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- T H E A N A L Y T I C H I E R A R C H Y P R O C E S S
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- USER'S GUIDE AND REFERENCE MANUAL
-
- Release 3.01
-
-
- ___________________________________________________________________________
-
- This software is provided to you for evaluation use only. If you
- find the software useful, please register it. With your registration
- you will not only receive technical support and the latest version
- of software, but you will also be sponsoring the continued support
- and future enhancements of this product.
- ___________________________________________________________________________
-
-
-
- AHP - Analytic Hierarchy Process, Release 3.01
- The Modern Art of Decision Making
- Program Serial No. 9317420
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-
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- 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
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- 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
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- 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
-
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- 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
-
-
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- 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
-
-