looking at level 2, Mustang GT has a weight of 19, Tempo Sport has a weight of 25, Prelude 13, Corolla GTS 23 and VW GTI 21. The alternative with the highest weight is the one which is preferred over the rest. In this case, a Tempo Sport should be the car purchased because it 'scores' better than the other alternatives on the combined set of criteria which was considered. To get a graphical representation of these scores, position the cursor anywhere in level 2 and push F4-GRAPH. Bar Graph of Preference Weights for level 2 Inconsistency= 0.16 (acceptable) Tempo Sport 24.6 ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ Corolla GTS 22.6 ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ VW GTI 21.2 ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ Mustang GT 18.7 ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ Prelude 12.9 ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ AHP Pg. 9 1.4 SAMPLE PROBLEMS 1.4.1 Estimating relative lengths of lines This example is intended to give you an idea of how to compare two elements at a time, and to provide you with a feel for the 1-9 subjective scale used in the AHP program. The way we will do this is we will first estimate the relative lengths of seven straight lines. Following this, we will compare our subjective results with actual values. Since our goal will be to estimate relative line lengths, the hierarchy for this problem will only consist of the seven lines being listed in level 1; L1, L2, ..., L7. These lines are presented in figure 1.2, below: L1 ■■■■■■■■■■■■■■■ L2 ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ L3 ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ L4 ■■■■■■■■■■ L5 ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ L6 ■■■■■ L7 ■■■■■■■■■■■■■■■■■■■■ Figure 1.2. Straight lines used for pairwise comparison analysis. The data supplied for this exercise is found on your program diskette in file LINE.AHP, it is also listed below: Pairwise Comparison Data for level 1, with respect to: GOAL A B C D E F G WEIGHTS A -3 -4 2 -2 3 -2 A L1 8.2 ▒▒ B -2 4 2 7 2 B L2 22.9 ▒▒▒▒▒▒ C 5 2 8 3 C L3 32.4 ▒▒▒▒▒▒▒▒▒ D -3 2 -2 D L4 5.5 ▒▒ E 6 2 E L5 16.6 ▒▒▒▒▒ F -4 F L6 3.0 ▒ G G L7 11.4 ▒▒▒ Several observations must be made with regard to this example. First, note the negative pairwise comparisons. The very first element in the matrix, for example, is a -3. This indicates that when comparing L1 and L2, L2 is moderately longer than L1. If, on the other hand, L1 were the longer line, then the first element in the matrix would be a positive number. This relation holds throughout the matrix. If when entering your own data, you enter a positive number when it really should be negative, then all is not lost, the program will in most cases flag this error as an inconsistent judgment. You would then go back and revise your data. AHP Pg. 10 The second point which must be made clear is; before you start entering any data into a pairwise comparison matrix, consider all of the alternatives in your mind. In particular consider the worst and best, or as in this example the shortest and longest line. This will provide you with a feel for the relative scale you will need to use. Pairwise comparisons for elements in a matrix must be relative to each other. Therefore, a subjective scale used on one problem need not be the same as the scale used in another. For example, in this problem it was decided that L2 is moderately longer than L1 only after we looked at the longest and shortest line, L3 and L6. If the difference between these two extremes was greater, then it is possible that a different scale could have been used. Briefly, the following comparisons can be made between the actual relative lengths and those estimated with the AHP program: ACTUAL LENGTH CALCULATED SUBJECTIVE LINE (Units) RELATIVE LENGTH RELATIVE LENGTH L1 15 8.6 8.2 L2 40 22.9 22.9 L3 55 31.4 32.4 L4 10 5.7 5.5 L5 30 17.1 16.6 L6 5 2.9 3.0 L7 20 11.4 11.4 As you can see, the actual values and those subjectively estimated, are very close. Since in this example you know what the answers should be, try to input your own data and see what kind of results you get. If you feel your results are unsatisfactory, then revise your judgments. This way, using trial and error, you will gain a better feeling for the subjective scale used by this method. You may also devise your own problem where you can compare estimated results with actual values. Some examples are: 1. Estimating relative weights of objects. 2. Estimating the relative brightness of similar objects at varying distances from a common light source. Your results should indicate an inverse square relationship between the brightness of an object and its distance from the light source. 3. Estimating the relative areas of various two dimensional geometric shapes. AHP Pg. 11 1.4.2 Benefit/Cost analysis This example will illustrate two key points: First it will show you how to do a benefit to cost analysis, and second it will indicate that not all elements in a lower level need to be connected to all the elements in the immediately higher level. Many decisions made in your personal or professional life require weighing benefits against costs. Benefits of alternative courses of action may be calculated by considering a hierarchy of objectives, attributes of alternatives, and the alternatives themselves. This will tell us how much each alternative contributes to the fulfillment of the objectives. A hierarchy of costs for bringing about the alternatives may be constructed by considering the problems which will be caused by each alternative. The costs of the problems themselves, or the costs of solutions designed to eliminate these problems are then analyzed in the hierarchy. Once the two hierarchies have been constructed and the relative weights of each alternative have been computed with respect to both costs and benefits, then a benefit to cost ratio test may be calculated for each alternative. The alternative with the highest ratio should be the alternative selected. This will be the alternative which will yield the greatest amount of benefit from a unit measure of cost. The problem which we will model, will involve the selection of a transportation project designed to bring people to the downtown core of a large metropolitan city. The alternatives under study involve the construction of an expressway, a subway, or an improvement in the present bus service. The benefits of the project have been grouped into economic, social and personal benefits. Economic benefits are further subdivided into a time savings to get to downtown, the number of jobs created by each project and the improvement of downtown commerce due to more business. Benefits to society are viewed as abstract quantities. They have been subdivided into the degree of community pride generated by each alternative and the greater number of trips to the downtown that will result. Personal benefits have been defined by their contribution to the individual. For example the reduction of traffic and parking problems, and the comfort and accessibility of using each alternative. The benefit hierarchy is illustrated in Figure 1.3. Project costs have been grouped into economic, social, and environmental costs. Economic costs are subdivided into both capital and operational or maintenance costs. Social costs represent costs to society as a whole. They are defined as the disruption of people's lifestyles, the dislocation of people from their homes, and the general disruption to people caused by, for example, the different levels of traffic congestion. Environmental costs are viewed in terms of the pollution and decrease in parkland resulting from each alternative. The cost hierarchy is illustrated in Figure 1.4. AHP Pg. 12 ╔═════════════════════╗ Level 0 ║ BENEFITS OF PROJECT ║ ╚══════════╤══════════╝ │ ┌──────────────────────────┼─────────────────────────┐ │ │ │ ┌───────────┴───────────┐ ┌───────────┴───────────┐ ┌──────────┴──────────┐ Level 1 │ ECONOMIC │ │ SOCIAL │ │ PERSONAL │ └─┬─────────────────────┘ └─┬─────────────────────┘ └─┬───────────────────┘ │┌────────────────────┐ │┌────────────────────┐ │┌──────────────────┐ Level 2 ├┤TIME SAVINGS │ ├┤COMMUNITY PRIDE │ ├┤TRAFFIC VOLUME │ │├────────────────────┤ │├────────────────────┤ │├──────────────────┤ ├┤JOB CREATION │ └┤MORE TRIPS DOWNTOWN │ ├┤PARKING │ │├────────────────────┤ └────────┬───────────┘ │├──────────────────┤ └┤COMMERCE │ │ ├┤COMFORT │ └────────┬───────────┘ │ │├──────────────────┤ │ │ └┤ACCESSIBILITY │ │ │ └───────┬──────────┘ ├──────────────────────────┼─────────────────────────┤ ┌───────────┴───────────┐ ┌───────────┴───────────┐ ┌──────────┴──────────┐ Level 3 │ BUILD EXPRESSWAY │ │ BUILD SUBWAY │ │ IMPROVE BUS SERVICE │ └───────────────────────┘ └───────────────────────┘ └─────────────────────┘ Figure 1.3. Benefit hierarchy for transportation project. ╔═════════════════════╗ Level 0 ║ COSTS OF PROJECT ║ ╚══════════╤══════════╝ │ ┌──────────────────────────┼─────────────────────────┐ │ │ │ ┌───────────┴───────────┐ ┌───────────┴───────────┐ ┌──────────┴──────────┐ Level 1 │ ECONOMIC │ │ SOCIAL │ │ ENVIRONMENTAL │ └─┬─────────────────────┘ └─┬─────────────────────┘ └─┬───────────────────┘ │┌────────────────────┐ │┌────────────────────┐ │┌──────────────────┐ Level 2 ├┤CAPITAL │ ├┤LIFESTYLE CHANGES │ ├┤POLLUTION │ │├────────────────────┤ │├────────────────────┤ │├──────────────────┤ └┤OPERATIONAL │ ├┤PEOPLE DISLOCATION │ └┤DECREASED PARKLAND│ └────────┬───────────┘ │├────────────────────┤ └───────┬──────────┘ │ └┤GENERAL DISRUPTION │ │ │ └────────┬───────────┘ │ │ │ │ ├──────────────────────────┼─────────────────────────┤ │ │ │ ┌───────────┴───────────┐ ┌───────────┴───────────┐ ┌──────────┴──────────┐ Level 3 │ BUILD EXPRESSWAY │ │ BUILD SUBWAY │ │ IMPROVE BUS SERVICE │ └───────────────────────┘ └───────────────────────┘ └─────────────────────┘ Figure 1.4. Cost hierarchy for transportation project. The data and results of the analysis as generated by the program are given on the next few pages. The results can be summarized here as follows: ┌────────────┬────────┬─────────────┐ │ EXPRESSWAY │ SUBWAY │ IMPROVE BUS │ ┌────────────────────┼────────────┼────────┼─────────────┤ │ BENEFITS │ 36 │ 55 │ 9 │ ├────────────────────┼────────────┼────────┼─────────────┤ │ COSTS │ 37 │ 52 │ 10 │ ├────────────────────┼────────────┼────────┼─────────────┤ │ BENEFIT/COST RATIO │ 0.97 │* 1.06 *│ 0.9 │ └────────────────────┴────────────┴────────┴─────────────┘ AHP Pg. 13 In this analysis, the benefit to cost ratios of all 3 alternatives are fairly close to each other. Nevertheless, the subway option scores slightly better than the other two, and the expressway option scores better than the bus option. Therefore, if enough resources and money are available then a subway should be built. If, however, there is not enough money to build the subway, but there is enough for an expressway, then the expressway option should be selected. If this is the case, and the subway option is not a feasible alternative, then it should not have been considered in the first place. The next few pages list the data for this problem which has been supplied your diskette. The benefit data is found in file BENEFIT.AHP, while the cost data is found in file COST.AHP. If you will recall, one of the purposes of this example was to show that not all elements in a lower level, need to be connected to all elements in the immediately higher level. In figures 1.3 and 1.4, elements in level 2, are not all connected to all elements in level 1. For example, it would not help us much to make a connection between the pride generated for an alternative to economic benefits. One can argue, that pride could reap some economic benefits, however, its effects would be negligible when compared with the other criteria considered, therefore no connection is made. Looking at the data for level 2, you can see how a connection is identified in the pairwise comparison matrix. If no connection exists for a certain element, then no pairwise comparison is input in both the row and column of this element. Keep in mind that, if N elements are being compared, then N(N-1)/2 comparisons are required. FILE:> C:BENEFIT .AHP Copyright (C) 1986-1993, ARMADA SYSTEMS Decision Tree Hierarchy GOAL: To determine the benefits of a transportation project to downtown core. ╔══════════════╤══════════════╤══════════════╤══════════════╤══════════════╗ ║ Level 1 │ Level 2 │ Level 3 │ Level 4 │ Level 5 ║ ╔═══╬══════════════╪══════════════╪══════════════╪══════════════╪══════════════╣ ║ 1 ║Economic 67│Time saving 5│Expressway 36│ │ ║ ║ 2 ║Social 11│Job creatin 46│Subway 55│ │ ║ ║ 3 ║Personal 22│Commerce 16│Improve Bus 9│ │ ║ ║ 4 ║ │Pride 3│ │ │ ║ ║ 5 ║ │More trips 8│ │ │ ║ ║ 6 ║ │Traffic 8│ │ │ ║ ║ 7 ║ │Parking 8│ │ │ ║ ║ 8 ║ │Comfort 2│ │ │ ║ ║ 9 ║ │Accessible 4│ │ │ ║ ║10 ║ │ │ │ │ ║ ║11 ║ │ │ │ │ ║ ║12 ║ │ │ │ │ ║ ║13 ║ │ │ │ │ ║ ║14 ║ │ │ │ │ ║ ║15 ║ │ │ │ │ ║ ║16 ║ │ │ │ │ ║ ╚═══╩══════════════╧══════════════╧══════════════╧══════════════╧══════════════╝ Overall average inconsistency= 0.46 (acceptable) Pairwise Comparison Data for level 1, with respect to: GOAL A B C WEIGHTS A 6 3 A Economic 66.7 ▒▒▒▒▒▒▒▒▒ B -2 B Social 11.1 ▒▒ C C Personal 22.2 ▒▒▒ AHP Pg. 14 Pairwise Comparison Data for level 2, with respect to: Economic A B C D E F G H I WEIGHTS A -7 -5 A Time saving 6.9 ▒ B 4 B Job creatin 68.7 ▒▒▒▒▒▒▒▒▒ C C Commerce 24.4 ▒▒▒ D D Pride 0.0 E E More trips 0.0 F F Traffic 0.0 G G Parking 0.0 H H Comfort 0.0 I I Accessible 0.0 Pairwise Comparison Data for level 2, with respect to: Social A B C D E F G H I WEIGHTS A A Time saving 0.0 B B Job creatin 0.0 C C Commerce 0.0 D -3 D Pride 25.0 ▒▒▒ E E More trips 75.0 ▒▒▒▒▒▒▒▒▒ F F Traffic 0.0 G G Parking 0.0 H H Comfort 0.0 I I Accessible 0.0 Pairwise Comparison Data for level 2, with respect to: Personal A B C D E F G H I WEIGHTS A A Time saving 0.0 B B Job creatin 0.0 C C Commerce 0.0 D D Pride 0.0 E E More trips 0.0 F 1 4 2 F Traffic 35.9 ▒▒▒▒▒▒▒▒▒ G 4 2 G Parking 35.9 ▒▒▒▒▒▒▒▒▒ H -3 H Comfort 8.2 ▒▒ I I Accessible 20.0 ▒▒▒▒▒ AHP Pg. 15 Pairwise Comparison Data for level 3, with respect to: Time saving A B C WEIGHTS A 3 9 A Expressway 66.3 ▒▒▒▒▒▒▒▒▒ B 6 B Subway 27.8 ▒▒▒▒ C C Improve Bus 5.8 ▒ Pairwise Comparison Data for level 3, with respect to: Job creatin A B C WEIGHTS A -4 5 A Expressway 23.7 ▒▒▒ B 8 B Subway 69.9 ▒▒▒▒▒▒▒▒▒ C C Improve Bus 6.4 ▒ Pairwise Comparison Data for level 3, with respect to: Commerce A B C WEIGHTS A 2 7 A Expressway 58.2 ▒▒▒▒▒▒▒▒▒ B 6 B Subway 34.8 ▒▒▒▒▒ C C Improve Bus 6.9 ▒ Pairwise Comparison Data for level 3, with respect to: Pride A B C WEIGHTS A -5 5 A Expressway 20.7 ▒▒▒ B 9 B Subway 73.5 ▒▒▒▒▒▒▒▒▒ C C Improve Bus 5.8 ▒ Pairwise Comparison Data for level 3, with respect to: More trips A B C WEIGHTS A -3 3 A Expressway 25.0 ▒▒▒ B 6 B Subway 65.5 ▒▒▒▒▒▒▒▒▒ C C Improve Bus 9.5 ▒ Pairwise Comparison Data for level 3, with respect to: Traffic A B C WEIGHTS A 5 9 A Expressway 73.5 ▒▒▒▒▒▒▒▒▒ B 5 B Subway 20.7 ▒▒▒ C C Improve Bus 5.8 ▒ Pairwise Comparison Data for level 3, with respect to: Parking A B C WEIGHTS A -9 -7 A Expressway 5.5 ▒ B 3 B Subway 65.5 ▒▒▒▒▒▒▒▒▒ C C Improve Bus 29.0 ▒▒▒▒ Pairwise Comparison Data for level 3, with respect to: Comfort A B C WEIGHTS A -6 -4 A Expressway 8.5 ▒ B 3 B Subway 64.4 ▒▒▒▒▒▒▒▒▒ C C Improve Bus 27.1 ▒▒▒▒ Pairwise Comparison Data for level 3, with respect to: Accessible A B C WEIGHTS A 6 7 A Expressway 75.8 ▒▒▒▒▒▒▒▒▒ B 2 B Subway 15.1 ▒▒ C C Improve Bus 9.1 ▒ AHP Pg. 16 FILE:> C:COST .AHP Copyright (C) 1986-1993, ARMADA SYSTEMS Decision Tree Hierarchy GOAL: To estimate the costs of a transportation project to the downtown core. ╔══════════════╤══════════════╤══════════════╤══════════════╤══════════════╗ ║ Level 1 │ Level 2 │ Level 3 │ Level 4 │ Level 5 ║ ╔═══╬══════════════╪══════════════╪══════════════╪══════════════╪══════════════╣ ║ 1 ║Economic 74│Capital 65│Expressway 37│ │ ║ ║ 2 ║Social 17│Operational 9│Subway 52│ │ ║ ║ 3 ║Environment 9│Lifestyles 2│Improve Bus 10│ │ ║ ║ 4 ║ │People Disl 11│ │ │ ║ ║ 5 ║ │Disruption 4│ │ │ ║ ║ 6 ║ │Pollution 7│ │ │ ║ ║ 7 ║ │Parkland 2│ │ │ ║ ║ 8 ║ │ │ │ │ ║ ║ 9 ║ │ │ │ │ ║ ║10 ║ │ │ │ │ ║ ║11 ║ │ │ │ │ ║ ║12 ║ │ │ │ │ ║ ║13 ║ │ │ │ │ ║ ║14 ║ │ │ │ │ ║ ║15 ║ │ │ │ │ ║ ║16 ║ │ │ │ │ ║ ╚═══╩══════════════╧══════════════╧══════════════╧══════════════╧══════════════╝ Overall average inconsistency= 0.37 (acceptable) Pairwise Comparison Data for level 1, with respect to: GOAL A B C WEIGHTS A 5 7 A Economic 74.0 ▒▒▒▒▒▒▒▒▒ B 2 B Social 16.7 ▒▒ C C Environment 9.4 ▒ Pairwise Comparison Data for level 2, with respect to: Economic A B C D E F G WEIGHTS A 7 A Capital 87.5 ▒▒▒▒▒▒▒▒▒ B B Operational 12.5 ▒ C C Lifestyles 0.0 D D People Disl 0.0 E E Disruption 0.0 F F Pollution 0.0 G G Parkland 0.0 Pairwise Comparison Data for level 2, with respect to: Social A B C D E F G WEIGHTS A A Capital 0.0 B B Operational 0.0 C -5 -3 C Lifestyles 10.5 ▒ D 3 D People Disl 63.7 ▒▒▒▒▒▒▒▒▒ E E Disruption 25.8 ▒▒▒▒ F F Pollution 0.0 G G Parkland 0.0 Pairwise Comparison Data for level 2, with respect to: Environment A B C D E F G WEIGHTS A A Capital 0.0 B B Operational 0.0 C C Lifestyles 0.0 D D People Disl 0.0 E E Disruption 0.0 F 3 F Pollution 75.0 ▒▒▒▒▒▒▒▒▒ G G Parkland 25.0 ▒▒▒ AHP Pg. 17 Pairwise Comparison Data for level 3, with respect to: Capital A B C WEIGHTS A -4 7 A Expressway 25.3 ▒▒▒ B 9 B Subway 69.4 ▒▒▒▒▒▒▒▒▒ C C Improve Bus 5.3 ▒ Pairwise Comparison Data for level 3, with respect to: Operational A B C WEIGHTS A -2 -2 A Expressway 20.0 ▒▒▒▒▒ B 1 B Subway 40.0 ▒▒▒▒▒▒▒▒▒ C C Improve Bus 40.0 ▒▒▒▒▒▒▒▒▒ Pairwise Comparison Data for level 3, with respect to: Lifestyles A B C WEIGHTS A 7 5 A Expressway 73.1 ▒▒▒▒▒▒▒▒▒ B -3 B Subway 8.1 ▒ C C Improve Bus 18.8 ▒▒ Pairwise Comparison Data for level 3, with respect to: People Disl A B C WEIGHTS A 6 8 A Expressway 76.1 ▒▒▒▒▒▒▒▒▒ B 3 B Subway 16.6 ▒▒ C C Improve Bus 7.3 ▒ Pairwise Comparison Data for level 3, with respect to: Disruption A B C WEIGHTS A 3 4 A Expressway 62.5 ▒▒▒▒▒▒▒▒▒ B 2 B Subway 23.8 ▒▒▒ C C Improve Bus 13.6 ▒▒ Pairwise Comparison Data for level 3, with respect to: Pollution A B C WEIGHTS A 8 5 A Expressway 74.2 ▒▒▒▒▒▒▒▒▒ B -3 B Subway 7.5 ▒ C C Improve Bus 18.3 ▒▒ Pairwise Comparison Data for level 3, with respect to: Parkland A B C WEIGHTS A 8 8 A Expressway 80.0 ▒▒▒▒▒▒▒▒▒ B 1 B Subway 10.0 ▒ C C Improve Bus 10.0 ▒ AHP Pg. 18 1.4.3 Application to psychotherapy The hierarchical method may be used to provide insight into psychological problem areas, in the following manner: Consider an individual's overall well-being as the single top level entry in a hierarchy. Conceivably, this level is primarily affected by childhood, adolescent, and adult experiences. Factors in growth and maturity which impinge upon well- being may be the influences of the mother and father separately, as well as their influences together as parents, the socioeconomic background, sibling relationships, one's peer group, schooling, religious status, and so on. As an example, suppose that an individual feels that his self-confidence has been severely undermined and his social adjustments have been impaired by a restrictive situation during childhood. The following hierarchy is constructed, and the individual is questioned about his childhood experiences only. He is asked to relate the elements in the hierarchy on each level, with respect to elements in the previous level: Goal: To determine present overall well-being Level 1: Self-respect Sense of security Ability to adapt to new people and new circumstances Level 2: Visible affection shown for subject Ideas of strictness and ethics Actual disciplining of child Emphasis on personal adjustment with others Level 3: Influence of mother Influence of father Influence of both mother and father The therapy resulting from this analysis should depend on both the judgments and any considerable inconsistency involved. This is a highly restricted example, a more complete setting for a psychological history may include many more elements at each level, chosen by trained individuals and placed in such a way as to derive the maximum understanding of the subject. AHP Pg. 19 1.4.4 Calculating expected values Suppose that you wanted to forecast the average number of children born to North American families in the next 10 to 20 years. The first step would be to set up a hierarchy of factors which would influence the size of family in the future. You may consider the following hierarchy: Goal: To determine the average number of children born per family Level 1: Availability of birth controls and abortion Cost of raising children Family income Working mother Older age of motherhood Education of mother Social pressures Level 2: Number of children (0, 1, 2, 3, 4) Once you have entered your pairwise comparison judgments into the model, and the program has calculated the weights for level 2 with respect to the goal, the expected number of children per family may be calculated as follows: Suppose that the following weights are obtained: Number of children: 0 1 2 3 4 Weight for level 2: 2.8 17.4 49.5 23.9 6.4 The expected number of children per family is: (2.8x0 + 17.4x1 + 49.5x2 + 23.9x3 + 6.4x4)/100 = 2.14 As an example of another application, this method may be used to estimate sales increase of a corporation despite the impact of inflation, recession, and rise of energy cost. These factors, and any others which may be important to specific organizations may be placed in the first level in the hierarchy. The sales increases may be divided into ranges of 0-5%, 6-10%, 11-15%, 16-20% and placed in the second level. The average rate of increase is then calculated as in the family size problem above. AHP Pg. 20 1.4.5 Determining optimum type of coal plant The problem of determining the most desirable coal using energy system technology for a given community, may be regarded as a hierarchy with three major criteria. One is concerned with energy resource utilization (ERU) efficiency, a second with environmental impacts, and a third one with economics. Each of these criteria involves a number of subcriteria. For example under ERU efficiency we have four levels. The first level is concerned with season, topography, geography, etc. The second level is concerned with various energy requirements of a community such as heating and cooling, lighting etc. The third level is concerned with the method of energy supply, and the fourth with the type of plant which generates this energy. Goal: Determine coal plant ERU efficiency Level 1: Season, Topography, Geography, Climate, Form, Function, Density Level 2: Heating and cooling, Lighting, Water heating and cooking, Transportation, Industry, Recreation, Public services Level 3: Electrical, Thermal, Fuel Level 4: Stack gas cleaning with conventional boiler Fluidized bed combustion Low BTU gas High BTU gas Coal liquefaction Solvent refined coal For environmental impacts of the different plant types, we consider the various pollutants produced. This hierarchy contains two levels. Goal: Determine environmental impacts of coal plant Level 1: Sulfur dioxide, Carbon dioxide, Carbon monoxide, Water discharges, Solid wastes, Land use Level 2: Stack gas cleaning with conventional boiler Fluidized bed combustion Low BTU gas High BTU gas Coal liquefaction Solvent refined coal The economics criterion may be further broken down into capital and operating costs for the first level, and the coal plant alternatives in the last level. AHP Pg. 21 2.0 PROGRAM CONFIGURATION Push ALT+S to customize screen colors and to configure the printer. The following information will be displayed: - Make necessary changes and push the RTN key to SAVE these changes to disk. - To exit without saving changes, push the ESC key. Screen colors: Foreground Background Border Standard text: 7 0 0 Highlighted text: 10 0 0 Screen heading: 1 3 0 Printer control: Printer name: HP LaserJet II Character sequence to initialize and reset printer (base 10): Init. Printer: 27, 38, 97, 49, 51, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0 Reset Printer: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 Screen colors are specified by number. The following is a cross reference listing of the available screen color attributes. ┌──────────┬────────────┬────────────────┐ │ COLOR │ STANDARD │ HIGH-INTENSITY │ ├──────────┼────────────┼────────────────┤ │ Black │ 0 │ 8 │ │ Blue │ 1 │ 9 │ │ Green │ 2 │ 10 │ │ Cyan │ 3 │ 11 │ │ Red │ 4 │ 12 │ │ Magenta │ 5 │ 13 │ │ Brown │ 6 │ 14 │ │ White │ 7 │ 15 │ └──────────┴────────────┴────────────────┘ Printer control data must be entered in decimal (base 10) notation. If you wish to change any printer control data, then simply consult your printer user's manual for the control codes of functions you would like to make use of. You may, for example want to change the character pitch and font, or perhaps you would like to reduce the line spacing so that more lines can be printed on one page. The possibilities are limited only by your printer. When you have decided what functions you would like to utilize, make the necessary changes on screen and push RTN to save these to disk. AHP Pg. 22 3.0 ABOUT ARMADA SYSTEMS Armada Systems was established in 1986 with the purpose of developing unique but useful microcomputer software. Since that time, Armada Systems has expanded it's operations, and now specializes in the following key areas: * Custom PC software development. * Decision making software, seminars and consulting services. * CA-Clipper training. * Research and development of new software applications. In addition to the Analytic Hierarchy Process, Armada Systems publishes the Decision Matrix Expert (DME) and MyBASE software packages. The next several pages are devoted to providing you with a better understanding of what these software packages do, and how they can help you to become a more effective decision maker. AHP Pg. 23 3.1 THE DECISION MATRIX EXPERT (DME) The Decision Matrix Expert (DME), is an innovative, yet remarkably easy to use software package for decision analysis. It represents an objective, scientific approach to replace intuition and speculation, while preserving such qualitative factors as experience and judgment. The DME is not a 'black box' program, it relies upon the use of popular, well established Multiple Criteria Decision Making algorithms. Numerical results are provided for each stage in the analysis, so that the user can see what is happening and have confidence in the results. The use of popular, well established algorithms, with intermediate numerical results, is especially important to such users as educational institutions, government agencies and consultants. Consultants, who for example, are taxed to recommend the location for a new garbage dump, need a tool which will evaluate possible alternatives with as little bias as possible. Their recommendations will need to stand up to public scrutiny, and the public hearing process which usually takes place before a site is actually selected. This is where the use of well established decision analysis algorithms is useful. They can be explained and defended because quite a bit of research has gone into them. In the DME, decisions are portrayed in a matrix which contains all of the information required to arrive at a final decision. The columns of this matrix represent the criteria which are important to the decision, while the rows represent the various alternatives being considered. In the analysis, alternatives are scanned for dominance and to ensure that they meet the minimum cutoff constraints specified by the user. Final ranking of alternatives is performed using the Linear Assignment Method, Normalized Additive Weighting, ELECTRE, TOPSIS, and an aggregation and synthesis phase. Numerical results from each of these algorithm phases are available to the user for analysis. 3.1.1 Applications Location planning, cost/benefit analysis, strategic planning, recruiting, employee evaluation, resource allocation, taste testing, new product evaluations, problem analysis, market research, and many more. 3.1.2 System requirements The Decision Matrix Expert will work on any MS DOS compatible computer with at least 384K RAM. A printer is recommended but not required. AHP Pg. 24 3.2 MyBASE MyBASE is a very powerful, easy to use, multipurpose database system. You can use it in DOS or Windows to view, edit, sort, search, group, filter, replace, copy/paste, merge, print, fax or export data in many ways. Both indexing and filter methods are provided for searching, grouping, browsing and retrieving data. MyBASE also features a fully programmable merge utility. What is particu- larly noteworthy is that, besides allowing you to do the standard merging of text and data, commands may be embedded in the merge file to control how records and data are processed, where the output is sent to, and what external programs to call (ex. DOS functions, file viewers, word proces- sors, spreadsheets, graphics viewers, FAX software, and so on). For example, if you had a database of clients, you could create a merge file to send all your clients (or just a small group of them) a personal- ized letter. The merged letter could be sent to a printer to obtain a hardcopy, or it could just as easily be sent directly to your client, via FAX. If the letter was faxed, MyBASE would merge and FAX each letter completely unattended. A sample contact management system is included with this package. This contact management system includes, pre-defined view screens, field edit templates and field edit validation, default pop-up selection boxes and sample data. Also included are sample merge programs to print envelopes, letters, reports, and to send personalized faxes to multiple destinations. You can easily modify this contact management system to suit your own needs, or if you wish, you can just as easily create any number of new databases. 3.2.1 Quick overview of features * The program is small 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. AHP Pg. 25 * Database specific, three level password access system Can be turned either ON or OFF). * View data in table or record view mode (F3/TAB toggles between modes). * Quick and simple way of defining new ways of looking at data. Unique view windows may be defined for each database. The view windows will control how the data will be displayed on screen and in printed reports. * Merge print function to allow merging of text from an external text file with data from the database. Commands may be embedded in the external merge file to control how records and data are processed, where the output is sent to, and what external procedures to call (ex. DOS func- tions, word processors, graphics viewers, FAX software, label printers, and so on). * User configurable print drivers. Export data to printer or a DBF or ASCII delimited file. The ability to export data to a file is extremely useful since the exported data will be based on the current database view and filter conditions which you have set (ie. what you see is what you get). The exported data may then be imported into a word processor, spread- sheet, desktop publishing package, telecommunications or fax software, etc... * Tag individual records for printing, merging or replacing. * Filter database to display or print a group of selected data. * Skip through database, searching for specific data. * Quick, database wide, search and replacement of data. * Memo field support for free-form notes of up to 64K in size per record. * Copy and paste data for faster data input. * Automatic telephone dialer. * Calculate totals and averages for numeric data. * Support for EGA and VGA monitors to display more data on screen. * Allows for customization of screen colors, video size, date format, and use of sound. * Display or hide records marked for deletion. * NOTE: MyBASE is continually updated and refined. The latest version of MyBASE may have additional functionality and features not specified here. 3.2.2 System requirements A PC-DOS or MS-DOS compatible system with at least 640K RAM. A hard disk with at least 1.0 MB free. PC-DOS/MS-DOS 3.1 or higher. AHP Pg. 26 4.0 ORDERING SOFTWARE: WHAT YOU WILL RECEIVE When you purchase any software from Armada Systems, your satisfaction is 100% guaranteed. If for any reason you are not completely satisfied with the product you may return it within 30 days for a refund. In addition to this guarantee, you will receive the following: (1) The latest version of software. (2) Complete reference and user's guide. (3) Free technical support. (4) Notice of future updates and new products. (5) Eligibility for low cost upgrades. (6) Free shareware software, as follows: ┌────────────────────────────┬─────────────────────────────────┐ │ PROGRAM ORDERED │ FREE SHAREWARE YOU WILL RECEIVE │ ├────────────────────────────┼─────────────────────────────────┤ │ Analytic Hierarchy Process │ MyBASE │ │ Decision Matrix Expert │ MyBASE │ │ MyBASE │ Analytic Hierarchy Process │ └────────────────────────────┴─────────────────────────────────┘ To place your order, fill out the order form on the following page and mail it to Armada Systems, along with a company purchase order, cheque or money order payment, made out to "B. BORZIC". Payment must be in the quoted U.S. or Canadian funds. Site licensing and volume discounts (QTY. >= 5) are available, please write for details. ARMADA SYSTEMS SOFTWARE REGISTRATION AND ORDER FORM ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ To order software, please fill out this order form and mail it to the address given below, along with a company purchase order, cheque or money order payment, made out to "B. BORZIC". Payment must be in the quoted U.S. or Canadian funds. Site licensing and volume discounts (QTY. >= 5) are available, please write for details. When you purchase software from Armada Systems, your satisfaction is 100% guaranteed. If for any reason you are not completely satisfied with the product you may return it within 30 days for a refund. Boris Borzic, Armada Systems P.O. Box 637, Station A Downsview, Ontario M3M 3A9 CANADA Tel. (416) 889-2617 or (905) 889-2617 after October 4, 1993 NAME ____________________________ TITLE __________________________________ COMPANY _________________________ DEPARTMENT _____________________________ ADDRESS ___________________________________________________________________ CITY ____________________________ STATE/PROVINCE _________________________ ZIP/POSTAL CODE _________________ COUNTRY ________________________________ PHONE ___________________________ FAX ____________________________________ Would you like the program supplied on 5.25" or 3.5" disks? _______________ Where did you obtain the AHP software? ____________________________________ AHP 3.01 - 9317420 +-------------------------------------------------------------------------+ | DESCRIPTION | U.S. $ | CDN $ | QTY | TOTAL $ | |-------------------------------------|--------|--------|-----|-----------| | Analytic Hierarchy Process (AHP) | 99.00 | 119.00 | | | |-------------------------------------|--------|--------|-----|-----------| | Decision Matrix Expert (DME) | 99.00 | 119.00 | | | |-------------------------------------|--------|--------|-----|-----------| | MyBASE | 124.00 | 149.00 | | | |-------------------------------------|--------|--------|-----|-----------| | AHP + DME ordered together | 149.00 | 179.00 | | | |-------------------------------------|--------|--------|-----|-----------| | AHP + DME + MyBASE ordered together | 249.00 | 299.00 | | | +-------------------------------------------------------------|-----------| Purchase order processing charge | 15.00 | (cross out if payment is enclosed) | | |-----------| Shipping & handling | 8.00 | |-----------| Applicable taxes | | |-----------| TOTAL | | +-----------+ Signature ______________________________ Date ____________________________ Use the back of this sheet to add any comments or suggestions you may have. REFERENCES Alexander M. Joyce, Saaty L. Thomas: "Thinking With Models," Pergamon Press Chryssolouris G, Chan S., Cobb W.: "Decision Making in the Factory Floor," COMMLINE, May-June 1986 Green P.E., Wind Y.: "Multiattribute Decisions in Marketing: A Measurement Approach," Dryden Press, 1973 Ho K. James: "Analytic Hierarchies and Holistic Preferences," College of Business Administration The University of Tennessee, Knoxville, TN 37996 Hwang C.L., Yoon K.: "Multiple Attribute Decision Making, Methods and Applications," Springer-Verlang, 1981 Raiffa Howard: "Decision Analysis, Introductory Lectures on Choices Under Uncertainty," Addison-Wesley, 1968 Saaty L. Thomas: "The Analytic Hierarchy Process," McGraw-Hill, 1980 Szonyi A.J., Fenton R.G., White J.A., Agee M.H., Case K.E.: "Principles of Engineering Economic Analysis," John Wiley and Sons, 1982 Wagner M. Harvey: "Principles of Operations Research," Prentice-Hall, 1975 NOTES