The Analytic Hierarchy Process. Danny Hahn

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "The Analytic Hierarchy Process. Danny Hahn"

Transcription

1 The Analytic Hierarchy Process Danny Hahn

2 The Analytic Hierarchy Process (AHP) A Decision Support Tool developed in the 1970s by Thomas L. Saaty, an American mathematician, currently University Chair, Quantitative Group, Katz Graduate School of Business, University of Pittsburgh. A theory and methodology for modeling problems in the economic, social and management sciences. A problem solving framework used for: Determining the best of several alternatives Setting Priorities Allocating Resources Requires a pair-wise determination of the relative importance of each of the criteria. Expert Choice is one commercial software tool based on the AHP. Slide 2

3 The Process Break down an unstructured situation into its component parts. Arrange the parts or variables into a hierarchic order. Assign numerical values to subjective judgments on the relative importance of each variable. Synthesize the judgments to determine which variables have the highest priority and should be acted upon to influence the outcome of the situation. Slide 3

4 The Hierarchy Goal Factor 1 Factor 2 Factor 3 Option 1 Option 2 Slide 4

5 Scale of Relative Importance 1 Two factors are Equally Important 3 One factor is Slightly more Important than the other 5 One is Strongly more Important 7 One is Very strongly more Important 9 One is Absolutely more Important 2, 4, 6, 8 Intermediate Values of one criteria over the other Saaty s book, The Analytic Hierarchy Process, provides background and theory on why he chose the 1 9 scale and his validation of this judgment with measurable science. Slide 5

6 Step by Step Example Buy the Right Car Determine the Criteria (factors) Price (lower price is better) Body Style Miles per Gallon (more MPG is better) Interior Quality Engine Size Design the Hierarchy Use an analytic process to help make a decision Slide 6

7 The Car Decision Hierarchy Buy the Right Car Price Body Style MPG Interior Quality Engine Size X-Treem Yaawhee Zoomer Slide 7

8 My Preferences (My Judgments) Body style is more important than Price. I would pay more for the Body Style I want Price is more important than MPG. I would not pay extra for more MPG Interior Quality is more important than Price. I would pay more for better Interior Quality Engine Size is more important than Price. Body Style is more important than MPG. Etc. (see next slide) Slide 8

9 Pair-wise Comparison of Criteria More Important Equal More Important Price Body Style Price MPG Price Interior Quality Price Engine Size Body Style MPG Body Style Interior Quality Body Style Engine Size MPG Interior Quality MPG Engine Size Interior Quality Engine Size Slide 9

10 Matrix Review Price Body Style MPG Interior Quality Engine Size Price 1 1/4 3 1/5 1/5 Body Style /3 MPG 1/3 1/5 1 1/5 1/3 Interior Quality 5 1/ Engine Size /5 1 An n x n matrix is a square matrix where n is the number of rows and columns. In this case n = 5. An element is equally important when compared to itself therefore the main diagonal must be a 1. By convention, the comparison of strength is always of an activity appearing in the column on the left against an activity appearing in the row on top. Body Style is 5 times more important than MPG The reverse comparisons (B to A) produce the reciprocal of the basic comparison. This is called a reciprocal matrix. MPG is 1/5 as important as Body Style Slide 10

11 Convert Criteria Comparisons to a Matrix Convert the pair-wise comparisons from Slide 9 to a matrix. Prioritizing the 5 Criteria Price Body Style MPG Interior Quality Engine Size Price 1 1/4 3 1/5 1/5 Body Style /3 MPG 1/3 1/5 1 1/5 1/3 Interior Quality 5 1/ Engine Size /5 1 Column Sum Normalize the matrix by dividing each value by the column sum (e.g. 1 / = 0.065). Then compute the average value for each row. Price Body Style MPG Interior Quality Engine Size Average Price Body Style MPG Interior Quality Engine Size Looking at the average value of each row, notice that 33% of my objective weight is on Interior Quality, 29% on Body Style, 26% on Engine Size. These are the weights of the criteria. Slide 11

12 The Decision Candidates The cars under consideration X-Treem Yaawhee Zoomer Price $25,000 $27,000 $29,000 Body Style 4-door Mid-size 5-door SportWagon 4-door Full-size MPG Interior Quality Standard Deluxe Above Average Engine Size 3.8 Liter V Liter 4 Cyl. 5.0 Liter V-8 The next step is to evaluate all three cars on each of the five criteria as shown in the Hierarchy Chart on Slide 7 Slide 12

13 Evaluate Price for Each Car X-Treem = $25,000, Yaawhee = $27,000, Zoomer = $29,000 Price of three cars. Lower Cost is better. X is slightly more important than Y. X strongly more important than Z. Y is slightly more important than Z. X-Treem Yaawhee Zoomer X-treem Yaawhee 1/3 1 3 Zoomer 1/5 1/3 1 Column Sum Normalize the Price matrix by dividing each value by the column sum (e.g. 1 / = 0.652). Then compute the average value for each row. X-Treem Yaawhee Zoomer Average X-treem Yaawhee Zoomer Slide 13

14 Evaluate Body Style for Each Car X-Treem = Mid-sized, Yaawhee = Wagon, Zoomer = Full-sized Body Style of three cars. I prefer Full-size, then Wagon, then Mid-size. Z is slightly more important than Y. Z is strongly more important than X. Y is slightly more important than X. X-Treem Yaawhee Zoomer X-treem 1 1/3 1/5 Yaawhee 3 1 1/3 Zoomer Column Sum Normalized Body Style Matrix X-Treem Yaawhee Zoomer Average X-treem Yaawhee Zoomer Slide 14

15 Evaluate MPG for Each Car X-Treem = 19 MPG, Yaawhee = 22 MPG, Zoomer = 17 MPG MPG of three cars. Higher MPG is better. Y is slightly better than X. Y is strongly better than Z. X is slightly better than Z. X-Treem Yaawhee Zoomer X-treem 1 1/3 3 Yaawhee Zoomer 1/3 1/5 1 Column Sum Normalized MPG matrix X-Treem Yaawhee Zoomer Average X-treem Yaawhee Zoomer Slide 15

16 Evaluate Interior Quality X-Treem = Standard, Yaawhee = Deluxe, Zoomer = Above Average Interior Quality of three cars. I prefer Deluxe, then Above Avg, then Standard. Y is slightly better than Z. Y is strongly better than X. Z is slightly better than X. X-Treem Yaawhee Zoomer X-treem 1 1/5 1/3 Yaawhee Zoomer 3 1/3 1 Column Sum Normalized Interior Quality Matrix X-Treem Yaawhee Zoomer Average X-treem Yaawhee Zoomer Slide 16

17 Evaluate Engine Size X-Treem = 3.8 liter V-6, Yaawhee = 2.8 liter 4 Cyl, Zoomer = 5.0 liter V-8 Engine Size of three cars. I prefer V6, then V8, then 4-Cylinder X is slightly better than Z. X is strongly better than Y. Z is slightly better than Y. X-Treem Yaawhee Zoomer X-Treem Yaawhee 1/5 1 1/3 Zoomer 1/ Normalize the Engine Size matrix and compute the average of each row X-Treem Yaawhee Zoomer Average X-Treem Yaawhee Zoomer Slide 17

18 Compute the Final Result Relative Scores for each Objective. Collect all the computed average values from each normalized matrix and multiply the original criteria weights. X-Treem Yaawhee Zoomer Criteria Weight Price Body Style MPG Interior Quality Engine Size Use these relative scores for each objective and multiply by the original weights of the criteria: X-Treem = 0.633(.073) +.106(.293) +.260(.043) +.106(.327) +.633(.264) = Yaawhee = 0.260(.073) +.260(.293) +.633(.043) +.633(.327) +.106(.264) = Zoomer = 0.106(.073) +.633(.293) +.106(.043) +.260(.327) +.260(.264) = The winner is the Yaawhee. Slide 18

19 What Happened?? This is not the result I expected from my original preferences! I would not buy a 4-cylinder sport wagon. Should I have given Engine Size a wider separation in importance? I forgot to consider consistency. If A is bigger than B, and B is bigger than C, then A must be bigger than C. Perfect consistency would be if A is 2 times bigger than B, and B is 3 times bigger than C, then A must be 6 times bigger than C. Or if Body Style is 4 times more important than Price, and Price is 3 times more important than MPG, then Body Style must be 12 times more important than MPG. Determining the Consistency Index and the Consistency Ratio should have been done on the initial pair-wise comparisons. This was the very first matrix that defined the relative priorities of the criteria (Slide 11). Slide 19

20 Consistency Index and Consistency Ratio There are at least 2 methods to evaluate the weights for errors in judgment: logarithmic least squares, and Saaty s eigenvector method. Additionally there are several techniques available to estimate Saaty s eigenvector method. Important terms needed to understand Saaty s method: Lambda max. = the maximum eigenvalue (Perron root) of the matrix = Lmax = λmax C.I. = Consistency Index = (λmax n) / (n 1) R.I. = Random Index. For each matrix of size n, Saaty s team generated random matrices and computed their mean C.I. value and called it the Random Index. These values are shown in the next slide. C.R. = Consistency Ratio = (C.I.) / (R.I.). A value less than or equal to 0.1 is acceptable. Larger values require the decision maker to reduce the inconsistencies by revising judgments. Slide 20

21 Random Index Random Consistency Index Table n Random Index This table represents a composite of two different experiments performed by Saaty and his colleagues at the Oak Ridge National Laboratory and at the Wharton School of the University of Pennsylvania. 500 random reciprocal n x n matrices were generated for n = 3 to n = 15 using the 1 to 9 scale. The maximum eigenvalue was determined by raising each random matrix to increasing powers and normalizing the result until the process converged. The consistency index was then computed on each matrix for n = 1 through n = 15. Only n = 1 through n = 10 is presented here. Slide 21

22 Step by Step on Original Matrix Prioritizing the 5 Criteria Price Body Style MPG Interior Quality Engine Size Price 1 1/4 3 1/5 1/5 Body Style /3 MPG 1/3 1/5 1 1/5 1/3 Interior Quality 5 1/ Engine Size /5 1 Column Sum Add a new column (5 th Root) and compute the 5 th root of the product of the values in each row. 2. Sum this 5 th Root column. 3. Add another column (Priority Vector) and divide each value from Step 1 by the sum in Step Add a new row (Priority Row) under Column Sum row and multiply the Column Sum vector by the Priority Vector. 5. Lambda Max = the sum of the values computed in Step C.I. = (Lambda Max 5) / (4) 7. C.R. = (C.I.) / (R.I.) = Step 6 divided by 1.12 from the Random Index Table for n = 5 Slide 22

23 Determine My Consistency (Inconsistency?) Back to my original pair-wise comparisons Price Body Style MPG Interior Quality Engine Size 5th Root of Product Priority Vector Price 1 1/4 3 1/5 1/ Body Style / MPG 1/3 1/5 1 1/5 1/ Interior Quality 5 1/ Engine Size / Sum row Priority row Compute the n-th root of the product of the values in each row. (n is the number of criteria = 5) e.g = the fifth root of (1*1/4*3*1/5*1/5) This technique is called the geometric mean. Priority Vector is the nth root divided by the sum of the nth root values. e.g = (0.496 / 6.315) Sum row = sum of each column Priority row = (sum row value)*(priority vector) LambdaMax = = sum of Priority Row Consistency Index (CI) = = (LambdaMax -n) / (n-1) = ( ) / (4) Consistency Ratio (CR) = = (CI) / (Random Index) = / 1.12 CR should be less than 0.10 (up to 0.20 is tolerable) 38.3% is too inconsistent Slide 23

24 Reconsider My Judgments More Important Equal More Important Price Body Style Price MPG Price Interior Quality Price Engine Size Body Style MPG Body Style Interior Quality Body Style Engine Size MPG Interior Quality MPG Engine Size Interior Quality Engine Size Engine Size is slightly more important to me than Interior Quality, not vice versa. This was a mistake on my initial judgment matrix. After making this change my Consistency Ratio moved from to Saaty states if this value is more than 10%, the judgments may be somewhat random and should perhaps be revised. Engine Size is strongly more important than MPG. I really just changed my mind here to be more consistent. My Consistency Ratio then became Slide 24

25 Convert Revised Judgments to Matrix Convert the pair-wise comparisons to a matrix. Shaded items are changes from the original. Prioritizing the 5 Criteria for New Judgements Price Body Style MPG Interior Quality Engine Size Price 1 1/4 3 1/5 1/5 Body Style /3 MPG 1/3 1/5 1 1/5 1/5 Interior Quality 5 1/ /3 Engine Size Column Sum Normalize the matrix by dividing each value by the column sum (e.g. 1 / = 0.065). Then compute the average value for each row. Price Body Style MPG Interior Quality Engine Size Average Price Body Style MPG Interior Quality Engine Size Looking at the average value of each row, notice that 42% of my objective weight is now on Engine Size, 26% on Body Style, 19% on Interior Quality. These are the new weights of the criteria. Slide 25

26 Re- Determine My Consistency Price Body Style MPG Interior Quality Engine Size 5th Root of Product Priority Vector Price 1 1/4 3 1/5 1/ Body Style / MPG 1/3 1/5 1 1/5 1/ Interior Quality 5 1/ / Engine Size Column total Priority row Compute the n-th root of the product of the values in each row. (n is the matrix size = 5) e.g = the fifth root of (1*1/4*3*1/5*1/5) In Excel this formula is =Power(number,power) This technique is called the geometric mean. Priority Vector is the nth root divided by the sum of the nth root values. e.g = (0.496 / 6.803) Column Total = sum of each column Priority row = (sum row value)*(priority vector) LambdaMax = = sum of Priority Row Consistency Index (CI) = = (LambdaMax -n) / (n-1) = ( ) / (4) Consistency Ratio (CR) = = (CI) / (Random Index) = / 1.12 CR should be less than 0.10 (up to 0.20 is tolerable) I am now more consistent but still not perfect. Slide 26

27 Re-Compute Using New Criteria Weights Note the average scores comparing the criteria against each car remain unchanged. Only the Criteria Weights have changed. X-Treem Yaawhee Zoomer Criteria Weight Price Body Style MPG Interior Quality Engine Size Use the same relative scores for each objective and multiply by the revised weights of the criteria: X-Treem = 0.633(.080) +.106(.260) +.260(.048) +.106(.191) +.633(.421) = Yaawhee = 0.260(.080) +.260(.260) +.633(.048) +.633(.191) +.106(.421) = Zoomer = 0.106(.080) +.633(.260) +.106(.048) +.260(.191) +.260(.421) = The winner is the X-Treem, the Mid-sized V-6. This is the result I really expected. Slide 27

28 Summary 1. Define the problem and specify the solution desired. Lay out the elements of a problem as a hierarchy. Structure the hierarchy from the top levels to the level at which decisions to solve the problem is possible. 2. Do paired comparisons among the elements of a level as required by the criteria of the next higher level. Give a judgment that indicates the dominance as a whole number. Enter that number and its reciprocal in the appropriate position in the matrix. An element on the left is examined regarding its dominance over an element at the top of the matrix. 3. These comparisons produce priorities and finally, through synthesis, to overall priorities. Check for consistency. 4. Repeat steps 2 and 3 for all levels in the hierarchy. Slide 28

29 New Developments The example just presented used the Geometric Mean technique for approximating an eigenvector. This technique is described in Saaty s book, The Analytic Hierarchy Process, written in 1980, and is also the technique presented in Appendix D.9 of the INCOSE Systems Engineering Handbook, Version 2a, dated In 2001, Saaty wrote another book, Decision Making for Leaders, that in some respects differs from his original technique. He recomputed the Random Consistency Index. (Comparison on next slide.) For the approximation procedure to obtain Lambda Max, he states that the geometric mean method (using the n th root of the products) should only be used for a matrix of size n = 3. Otherwise the row average method should be used. The consistency ratio should be 5% or less for n = 3; 9% or less for n = 4; and 10% or less for n > 4. Both the Geometric Mean and the Row Average techniques for approximating the eigenvector of a reciprocal matrix are described in Saaty s 1980 book and in the reference sited in the INCOSE SE Handbook (IEEE Transactions on Engineering Management, August 1983). The INCOSE SE Handbook only presents the Geometric Mean technique. Slide 29

30 Random Consistency Index Changes Random Consistency Index Table n Random Index Random Consistency Index Table n Random Index In Saaty s 2001 book he notes these values were recently recalculated. What if I re-compute my consistency using these new developments? Slide 30

31 Re-Compute Consistency Prioritized New Judgments Price Body Style MPG Interior Quality Engine Size Price 1 1/4 3 1/5 1/5 Body Style /3 MPG 1/3 1/5 1 1/5 1/5 Interior Quality 5 1/ /3 Engine Size Column Sum Normalize the matrix above by dividing each entry by its column sum Add a column to sum each row and then take the average. Price Body Style MPG Interior Quality Engine Size Row Sum Priority Vector (Row sum average) Price Body Style MPG Interior Quality Engine Size Column sum Slide 31

32 Row Average Technique - Continued Multiply original non-normalized matrix by Priority Vector Total each Row Price Body Style MPG Interior Quality Engine Size Row Totals Price Body Style MPG Interior Quality Engine Size e.g. For the first row of the matrix on Slide *.08, ¼ *.26, 3 *.05, 1/5 *.19, and 1/5 *.42 Slide 32

33 Estimate the Eigenvector Take column of Row Totals and divide by the Priority Vector divide by 0.05 equals Now average the result to obtain Lambda Max ( ) / 5 Lambda Max 5.50 Consistency Index 0.13 = (LambdaMax -n) / (n-1) = (5.50-5) / (4) Consistency Ratio 0.12 = (CI) / (Random Index) = 0.13 / note new RI value used here Techniques compared: Row Average Geometric Mean Lambda Max Consistency Index Consistency Ratio The Row Average technique produces a consistency ratio that is slightly worse than the Geometric Mean technique (0.11). Slide 33

34 Summary Consistency in the pair-wise comparisons of your criteria in very important. My first attempt would have led to an incorrect decision. Revising my judgments changed my consistency ratio from 38% to 11%, where the goal is 10% or less. These more consistent judgments changed the results of my decision. Using Saaty s recommendations from his 2001 book instead of his original 1980 book produced a larger inconsistency (12%) of my judgments of the pair-wise comparisons. This implies I should go back to my judgments (pair-wise comparisons) of the criteria and reconsider their relative importance to me. Slide 34

35 References Golden, Bruce L., Wasil, Edward A, and Harker, Patrick T. (editors): The Analytic Hierarchy Process - Applications and Studies, Springer-Verlag, Berlin, INCOSE Systems Engineering Handbook, Version 2a, Appendix D.9, International Council on Systems Engineering, INCOSE-TP , Version 2a, 1 June Saaty, Thomas L.: Decision Making for Leaders, RWS Publications, Pittsburgh, Saaty, Thomas L.: Priority Setting in Complex Problems, IEEE Transactions on Engineering Management, Vol. EM-30, No. 3, August Saaty, Thomas L.: The Analytic Hierarchy Process, McGraw-Hill, Inc., New York, Slide 35

MULTIPLE-OBJECTIVE DECISION MAKING TECHNIQUE Analytical Hierarchy Process

MULTIPLE-OBJECTIVE DECISION MAKING TECHNIQUE Analytical Hierarchy Process MULTIPLE-OBJECTIVE DECISION MAKING TECHNIQUE Analytical Hierarchy Process Business Intelligence and Decision Making Professor Jason Chen The analytical hierarchy process (AHP) is a systematic procedure

More information

Decision-making with the AHP: Why is the principal eigenvector necessary

Decision-making with the AHP: Why is the principal eigenvector necessary European Journal of Operational Research 145 (2003) 85 91 Decision Aiding Decision-making with the AHP: Why is the principal eigenvector necessary Thomas L. Saaty * University of Pittsburgh, Pittsburgh,

More information

ANALYTIC HIERARCHY PROCESS (AHP) TUTORIAL

ANALYTIC HIERARCHY PROCESS (AHP) TUTORIAL Kardi Teknomo ANALYTIC HIERARCHY PROCESS (AHP) TUTORIAL Revoledu.com Table of Contents Analytic Hierarchy Process (AHP) Tutorial... 1 Multi Criteria Decision Making... 1 Cross Tabulation... 2 Evaluation

More information

How to do AHP analysis in Excel

How to do AHP analysis in Excel How to do AHP analysis in Excel Khwanruthai BUNRUAMKAEW (D) Division of Spatial Information Science Graduate School of Life and Environmental Sciences University of Tsukuba ( March 1 st, 01) The Analytical

More information

THE ANALYTIC HIERARCHY PROCESS (AHP)

THE ANALYTIC HIERARCHY PROCESS (AHP) THE ANALYTIC HIERARCHY PROCESS (AHP) INTRODUCTION The Analytic Hierarchy Process (AHP) is due to Saaty (1980) and is often referred to, eponymously, as the Saaty method. It is popular and widely used,

More information

Supplier Performance Evaluation and Selection in the Herbal Industry

Supplier Performance Evaluation and Selection in the Herbal Industry Supplier Performance Evaluation and Selection in the Herbal Industry Rashmi Kulshrestha Research Scholar Ranbaxy Research Laboratories Ltd. Gurgaon (Haryana), India E-mail : rashmi.kulshreshtha@ranbaxy.com

More information

USING THE ANALYTIC HIERARCHY PROCESS (AHP) TO SELECT AND PRIORITIZE PROJECTS IN A PORTFOLIO

USING THE ANALYTIC HIERARCHY PROCESS (AHP) TO SELECT AND PRIORITIZE PROJECTS IN A PORTFOLIO USING THE ANALYTIC HIERARCHY PROCESS (AHP) TO SELECT AND PRIORIZE PROJECTS IN A PORTFOLIO Ricardo Viana Vargas, MSc, IPMA-B, PMP Professor Fundação Getúlio Vargas (FGV) Brasil Professor Fundação Instituto

More information

An Illustrated Guide to the ANALYTIC HIERARCHY PROCESS

An Illustrated Guide to the ANALYTIC HIERARCHY PROCESS An Illustrated Guide to the ANALYTIC HIERARCHY PROCESS Dr. Rainer Haas Dr. Oliver Meixner Institute of Marketing & Innovation University of Natural Resources and Applied Life Sciences, Vienna http://www.boku.ac.at/mi/

More information

OPERATIONAL RISK EFFECT ON INSURANCE MARKET S ACTIVITY Darja Stepchenko, Irina Voronova, Gaida Pettere Riga Technical University, Latvia

OPERATIONAL RISK EFFECT ON INSURANCE MARKET S ACTIVITY Darja Stepchenko, Irina Voronova, Gaida Pettere Riga Technical University, Latvia OPERATIONAL RISK EFFECT ON INSURANCE MARKET S ACTIVITY Darja Stepchenko, Irina Voronova, Gaida Pettere Riga Technical University, Latvia Abstract. The main aim of Solvency II framework is to establish

More information

Multi-Criteria Decision-Making Using the Analytic Hierarchy Process for Wicked Risk Problems

Multi-Criteria Decision-Making Using the Analytic Hierarchy Process for Wicked Risk Problems Multi-Criteria Decision-Making Using the Analytic Hierarchy Process for Wicked Risk Problems Introduction It has become more and more difficult to see the world around us in a uni-dimensional way and to

More information

USING THE ANALYTIC HIERARCHY PROCESS FOR DECISION MAKING IN ENGINEERING APPLICATIONS: SOME CHALLENGES

USING THE ANALYTIC HIERARCHY PROCESS FOR DECISION MAKING IN ENGINEERING APPLICATIONS: SOME CHALLENGES Published in: Inter l Journal of Industrial Engineering: Applications and Practice, Vol. 2, No. 1, pp. 35-44, 1995. 1 USING THE ANALYTIC HIERARCHY PROCESS FOR DECISION MAKING IN ENGINEERING APPLICATIONS:

More information

An Evaluation Model for Determining Insurance Policy Using AHP and Fuzzy Logic: Case Studies of Life and Annuity Insurances

An Evaluation Model for Determining Insurance Policy Using AHP and Fuzzy Logic: Case Studies of Life and Annuity Insurances Proceedings of the 8th WSEAS International Conference on Fuzzy Systems, Vancouver, British Columbia, Canada, June 19-21, 2007 126 An Evaluation Model for Determining Insurance Policy Using AHP and Fuzzy

More information

Project Management Software Selection Using Analytic Hierarchy Process Method

Project Management Software Selection Using Analytic Hierarchy Process Method International Journal of Applied Science and Technology Vol. 4, No. ; November 04 Project Management Software Selection Using Analytic Hierarchy Process Method Birgul Kutlu Professor Bogazici University

More information

Analytic Hierarchy Process

Analytic Hierarchy Process MODULE 1 Analytic Hierarchy Process LEARNING OBJECTIVES After completing this module, students will be able to: 1. Use the multifactor evaluation process in making decisions that involve a number of factors,

More information

Design of Analytic Hierarchy Process Algorithm and Its Application for Vertical Handover in Cellular Communication

Design of Analytic Hierarchy Process Algorithm and Its Application for Vertical Handover in Cellular Communication Design of Analytic Hierarchy Process Algorithm and Its Application for Vertical Handover in Cellular Communication Under the Guidance of Asso. Prof. Mr. Saurav Dhar Deptt. of Electronics and Communication

More information

Analytical Hierarchy Process for Higher Effectiveness of Buyer Decision Process

Analytical Hierarchy Process for Higher Effectiveness of Buyer Decision Process P a g e 2 Vol. 10 Issue 2 (Ver 1.0), April 2010 Global Journal of Management and Business Research Analytical Hierarchy Process for Higher Effectiveness of Buyer Decision Process Razia Sultana Sumi 1 Golam

More information

Project Management Software Selection Using Analytic Hierarchy Process Method

Project Management Software Selection Using Analytic Hierarchy Process Method Project Management Software Selection Using Analytic Hierarchy Process Method ISSN - 35-055 Sweety Sen (B.tech: Information Technology) Dronacharya College of Engineering Gurgaon, India Phone no. : 00343

More information

Information Security and Risk Management

Information Security and Risk Management Information Security and Risk Management by Lawrence D. Bodin Professor Emeritus of Decision and Information Technology Robert H. Smith School of Business University of Maryland College Park, MD 20742

More information

Estimation of Unknown Comparisons in Incomplete AHP and It s Compensation

Estimation of Unknown Comparisons in Incomplete AHP and It s Compensation Estimation of Unknown Comparisons in Incomplete AHP and It s Compensation ISSN 0386-1678 Report of the Research Institute of Industrial Technology, Nihon University Number 77, 2005 Estimation of Unknown

More information

Analytic Hierarchy Process for Design Selection of Laminated Bamboo Chair

Analytic Hierarchy Process for Design Selection of Laminated Bamboo Chair Analytic Hierarchy Process for Design Selection of Laminated Bamboo Chair V. Laemlaksakul, S. Bangsarantrip Abstract This paper demonstrates the laminated bamboo chair design selection, the applicability

More information

Decision Making on Project Selection in High Education Sector Using the Analytic Hierarchy Process

Decision Making on Project Selection in High Education Sector Using the Analytic Hierarchy Process Decision Making on Project Selection in High Education Sector Using the Analytic Hierarchy Process Nina Begičević University of Zagreb, Faculty of Organization and Informatics, Pavlinska 2, Varaždin nina.begicevic@foi.hr

More information

Reproducing Calculations for the Analytical Hierarchy Process

Reproducing Calculations for the Analytical Hierarchy Process Reproducing Calculations for the Analytical Hierarchy Process Booz Allen Hamilton International Infrastructure Team Introduction Booz Allen supports clients in the application of the Analytical Hierarchy

More information

Vendor Evaluation and Rating Using Analytical Hierarchy Process

Vendor Evaluation and Rating Using Analytical Hierarchy Process Vendor Evaluation and Rating Using Analytical Hierarchy Process Kurian John, Vinod Yeldho Baby, Georgekutty S.Mangalathu Abstract -Vendor evaluation is a system for recording and ranking the performance

More information

Subcontractor Selection Using Analytic Hierarchy Process

Subcontractor Selection Using Analytic Hierarchy Process Volume 3 Number 3 2012 pp. 121-143 ISSN: 1309-2448 www.berjournal.com Subcontractor Selection Using Analytic Hierarchy Process Vesile Sinem Arıkan Kargı a Ahmet Öztürk b Abstract: Turkish textile firms

More information

Using Analytic Hierarchy Process (AHP) Method to Prioritise Human Resources in Substitution Problem

Using Analytic Hierarchy Process (AHP) Method to Prioritise Human Resources in Substitution Problem Using Analytic Hierarchy Process (AHP) Method to Raymond Ho-Leung TSOI Software Quality Institute Griffith University *Email:hltsoi@hotmail.com Abstract In general, software project development is often

More information

Research on supply chain risk evaluation based on the core enterprise-take the pharmaceutical industry for example

Research on supply chain risk evaluation based on the core enterprise-take the pharmaceutical industry for example Available online www.jocpr.com Journal of Chemical and Pharmaceutical Research, 2014, 6(6):593-598 Research Article ISSN : 0975-7384 CODEN(USA) : JCPRC5 Research on supply chain risk evaluation based on

More information

Talk:Analytic Hierarchy Process/Example Leader

Talk:Analytic Hierarchy Process/Example Leader Talk:Analytic Hierarchy Process/Example Leader 1 Talk:Analytic Hierarchy Process/Example Leader This is an example showing the use of the AHP in a practical decision situation. Click HERE to return to

More information

Performance Management for Inter-organization Information Systems Performance: Using the Balanced Scorecard and the Fuzzy Analytic Hierarchy Process

Performance Management for Inter-organization Information Systems Performance: Using the Balanced Scorecard and the Fuzzy Analytic Hierarchy Process Performance Management for Inter-organization Information Systems Performance: Using the Balanced Scorecard and the Fuzzy Analytic Hierarchy Process Y. H. Liang Department of Information Management, I-SHOU

More information

Adopting an Analytic Hierarchy Process to Select Internet Advertising Networks

Adopting an Analytic Hierarchy Process to Select Internet Advertising Networks Adopting an Analytic Hierarchy Process to Select Internet Advertising Networks Chin-Tasi Lin 1), Pi-Fang Hsu 2) 1) Yuanpei Institute of Science and Technology, Department of Information Management, Taiwan

More information

Quantifying energy security: An Analytic Hierarchy Process approach

Quantifying energy security: An Analytic Hierarchy Process approach ERG/200906 Quantifying energy security: An Analytic Hierarchy Process approach Larry Hughes, PhD Energy Research Group Department of Electrical and Computer Engineering Dalhousie University Halifax, Nova

More information

Early FP Estimation and the Analytic Hierarchy Process

Early FP Estimation and the Analytic Hierarchy Process Early FP Estimation and the Analytic Hierarchy Process Luca Santillo (luca.santillo@gmail.com) Abstract Several methods exist in order to estimate the size of a software project, in a phase when detailed

More information

Chapter 4 SUPPLY CHAIN PERFORMANCE MEASUREMENT USING ANALYTIC HIERARCHY PROCESS METHODOLOGY

Chapter 4 SUPPLY CHAIN PERFORMANCE MEASUREMENT USING ANALYTIC HIERARCHY PROCESS METHODOLOGY Chapter 4 SUPPLY CHAIN PERFORMANCE MEASUREMENT USING ANALYTIC HIERARCHY PROCESS METHODOLOGY This chapter highlights on supply chain performance measurement using one of the renowned modelling technique

More information

A Fuzzy AHP based Multi-criteria Decision-making Model to Select a Cloud Service

A Fuzzy AHP based Multi-criteria Decision-making Model to Select a Cloud Service Vol.8, No.3 (2014), pp.175-180 http://dx.doi.org/10.14257/ijsh.2014.8.3.16 A Fuzzy AHP based Multi-criteria Decision-making Model to Select a Cloud Service Hong-Kyu Kwon 1 and Kwang-Kyu Seo 2* 1 Department

More information

Framework of Measuring Key Performance Indicators for Decision Support in Higher Education Institution

Framework of Measuring Key Performance Indicators for Decision Support in Higher Education Institution Journal of Applied Sciences Research, 3(12): 1689-1695, 2007 2007, INSInet Publication Framework of Measuring Key Performance Indicators for Decision Support in Higher Education Institution Kadarsah Suryadi

More information

2008 Jordan Journal of Mechanical and Industrial Engineering. All rights reserved - Volume 2, Number 2 (ISSN 1995-6665) Goal

2008 Jordan Journal of Mechanical and Industrial Engineering. All rights reserved - Volume 2, Number 2 (ISSN 1995-6665) Goal JJMIE Jordan Journal of Mechanical and Industrial Engineering Volume 2, Number 2, Jun. 2008 ISSN 1995-6665 Pages 77-84 Evaluating and Benchmarking Non-Governmental Training Programs: An Analytic Hierarchy

More information

Prize: an R package for prioritization estimation based on analytic hierarchy process

Prize: an R package for prioritization estimation based on analytic hierarchy process Prize: an R package for prioritization estimation based on analytic hierarchy process Daryanaz Dargahi October 14, 2015 daryanazdargahi@gmail.com Contents 1 Licensing 2 2 Overview 2 3 Relative AHP 3 3.1

More information

Analytic Hierarchy Process for Effective Decision Making in Project Management. Glenn Hamamura Dr. Lawrence Rowland

Analytic Hierarchy Process for Effective Decision Making in Project Management. Glenn Hamamura Dr. Lawrence Rowland Analytic Hierarchy Process for Effective Decision Making in Project Management Glenn Hamamura Dr. Lawrence Rowland Decision Making We are all fundamentally decision makers. Everything we do consciously

More information

Journal of Chemical and Pharmaceutical Research, 2014, 6(3):34-39. Research Article. Analysis of results of CET 4 & CET 6 Based on AHP

Journal of Chemical and Pharmaceutical Research, 2014, 6(3):34-39. Research Article. Analysis of results of CET 4 & CET 6 Based on AHP Available online www.jocpr.com Journal of Chemical and Pharmaceutical Research, 2014, 6(3):34-39 Research Article ISSN : 0975-7384 CODEN(USA) : JCPRC5 Analysis of results of CET 4 & CET 6 Based on AHP

More information

International Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research)

International Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research) International Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research) International Journal of Engineering, Business and Enterprise

More information

1604 JOURNAL OF SOFTWARE, VOL. 9, NO. 6, JUNE 2014

1604 JOURNAL OF SOFTWARE, VOL. 9, NO. 6, JUNE 2014 1604 JOURNAL OF SOFTWARE, VOL. 9, NO. 6, JUNE 2014 Combining various trust factors for e-commerce platforms using Analytic Hierarchy Process Bo Li a, Yu Zhang b,, Haoxue Wang c, Haixia Xia d, Yanfei Liu

More information

ISAHP 2007, Viña Del Mar, Chile, August 3, 2007

ISAHP 2007, Viña Del Mar, Chile, August 3, 2007 ISAHP 2007, Viña Del Mar, Chile, August 3, 2007 Key Performance Indicators Measurement Model Based on Analytic Hierarchy Process and Trend-Comparative Dimension in Higher Education Institution Kadarsah

More information

Approaches to Qualitative Evaluation of the Software Quality Attributes: Overview

Approaches to Qualitative Evaluation of the Software Quality Attributes: Overview 4th International Conference on Software Methodologies, Tools and Techniques Approaches to Qualitative Evaluation of the Software Quality Attributes: Overview Presented by: Denis Kozlov Department of Computer

More information

ANALYTICAL HIERARCHY PROCESS AS A TOOL FOR SELECTING AND EVALUATING PROJECTS

ANALYTICAL HIERARCHY PROCESS AS A TOOL FOR SELECTING AND EVALUATING PROJECTS ISSN 1726-4529 Int j simul model 8 (2009) 1, 16-26 Original scientific paper ANALYTICAL HIERARCHY PROCESS AS A TOOL FOR SELECTING AND EVALUATING PROJECTS Palcic, I. * & Lalic, B. ** * University of Maribor,

More information

Applying the Analytic Hierarchy Process to Health Decision Making: Deriving Priority Weights

Applying the Analytic Hierarchy Process to Health Decision Making: Deriving Priority Weights Applying the to Health Decision Making: Deriving Priority Weights Tomás Aragón, MD, DrPH Principal Investigator, Cal PREPARE,. CIDER UC Berkeley School of Public Health Health Officer, City & County of

More information

INFORMATION SECURITY RISK ASSESSMENT: BAYESIAN PRIORITIZATION FOR AHP GROUP DECISION MAKING. Zeynep Filiz Eren-Dogu and Can Cengiz Celikoglu

INFORMATION SECURITY RISK ASSESSMENT: BAYESIAN PRIORITIZATION FOR AHP GROUP DECISION MAKING. Zeynep Filiz Eren-Dogu and Can Cengiz Celikoglu International Journal of Innovative Computing, Information and Control ICIC International c 2012 ISSN 1349-4198 Volume 8, Number 11, November 2012 pp. 8019 8032 INFORMATION SECURITY RISK ASSESSMENT: BAYESIAN

More information

Accomplishment of Critical Success Factor in Organization; Using Analytic Hierarchy Process

Accomplishment of Critical Success Factor in Organization; Using Analytic Hierarchy Process International Journal of Academic Research in Management (IJARM) Vol. 1, No. 1, November 2012, Page:1-9, ISSN: 2296-1747 Helvetic Editions LTD, Switzerland www.elvedit.com Accomplishment of Critical Success

More information

The Analytic Network Process

The Analytic Network Process The Analytic Network Process Thomas L. Saaty University of Pittsburgh saaty@katz.pitt.edu Abstract The Analytic Network Process (ANP) is a generalization of the Analytic Hierarchy Process (AHP). The basic

More information

Cellular Manufacturing Layout Design and Selection: A Case Study of Electronic Manufacturing Service Plant

Cellular Manufacturing Layout Design and Selection: A Case Study of Electronic Manufacturing Service Plant Cellular Manufacturing Layout Design and Selection: A Case Study of Electronic Manufacturing Service Plant Nittaya Ngampak and Busaba Phruksaphanrat Abstract In this research, cellular manufacturing layout

More information

ABC AHP Decision Tool Manual

ABC AHP Decision Tool Manual Project Number: TPF-5(221) ABC AHP Decision Tool Manual Final March, 2012 1 Introduction... 1 1.1 Software Overview... 1 1.2 Graphical User Interface... 1 1.3 Software Requirements... 2 1.4 How to Initiate

More information

An analytical hierarchy process and fuzzy inference system tsukamoto for production planning: a review and conceptual research

An analytical hierarchy process and fuzzy inference system tsukamoto for production planning: a review and conceptual research An analytical hierarchy process and fuzzy inference system tsukamoto for production planning: a review and conceptual research Abdul Talib Bon; Silvia Firda Utami Department of Production and Operations

More information

FINDING THE MOST PREFERRED ALLIANCE STRUCTURE BETWEEN BANKS AND INSURANCE COMPANIES

FINDING THE MOST PREFERRED ALLIANCE STRUCTURE BETWEEN BANKS AND INSURANCE COMPANIES Pekka Korhonen Raimo Voutilainen FINDING THE MOST PREFERRED ALLIANCE STRUCTURE BETWEEN BANKS AND INSURANCE COMPANIES HELSINKI SCHOOL OF ECONOMICS WORKING PAPERS W-368 Pekka Korhonen Raimo Voutilainen FINDING

More information

An experimental comparison of five prioritization methods - Investigating ease of use, accuracy and scalability

An experimental comparison of five prioritization methods - Investigating ease of use, accuracy and scalability Master Thesis Software Engineering Thesis no: MSE-2005-11 August 2005 An experimental comparison of five prioritization methods - Investigating ease of use, accuracy and scalability Viggo Ahl School of

More information

THE SELECTION OF BRIDGE MATERIALS UTILIZING THE ANALYTICAL HIERARCHY PROCESS

THE SELECTION OF BRIDGE MATERIALS UTILIZING THE ANALYTICAL HIERARCHY PROCESS THE SELECTION OF BRIDGE MATERIALS UTILIZING THE ANALYTICAL HIERARCHY PROCESS Robert L. Smith Assistant Professor/Extension Specialist, Virginia Tech Robert J. Bush Associate Professor, Virginia Tech and

More information

CHAPTER 3 IDENTIFICATION OF MOST PREFERRED KEY PERFORMANCE INDICATOR IN INDIAN CALL CENTRES

CHAPTER 3 IDENTIFICATION OF MOST PREFERRED KEY PERFORMANCE INDICATOR IN INDIAN CALL CENTRES 49 CHAPTER 3 IDENTIFICATION OF MOST PREFERRED KEY PERFORMANCE INDICATOR IN INDIAN CALL CENTRES 3.1 INTRODUCTION Key Performance Indicators (KPIs) is means for assessment of an organisations current position

More information

OBJECT ORIENTED SOFTWARE SYSTEM BASED ON AHP

OBJECT ORIENTED SOFTWARE SYSTEM BASED ON AHP OBJECT ORIENTED SOFTWARE SYSTEM BASED ON AHP Soumi Ghosh Department of Computer Science & Engineering Amity School of Engineering and Technology Amity University, Sec-125, NOIDA, (U.P.), INDIA noni.soumi@gmail.com

More information

A Controlled Experiment on Analytical Hierarchy Process and Cumulative Voting -

A Controlled Experiment on Analytical Hierarchy Process and Cumulative Voting - Master Thesis Software Engineering Thesis no: MSE-2007-17 June 2007 A Controlled Experiment on Analytical Hierarchy Process and Cumulative Voting - Investigating Time, Scalability, Accuracy, Ease of use

More information

Analytical Hierarchy Process (AHP)

Analytical Hierarchy Process (AHP) SIX SIG NTGE,Inc for Software evelopment nalytical Hierarchy Process (HP) Simple Excel HP Tool Expert Choice T Tool Overview 2003 Six Sigma dvantage, Inc ll rights reserved FSS: easure 44 FSS: easure 44

More information

DATA ANALYSIS II. Matrix Algorithms

DATA ANALYSIS II. Matrix Algorithms DATA ANALYSIS II Matrix Algorithms Similarity Matrix Given a dataset D = {x i }, i=1,..,n consisting of n points in R d, let A denote the n n symmetric similarity matrix between the points, given as where

More information

A Novel Method of Real Estate Development Project's Feasibility Research Based on SWOT Method and Analytic Hierarchy Process

A Novel Method of Real Estate Development Project's Feasibility Research Based on SWOT Method and Analytic Hierarchy Process A Novel Method of Real Estate Development Project's Feasibility Research Based on SWOT Method and Analytic Hierarchy Process Yu Bin Management College Shanghai University of Engineering Science (SUES)

More information

Applying the ANP Model for Selecting the Optimal Full-service Advertising Agency

Applying the ANP Model for Selecting the Optimal Full-service Advertising Agency International Journal of Operations Research International Journal of Operations Research Vol.8, No. 4, 4858 (2011) Applying the ANP Model for Selecting the Optimal Full-service Advertising Agency Pi-Fang

More information

Application of the Multi Criteria Decision Making Methods for Project Selection

Application of the Multi Criteria Decision Making Methods for Project Selection Universal Journal of Management 3(1): 15-20, 2015 DOI: 10.13189/ujm.2015.030103 http://www.hrpub.org Application of the Multi Criteria Decision Making Methods for Project Selection Prapawan Pangsri Faculty

More information

Development of Virtual Lab System through Application of Fuzzy Analytic Hierarchy Process

Development of Virtual Lab System through Application of Fuzzy Analytic Hierarchy Process Development of Virtual Lab System through Application of Fuzzy Analytic Hierarchy Process Chun Yong Chong, Sai Peck Lee, Teck Chaw Ling Faculty of Computer Science and Information Technology, University

More information

Klaus D. Goepel No 10 Changi Business Park Central 2 Hansapoint@CBP #06-01/08 Singapore 486030 E-mail: drklaus@bpmsg.com ABSTRACT

Klaus D. Goepel No 10 Changi Business Park Central 2 Hansapoint@CBP #06-01/08 Singapore 486030 E-mail: drklaus@bpmsg.com ABSTRACT IMPLEMENTING THE ANALYTIC HIERARCHY PROCESS AS A STANDARD METHOD FOR MULTI-CRITERIA DECISION MAKING IN CORPORATE ENTERPRISES A NEW AHP EXCEL TEMPLATE WITH MULTIPLE INPUTS Klaus D. Goepel No 0 Changi Business

More information

European Scientific Journal October 2015 edition vol.11, No.28 ISSN: 1857 7881 (Print) e - ISSN 1857-7431

European Scientific Journal October 2015 edition vol.11, No.28 ISSN: 1857 7881 (Print) e - ISSN 1857-7431 MICRO-FACTORS INFLUENCING SITE SELECTION FOR SMALL AND MEDIUM ENTERPRISES (SMES) IN SAUDI ARABIA: AL- HASSA AREA USING ANALYTICAL HIERARCHY PROCESS (AHP) ANALYSIS Hussain, Al-Salamin. MBA King Faisal University,

More information

RANKING REFACTORING PATTERNS USING THE ANALYTICAL HIERARCHY PROCESS

RANKING REFACTORING PATTERNS USING THE ANALYTICAL HIERARCHY PROCESS RANKING REFACTORING PATTERNS USING THE ANALYTICAL HIERARCHY PROCESS Eduardo Piveta 1, Ana Morra 2, Maelo Penta 1 João Araújo 2, Pedro Guerrro 3, R. Tom Price 1 1 Instituto de Informática, Universidade

More information

Content-Based Discovery of Twitter Influencers

Content-Based Discovery of Twitter Influencers Content-Based Discovery of Twitter Influencers Chiara Francalanci, Irma Metra Department of Electronics, Information and Bioengineering Polytechnic of Milan, Italy irma.metra@mail.polimi.it chiara.francalanci@polimi.it

More information

Comparison between Vertical Handoff Decision Algorithms for Heterogeneous Wireless Networks

Comparison between Vertical Handoff Decision Algorithms for Heterogeneous Wireless Networks Comparison between Vertical Handoff Decision Algorithms for Heterogeneous Wireless Networks Enrique Stevens-Navarro and Vincent W.S. Wong Department of Electrical and Computer Engineering The University

More information

Using Analytic Hierarchy Process Method in ERP system selection process

Using Analytic Hierarchy Process Method in ERP system selection process Using Analytic Hierarchy Process Method in ERP system selection process Rima Tamošiūnienė 1, Anna Marcinkevič 2 Abstract. IT and business alignment has become of the strategic importance and the enterprise

More information

Analytical hierarchy process for evaluation of general purpose lifters in the date palm service industry

Analytical hierarchy process for evaluation of general purpose lifters in the date palm service industry Journal of Agricultural Technology 2011 Vol. 7(4): 923-930 Available online http://www.ijat-aatsea.com ISSN 1686-9141 Analytical hierarchy process for evaluation of general purpose lifters in the date

More information

Contractor selection using the analytic network process

Contractor selection using the analytic network process Construction Management and Economics (December 2004) 22, 1021 1032 Contractor selection using the analytic network process EDDIE W. L. CHENG and HENG LI* Department of Building and Real Estate, The Hong

More information

[1] Diagonal factorization

[1] Diagonal factorization 8.03 LA.6: Diagonalization and Orthogonal Matrices [ Diagonal factorization [2 Solving systems of first order differential equations [3 Symmetric and Orthonormal Matrices [ Diagonal factorization Recall:

More information

Evaluation of educational open-source software using multicriteria decision analysis methods

Evaluation of educational open-source software using multicriteria decision analysis methods 1 Evaluation of educational open-source software using multicriteria decision analysis methods Georgia Paschalidou 1, Nikolaos Vesyropoulos 1, Vassilis Kostoglou 2, Emmanouil Stiakakis 1 and Christos K.

More information

College Algebra. Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1

College Algebra. Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1 College Algebra Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1 Course Description This course provides

More information

Elicitation and Prioritization of Software Requirements

Elicitation and Prioritization of Software Requirements Elicitation and Prioritization of Software Requirements Mohd. Sadiq Computer Engineering Section, University Polytechnic, Faculty of Engineering and Technology Jamia Millia Islamia (A Central University),

More information

A Development of the Effectiveness Evaluation Model for Agile Software Development using the Balanced Scorecard

A Development of the Effectiveness Evaluation Model for Agile Software Development using the Balanced Scorecard , March 13-15, 2013, Hong Kong A Development of the Effectiveness Evaluation Model for Agile Development using the Balanced Scorecard Sunisa Atiwithayaporn 1, Wanchai Rivepiboon 2 Abstract Most of standard

More information

Study of data structure and algorithm design teaching reform based on CDIO model

Study of data structure and algorithm design teaching reform based on CDIO model Study of data structure and algorithm design teaching reform based on CDIO model Li tongyan, Fu lin (Chengdu University of Information Technology, 610225, China) ABSTRACT CDIO is a new and innovative engineering

More information

A Quality Based Method to Analyze Software Architectures

A Quality Based Method to Analyze Software Architectures www.ijcsi.org A Quality Based Method to Analyze Software Architectures Farzaneh Hoseini Jabali, Sayed Mehran Sharafi and Kamran Zamanifar3 Computer Department, Islamic Azad University, Naafabad Branch,

More information

Maintainability Estimation of Component Based Software Development Using Fuzzy AHP

Maintainability Estimation of Component Based Software Development Using Fuzzy AHP International journal of Emerging Trends in Science and Technology Maintainability Estimation of Component Based Software Development Using Fuzzy AHP Author Sengar Dipti School of Computing Science, Galgotias

More information

GIS-based Multi-Criteria Decision Analysis (in Natural Resource Management)

GIS-based Multi-Criteria Decision Analysis (in Natural Resource Management) GIS-based Multi-Criteria Decision Analysis (in Natural Resource Management) Ronald C. Estoque (Student ID Number: 201030243) D1 Division of Spatial Information Science 2011 Learning objective The aim of

More information

A Tool Selection Framework for Cross Platform Mobile App Development

A Tool Selection Framework for Cross Platform Mobile App Development A Tool Selection Framework for Cross Platform Mobile App Development Felix Appiah J. B. Hayfron-Acquah Joseph K. Panford Frimpong Twum PG Student, Department Of Computer Science PhD Department Of Computer

More information

A strategic decision framework for green supply chain management

A strategic decision framework for green supply chain management Journal of Cleaner Production 11 (2003) 397 409 www.cleanerproduction.net A strategic decision framework for green supply chain management Joseph Sarkis Clark University, Graduate School of Management,

More information

15.062 Data Mining: Algorithms and Applications Matrix Math Review

15.062 Data Mining: Algorithms and Applications Matrix Math Review .6 Data Mining: Algorithms and Applications Matrix Math Review The purpose of this document is to give a brief review of selected linear algebra concepts that will be useful for the course and to develop

More information

The Analytic Hierarchy Process and SDSS

The Analytic Hierarchy Process and SDSS The Analytic Hierarchy Process and SDSS RNR/GEOG 420-520 Preview Week 12 Spatial Decision Support Systems (SDSS) and the Analytic Hierarchy Process (AHP) Week 13 Designing Geodatabase Models Week 14 GeoVisualization

More information

AGGREGATING PAIR-WISE COMPARISONS GIVEN IN SCALES OF DIFFERENT DETAIL DEGREE

AGGREGATING PAIR-WISE COMPARISONS GIVEN IN SCALES OF DIFFERENT DETAIL DEGREE of Different Detail Degree / 2014, AGGREGATING PAIR-WISE COMPARISONS GIVEN IN SCALES OF DIFFERENT DETAIL DEGREE V.V.Tsyganok E-mail: vitaliy.tsyganok@gmail.com O.V.Andriichuk E-mail: andreychuck@ukr.net

More information

Using the Analytic Hierarchy Process in Engineering Education*

Using the Analytic Hierarchy Process in Engineering Education* Int. J. Engng Ed. Vol. 14, No. 3, p. 191±196, 1998 0949-149X/91 $3.00+0.00 Printed in Great Britain. # 1998 TEMPUS Publications. Using the Analytic Hierarchy Process in Engineering Education* P. R. DRAKE

More information

INVOLVING STAKEHOLDERS IN THE SELECTION OF A PROJECT AND PORTFOLIO MANAGEMENT TOOL

INVOLVING STAKEHOLDERS IN THE SELECTION OF A PROJECT AND PORTFOLIO MANAGEMENT TOOL INVOLVING STAKEHOLDERS IN THE SELECTION OF A PROJECT AND PORTFOLIO MANAGEMENT TOOL Vassilis C. Gerogiannis Department of Project Management, Technological Research Center of Thessaly, Technological Education

More information

Evaluating Cloud Services Using DEA, AHP and TOPSIS model Carried out at the

Evaluating Cloud Services Using DEA, AHP and TOPSIS model Carried out at the A Summer Internship Project Report On Evaluating Cloud Services Using DEA, AHP and TOPSIS model Carried out at the Institute of Development and Research in Banking Technology, Hyderabad Established by

More information

Use Analytic Hierarchy Process For Project Selection

Use Analytic Hierarchy Process For Project Selection P R OJECT SELECTON Use Analytic Hierarchy Process For Project Selection THE METHOD CAN ASSST STRATEGY FOCUSED ORGANZATONS N PROPERLY MANAGNG BUSNESS PROCESS MPROVEMENT PROGRAMS. By John David Kendrick

More information

Selection of Mobile Network Operator Using Analytic Hierarchy Process (AHP) Nasruddin Hassan, Norfaieqah Ahmad and Wan Malissa Wan Aminuddin

Selection of Mobile Network Operator Using Analytic Hierarchy Process (AHP) Nasruddin Hassan, Norfaieqah Ahmad and Wan Malissa Wan Aminuddin Advances in Natural and Applied Sciences, 7(1): 1-5, 2013 ISSN 1995-0772 1 This is a refereed journal and all articles are professionally screened and reviewed ORIGINAL ARTICLE Selection of Mobile Network

More information

Chapter 6. Orthogonality

Chapter 6. Orthogonality 6.3 Orthogonal Matrices 1 Chapter 6. Orthogonality 6.3 Orthogonal Matrices Definition 6.4. An n n matrix A is orthogonal if A T A = I. Note. We will see that the columns of an orthogonal matrix must be

More information

Question 2: How do you solve a matrix equation using the matrix inverse?

Question 2: How do you solve a matrix equation using the matrix inverse? Question : How do you solve a matrix equation using the matrix inverse? In the previous question, we wrote systems of equations as a matrix equation AX B. In this format, the matrix A contains the coefficients

More information

Similarity and Diagonalization. Similar Matrices

Similarity and Diagonalization. Similar Matrices MATH022 Linear Algebra Brief lecture notes 48 Similarity and Diagonalization Similar Matrices Let A and B be n n matrices. We say that A is similar to B if there is an invertible n n matrix P such that

More information

Corresponding Author email: s.esfandi.7@gmail.com

Corresponding Author email: s.esfandi.7@gmail.com International Research Journal of Applied and Basic Sciences 2015 Available online at www.irjabs.com ISSN 2251-838X / Vol, 9 (4): 542-546 Science Explorer Publications Review and Prioritization of the

More information

10.3 POWER METHOD FOR APPROXIMATING EIGENVALUES

10.3 POWER METHOD FOR APPROXIMATING EIGENVALUES 58 CHAPTER NUMERICAL METHODS. POWER METHOD FOR APPROXIMATING EIGENVALUES In Chapter 7 you saw that the eigenvalues of an n n matrix A are obtained by solving its characteristic equation n c nn c nn...

More information

Standard Preference Table

Standard Preference Table What is AHP? According to Operations Management 4th Edition by Russell and Taylor III it is a quantitative method for ranking decision alternatives and selection the one given multiple criteria. AHP is

More information

Aircraft Selection Using Analytic Network Process: A Case for Turkish Airlines

Aircraft Selection Using Analytic Network Process: A Case for Turkish Airlines Proceedings of the World Congress on Engineering 211 Vol II WCE 211, July 6-8, 211, London, U.K. Aircraft Selection Using Analytic Network Process: A Case for Turkish Airlines Yavuz Ozdemir, Huseyin Basligil,

More information

Corporate Social Responsibility Program Toward Sustainability Crude Palm Oil Industry Using Analytic Hierarchy Process

Corporate Social Responsibility Program Toward Sustainability Crude Palm Oil Industry Using Analytic Hierarchy Process Corporate Social Responsibility Program Toward Sustainability Crude Palm Oil Industry Using Analytic Hierarchy Process Fuad Halimoen 1, Alvi Syahrin 2, Herman Mawengkang 3 1 Graduate School of Management,

More information

Requirements on document management systems recorded using the Analytic Hierarchy Process and transferred into a Quality Function Deployment

Requirements on document management systems recorded using the Analytic Hierarchy Process and transferred into a Quality Function Deployment Requirements on document management systems recorded using the Analytic Hierarchy Process and transferred into a Quality Function Deployment H.-A. Crostack; I. Hackenbroich; R. Refflinghaus Chair of Quality

More information

Characterization and Modeling of Packet Loss of a VoIP Communication

Characterization and Modeling of Packet Loss of a VoIP Communication Characterization and Modeling of Packet Loss of a VoIP Communication L. Estrada, D. Torres, H. Toral Abstract In this work, a characterization and modeling of packet loss of a Voice over Internet Protocol

More information

Evaluating Simulation Software Alternatives through ANP

Evaluating Simulation Software Alternatives through ANP Proceedings of the 2011 International Conference on Industrial Engineering and Operations Management Kuala Lumpur, Malaysia, January 22 24, 2011 Evaluating Simulation Software Alternatives through ANP

More information