MULTIPLE-OBJECTIVE DECISION MAKING TECHNIQUE Analytical Hierarchy Process

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "MULTIPLE-OBJECTIVE DECISION MAKING TECHNIQUE Analytical Hierarchy Process"

Transcription

1 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 for representing the elements of any problem, hierarchically. It organizes the basic rationality by breaking down a problem into its smaller and smaller constituent parts and then guides decision makers through a series of pairwise comparison judgments to express the relative strength or intensity of impact of the elements in the hierarchy. These judgments are then translated to numbers. The steps of creating an AHP is summarized as follows:. Define the problem and determine what you want to know.. Structure the hierarchy from the top (the objectives from a managerial viewpoint) through the intermediate levels (criteria on which subsequent levels depend) to the lowest level (which usually is a list of the alternatives).. Construct a set of pairwise comparison matrices for each of the lower levels - one matrix for each element in the level immediately above. An element in the higher level is said to be a governing element for those in the lower level since it contributes to it or affects it. In a complete simple hierarchy, every element in the lower level affects every element in the upper level. The elements in the lower level are then compared to each other based on their effect on the governing element above. This yields a square matrix of judgments. The pairwise comparisons are done in terms of which element dominates the other. These judgments are then expressed as integers (see table below for judgment values). If element A dominates element B, then the whole number (integer) is entered in row A, column B and the reciprocal (fraction) is entered in row B, column A. Of course, if element B dominates element A then the reverse occurs. The whole number is then placed in the B, A position with the reciprocal automatically being assigned to the A, B position. If A and B are judged to be equal, a one is assigned to both positions.. There are n (n-)/ judgments required to develop each matrix in step (remember, reciprocals are automatically assigned in each pairwise comparison). 5. Having made all the pairwise comparisons and entered the data, the consistency is determined using the eigenvalue. The consistency index is tested then using the departure of from ncompared with corresponding average values for random entries yielding the consistency ratio C.R. (See Random Indices Table below). 6. Steps, and 5 are performed for all levels and clusters in the hierarchy. 7. Hierarchical synthesis is now used to weight the eigenvectors by the weights of the criteria and the sum is taken over all weighted eigenvector entries corresponding to those in the next lower level of the hierarchy. 8. The consistency of the entire hierarchy is found by multiplying each consistency index by the priority of the corresponding criterion and adding them together. The result is then divided by the same type of expression using the random consistency index corresponding to the dimensions of each matrix weighted by the priorities as before. Note first the consistency ratio (C.R.) should be about 0%, or less to be acceptable. If not, the quality of the judgments should be improved, perhaps by revising the manner in which questions are asked in making the pairwise comparisons. If this should fail to improve consistency then it is likely that the max AHP Page-

2 problem should be more accurately structured; that is, grouping similar elements under more meaningful criteria. A return to step would be required, although only the problematic parts of the hierarchy may need revision. (The reader can calculate the consistency of the hierarchy of the house buying example and show its value to be.08 which is acceptable.) Scale of Relative Importance Intensity of Definition Explanation relative importance Equal importance Two activities contribute Moderate importance of one over another equally to the objectives Experience and judgment slightly favor one activity over another 5 Essential or strong importance Experience and judgment strongly favor one activity over another 7 Demonstrated importance An activity is strongly favored and its dominance is demonstrated in practice 9 Extreme importance The evidence favoring one activity over another is of the highest possible order of affirmation.,, 6, 8 Intermediate value between the two adjacent judgments Reciprocals of above non-zero numbers If an activity has one of the above numbers (e.g., ) compared with a second activity, then the second activity has the reciprocal value (i.e., /) when compared to the first. When compromise is needed. Random Indices (R.I.) for Consistency Check n R.I Reference Satty, Thomas L. & Kearns, Kevin P. (985), Analytical Planning: The Organization of Systems, Pergamon Press AHP Page-

3 Application Case of AHP: Jane is about to graduate from college and is trying to determine which job offer to accept. She plans to choose between three offers by determining how well each offer meets the following criteria (objectives): High starting salary of life in city where job is located of work of job to family Assumptions: Jane has hard time in prioritizing those criteria. In other words, she needs to find one way to decide the weights for those criteria. AHP provides such a function.. Determine the problem: What job offer will give Jane possibly highest satisfaction?. Structure the hierarchy by putting the top objective (satisfaction with job), criteria, and alternatives as follows. Satisfaction with a job Starting salary Life to family. Construct a pairwise comparison matrix for the criteria level as follows. And then compare those criteria to each other with respect to the top objective. Take the first row as an example, we may ask: With respect to Satisfaction with a job, comparing Starting Salary to Life, which is more important than the other? How much more important it is than the other? Here, the author assumes that Starting Salary is strongly more important than Life. That is why 5 is entered into the Salary row and column. Compared to, Salary is just a little bit more important. That is why is entered into Salary row and column. Satisfaction with a job Salary Salary / 5 / / 5 / / / (six judgments) AHP Page-

4 . After pairwise comparisons, we need to determine the weights of the four criteria. First, normalizing the entries by adding entries in each column and then divide each entry in the column by the sum of the column. For example, the sum of the entries in the Salary column is.95 (=+0.++) and each entry in the Salary column is divided by.95. The same procedure is applied to other columns. A normal = Salary Salary Second, estimate weights by calculating averages of entries in each row. Thus, the weight of Salary is the weight of is the weight of is the weight of is w w w w Using the same steps of and to determine the score of each alternative on each criterion. Take the first criterion Salary as an example. One pairwise matrix is constructed as follows: A SALARY / / / Using the procedure in to normalize the matrix and calculate the score of each job on the Salary criterion. SALARY A (Normalized pairwise matrix) Calculate the average of entries in row to obtain the vector of scores for the three jobs on Salary. AHP Page-

5 S Repeating the same procedure to calculate scores of these three jobs on criteria Life,, and. A / / / S A Job 7 A / 7 / / S A Job 7 A / / 7 / S Determining the overall weights by combining the relative importance matrix with scores matrices. Starting Life Overall Salary Relative Importance The computation for obtaining the overall weights is as follows: Thus, according to the overall score, the AHP suggests that Jane should take job B, which has the highest score among three jobs. AHP Page-5

6 8. Check for consistency. Calculating consistency index (C.I) by multiplying the comparison (judgment) matrix by the vector of priority as follows: /5 Aw / / 5 / / / And then calculate the largest eigenvalue of the judgment matrix A. max = max n.077 C. I n (largest eigenvalue of A) and then compare the value of C.I. to the value of random index (R.I). If the ratio of C.I. to R.I. is less than 0%, then we can say the judgment process is relatively consistent and the matrix is acceptable. Otherwise, the decision maker may need to re-examine the judgment process and re-compare criteria or alternatives. The consistency ratio (C.R.) is computed as follows: C.R. = C.I. / R.I. = 0.059/0.9 = =.7% < 0% Therefore, the judgment process is relatively consistent and the matrix is acceptable. The software (Web-HIPRE) is available at or (note that you may need to update java component if the software is not working properly) AHP Page-6

The Analytic Hierarchy Process. Danny Hahn

The Analytic Hierarchy Process. Danny Hahn The Analytic Hierarchy Process Danny Hahn The Analytic Hierarchy Process (AHP) A Decision Support Tool developed in the 1970s by Thomas L. Saaty, an American mathematician, currently University Chair,

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

A new Environmental Performance Index using analytic hierarchy process: A case of ASEAN countries

A new Environmental Performance Index using analytic hierarchy process: A case of ASEAN countries Article A new Environmental Performance Index using analytic hierarchy process: A case of ASEAN countries Wan Khadijah Wan Ismail, Lazim Abdullah Department of Mathematics, Faculty of Science and Technology,

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

IDENTIFYING AND PRIORITIZING THE FINANCING METHODS (A HYBRID APPROACH DELPHI - ANP )

IDENTIFYING AND PRIORITIZING THE FINANCING METHODS (A HYBRID APPROACH DELPHI - ANP ) IDENTIFYING AND PRIORITIZING THE FINANCING METHODS (A HYBRID APPROACH DELPHI - ANP ) Pezhman Arzhang 1, Naser Hamidi 2 1 MSc.Business Administration, Department of Business Management, Qazvin Branch, Islamic

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

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

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

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

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

ASSESSMENT OF FACTORS AFFECTING EMPOWERMENT OF HUMAN RESOURCES USING ANALYTICAL HIERARCHY PROCESS

ASSESSMENT OF FACTORS AFFECTING EMPOWERMENT OF HUMAN RESOURCES USING ANALYTICAL HIERARCHY PROCESS ASSESSMENT OF FACTORS AFFECTING EMPOWERMENT OF HUMAN RESOURCES USING ANALYTICAL HIERARCHY PROCESS * Hamid Reza Moosavi and Maryam Moradi 1 1 College of Human Science, Islamic Azad University Neyshabur

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

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

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

The Application of ANP Models in the Web-Based Course Development Quality Evaluation of Landscape Design Course

The Application of ANP Models in the Web-Based Course Development Quality Evaluation of Landscape Design Course , pp.291-298 http://dx.doi.org/10.14257/ijmue.2015.10.9.30 The Application of ANP Models in the Web-Based Course Development Quality Evaluation of Landscape Design Course Xiaoyu Chen 1 and Lifang Qiao

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

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

NEW VERSION OF DECISION SUPPORT SYSTEM FOR EVALUATING TAKEOVER BIDS IN PRIVATIZATION OF THE PUBLIC ENTERPRISES AND SERVICES

NEW VERSION OF DECISION SUPPORT SYSTEM FOR EVALUATING TAKEOVER BIDS IN PRIVATIZATION OF THE PUBLIC ENTERPRISES AND SERVICES NEW VERSION OF DECISION SUPPORT SYSTEM FOR EVALUATING TAKEOVER BIDS IN PRIVATIZATION OF THE PUBLIC ENTERPRISES AND SERVICES Silvija Vlah Kristina Soric Visnja Vojvodic Rosenzweig Department of Mathematics

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

Applications of Analytic Network Process in Entertainment 1

Applications of Analytic Network Process in Entertainment 1 Iranian Journal of Operations Research Vol. 1, No. 2, 2009, pp.41-55 Applications of Analytic Network Process in Entertainment 1 Thomas L. Saaty 2 In this paper we present a real application of ANP in

More information

Eigenvalues, Eigenvectors, Matrix Factoring, and Principal Components

Eigenvalues, Eigenvectors, Matrix Factoring, and Principal Components Eigenvalues, Eigenvectors, Matrix Factoring, and Principal Components The eigenvalues and eigenvectors of a square matrix play a key role in some important operations in statistics. In particular, they

More information

Data Mining Cluster Analysis: Basic Concepts and Algorithms. Lecture Notes for Chapter 8. Introduction to Data Mining

Data Mining Cluster Analysis: Basic Concepts and Algorithms. Lecture Notes for Chapter 8. Introduction to Data Mining Data Mining Cluster Analysis: Basic Concepts and Algorithms Lecture Notes for Chapter 8 Introduction to Data Mining by Tan, Steinbach, Kumar Tan,Steinbach, Kumar Introduction to Data Mining 4/8/2004 Hierarchical

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

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

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

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

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

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

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

Chinese Automobile Brand International Marketing Target Market Selection Model Based on AHP

Chinese Automobile Brand International Marketing Target Market Selection Model Based on AHP Chinese Automobile Brand International Marketing Target Market Selection Model Based on AHP Xiaoming-Tao School of Management Shanghai University of Engineering Science Shanghai, China Yubin-Qian Shanghai

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

Comparative Analysis of FAHP and FTOPSIS Method for Evaluation of Different Domains

Comparative Analysis of FAHP and FTOPSIS Method for Evaluation of Different Domains International Journal of Research Studies in Computer Science and Engineering (IJRSCSE) August 2015, PP 58-62 ISSN 2349-4840 (Print) & ISSN 2349-4859 (Online) www.arcjournals.org Comparative Analysis of

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 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

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

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

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

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

CHOOSING A COLLEGE. Teacher s Guide Getting Started. Nathan N. Alexander Charlotte, NC

CHOOSING A COLLEGE. Teacher s Guide Getting Started. Nathan N. Alexander Charlotte, NC Teacher s Guide Getting Started Nathan N. Alexander Charlotte, NC Purpose In this two-day lesson, students determine their best-matched college. They use decision-making strategies based on their preferences

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

Introduction to Matrix Algebra

Introduction to Matrix Algebra Psychology 7291: Multivariate Statistics (Carey) 8/27/98 Matrix Algebra - 1 Introduction to Matrix Algebra Definitions: A matrix is a collection of numbers ordered by rows and columns. It is customary

More information

Review Jeopardy. Blue vs. Orange. Review Jeopardy

Review Jeopardy. Blue vs. Orange. Review Jeopardy Review Jeopardy Blue vs. Orange Review Jeopardy Jeopardy Round Lectures 0-3 Jeopardy Round $200 How could I measure how far apart (i.e. how different) two observations, y 1 and y 2, are from each other?

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

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

Similar matrices and Jordan form

Similar matrices and Jordan form Similar matrices and Jordan form We ve nearly covered the entire heart of linear algebra once we ve finished singular value decompositions we ll have seen all the most central topics. A T A is positive

More information

Uncertainties in the Analytic Hierarchy Process

Uncertainties in the Analytic Hierarchy Process Uncertainties in the Analytic Hierarchy Process Lewis Warren Command and Control Division Information Sciences Laboratory DSTO-TN-0597 ABSTRACT When choosing a decision analysis technique to model a particular

More information

Factor Analysis. Advanced Financial Accounting II Åbo Akademi School of Business

Factor Analysis. Advanced Financial Accounting II Åbo Akademi School of Business Factor Analysis Advanced Financial Accounting II Åbo Akademi School of Business Factor analysis A statistical method used to describe variability among observed variables in terms of fewer unobserved variables

More information

by the matrix A results in a vector which is a reflection of the given

by the matrix A results in a vector which is a reflection of the given Eigenvalues & Eigenvectors Example Suppose Then So, geometrically, multiplying a vector in by the matrix A results in a vector which is a reflection of the given vector about the y-axis We observe that

More information

Appraisal of Trust Degree among Innovation Team Members Based on Analytic Hierarchy Process

Appraisal of Trust Degree among Innovation Team Members Based on Analytic Hierarchy Process 1094 Appraisal of Trust Degree among Innovation Team Members Based on Analytic Hierarchy Process Gao Xia Department of Business Administration, ZhengZhou Institute of Aeronautical Industry Management,

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

Here are some examples of combining elements and the operations used:

Here are some examples of combining elements and the operations used: MATRIX OPERATIONS Summary of article: What is an operation? Addition of two matrices. Multiplication of a Matrix by a scalar. Subtraction of two matrices: two ways to do it. Combinations of Addition, Subtraction,

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

Analytic hierarchy process to assess and optimize distribution network

Analytic hierarchy process to assess and optimize distribution network Available online at www.sciencedirect.com Applied Mathematics and Computation 202 (2008) 256 265 www.elsevier.com/locate/amc Analytic hierarchy process to assess and optimize distribution network Mithun

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

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

MATH 423 Linear Algebra II Lecture 38: Generalized eigenvectors. Jordan canonical form (continued).

MATH 423 Linear Algebra II Lecture 38: Generalized eigenvectors. Jordan canonical form (continued). MATH 423 Linear Algebra II Lecture 38: Generalized eigenvectors Jordan canonical form (continued) Jordan canonical form A Jordan block is a square matrix of the form λ 1 0 0 0 0 λ 1 0 0 0 0 λ 0 0 J = 0

More information

Presentation 3: Eigenvalues and Eigenvectors of a Matrix

Presentation 3: Eigenvalues and Eigenvectors of a Matrix Colleen Kirksey, Beth Van Schoyck, Dennis Bowers MATH 280: Problem Solving November 18, 2011 Presentation 3: Eigenvalues and Eigenvectors of a Matrix Order of Presentation: 1. Definitions of Eigenvalues

More information

ISOMORPHISM BETWEEN AHP AND DOUBLE ENTRY BOOK KEEPING SYSTEM

ISOMORPHISM BETWEEN AHP AND DOUBLE ENTRY BOOK KEEPING SYSTEM ISOMORPHISM BETWEEN AHP AND DOUBLE ENTRY BOOK KEEPING SYSTEM Masaaki Shinohara* Nihon University Izumi-chou, Narashino Chiba 275-8575, Japan shinohara.masaaki@nihon-u.ac.jp Keikichi Osawa Nihon University

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

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

Math 115A HW4 Solutions University of California, Los Angeles. 5 2i 6 + 4i. (5 2i)7i (6 + 4i)( 3 + i) = 35i + 14 ( 22 6i) = 36 + 41i.

Math 115A HW4 Solutions University of California, Los Angeles. 5 2i 6 + 4i. (5 2i)7i (6 + 4i)( 3 + i) = 35i + 14 ( 22 6i) = 36 + 41i. Math 5A HW4 Solutions September 5, 202 University of California, Los Angeles Problem 4..3b Calculate the determinant, 5 2i 6 + 4i 3 + i 7i Solution: The textbook s instructions give us, (5 2i)7i (6 + 4i)(

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

Resource Allocation in Project Scheduling Application of Fuzzy AHP

Resource Allocation in Project Scheduling Application of Fuzzy AHP Resource Allocation in Project Scheduling Application of Fuzzy AHP CH. Lakshmi Tulasi A. Ramakrishna Rao S.V.U.College of Engineering (chavalimadhavi@yahoo.co.in) (arrsvume@gmail.com) Several approaches

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