BUSINESS PERFORMANCE MANAGEMENT Analytical Hierarchy Process AHP A

BUSINESS PERFORMANCE MANAGEMENT Analytical Hierarchy Process (AHP): A Multi-Objective Decision Making Technique Jason C. H. Chen, Ph. D. Professor of MIS School of Business Gonzaga University Spokane, WA 99258 chen@gonzaga. edu Dr. Chen – Business Intelligence AHP -

Analytical Hierarchy Process • In many situations one may not be able to assign weights to the different decision factors. Therefore one must rely on a technique that will allow the estimation of the weights. • What is a solution? • One such process, The Analytical Hierarchy Process (AHP), involves pairwise comparisons between the various factors. Dr. Chen – Business Intelligence AHP - 2

Analytical Hierarchy Process (cont. ) • The process is started by the decision maker creating the value tree associated with the problem. • Then proceed by carrying out pairwise comparisons, both between – Alternatives on each factor, and – Factors at a given node. Dr. Chen – Business Intelligence AHP - 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 Quality of life in city where job is located Interest of work Nearness of job to family Dr. Chen – Business Intelligence AHP - 4

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. Dr. Chen – Business Intelligence AHP - 5

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. Dr. Chen – Business Intelligence AHP - 6

Structure of the Problem Satisfaction with a Job criteria; n=4 Starting Salary Job A Dr. Chen – Business Intelligence Life Quality Job B Interest Nearness to Family Job C AHP - 7

Structure of the Problem Satisfaction with a Job Starting Salary Job A Life Quality Job B Web site: http: //hipre. aalto. fi/ Dr. Chen – Business Intelligence Interest Nearness to Family Job C AHP - 8

The Principle of the AHP … • The principle of the AHP relies on the pairwise comparison. This comparison is carried out using a scale from 1 to 9 as follows: – – – – – 1 Equally preferred 2 Equally to Moderately preferred 3 Moderately preferred 4 Moderately to Strongly preferred 5 Strongly preferred 6 Strongly to Very Strongly preferred 7 Very Strongly preferred 8 Very to Extremely Strongly preferred 9 Extremely preferred Dr. Chen – Business Intelligence AHP - 9

A pairwise comparison matrix for the criteria level Satisfaction with a Job § We assume that “Starting Salary” is strongly more important than “Life Quality”. That is why 5 is entered into the Salary row and Quality column. § Compared to Interest, Salary is just a little bit more important. That is why 2 is entered into Salary row and Quality column. § Similarly, Salary is moderately to strongly preferred than “Nearness”. That is why 4 is entered into the Salary row and Nearness column. Dr. Chen – Business Intelligence AHP - 10

A pairwise comparison matrix for the criteria level Satisfaction with a Job Since n=4, there are 6 [n*(n-1)/2] judgments required to develop each matrix. Why? Dr. Chen – Business Intelligence AHP - 11

Using the same steps of 3 and 4 (see handout) 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 (details see step 4 on the handout): In terms of criterion of “Salary”, Job A is moderately important (“ 2”) than Job B. However, Job A is essentially more important (“ 4”) than Job C. Dr. Chen – Business Intelligence AHP - 12

The next two pairwise matrices (for “Life Quality” and “Interest”) are as follows (see step#6 on the handout): Dr. Chen – Business Intelligence AHP - 13

The last pairwise matrix (for “Nearness to family”) is listed below: Dr. Chen – Business Intelligence AHP - 14

How to verify that the data entered in the comparison matrices is acceptable Consistency Index (C. I) is computed as follows (see handout, p. 6) We 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 10%, 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. 0159/0. 9 = 0. 0176666 = 1. 7% < 10% Random Indices (R. I. ) for Consistency Check n R. I. 2 0 3. 58 Dr. Chen – Business Intelligence 4. 90 5 1. 12 6 1. 24 7 1. 32 8 1. 41 9 1. 45 10 1. 51 AHP - 15

Satisfaction with a Job Dr. Chen – Business Intelligence AHP - 16

We will open an existing model http: //hipre. aalto. fi File name: Mbus 626_chen. jmd mbus 673. jmd Dr. Chen – Business Intelligence AHP - 17

JAVA update (might be needed) The site list to add should be: http: //hipre. aalto. fi/ Dr. Chen – Business Intelligence AHP - 18

Dr. Chen – Business Intelligence AHP - 19

Scroll down Dr. Chen – Business Intelligence AHP - 20

Display the “weights” entered in the “Goal” or “Criteria” 1) Double click or 2) Select an “Element” then click Priorities then AHP Double click double click Dr. Chen – Business Intelligence AHP - 21

(p. 4 of Handout) Dr. Chen – Business Intelligence AHP - 22

Result from double clicking “salary” Dr. Chen – Business Intelligence AHP - 23

Result from double clicking “life quality” Dr. Chen – Business Intelligence AHP - 24

Result from double clicking “interest” Dr. Chen – Business Intelligence AHP - 25

Result from double clicking “nearness to family” Dr. Chen – Business Intelligence AHP - 26

Perform Analysis click Dr. Chen – Business Intelligence AHP - 27

Perform Analysis Dr. Chen – Business Intelligence AHP - 28

Result from “Analysis of Composite Priorities … “ click According to the BAR chart, AHP suggests that Jane should take Job B. Why? Dr. Chen – Business Intelligence AHP - 29

Result from “Analysis of Composite Priorities … “ – with Values According to the “Values”, AHP suggests that Jane should take Job B (you need to “Add total” , see the next slide) Dr. Chen – Business Intelligence AHP - 30

Result as Text Dr. Chen – Business Intelligence Value Tree 0 satisfaction with a job 1 salary 0. 512 2 job A 0. 571 2 job B 0. 286 2 job C 0. 143 1 life quality 0. 098 2 job A 0. 163 2 job B 0. 540 2 job C 0. 297 1 interest 0. 244 2 job A 0. 088 2 job B 0. 669 2 job C 0. 243 1 nearness to family 0. 146 2 job A 0. 082 2 job B 0. 315 2 job C 0. 603 Composite Priorities job A job B job C salary 0. 293 0. 146 0. 073 life quali 0. 016 0. 053 0. 029 interest 0. 021 0. 163 0. 059 nearness t 0. 012 0. 046 0. 088 Overall 0. 342 0. 408 0. 249 step 7 (p. 5) AHP - 31

Your Turn … How to create an AHP model for “a Job Selection” Project Dr. Chen – Business Intelligence AHP - 32

We will open an existing model http: //hipre. aalto. fi File name: Mbus 626_chen. jmd mbus 673. jmd Dr. Chen – Business Intelligence AHP - 33

JAVA update (might be needed) The site list to add should be: http: //hipre. aalto. fi/ Dr. Chen – Business Intelligence AHP - 34

Step 1: Click on “Bring Web-HIPRE to Front” Dr. Chen – Business Intelligence AHP - 35

Step 2: Click on “Run” to skip Java Update (if you already added the AHP software site to the Java list”) Step 3: “Start Web. HIPRE” link is available. Click on the box Dr. Chen – Business Intelligence AHP - 36

You will learn how to create an AHP model for “a Job Selection” listed below Dr. Chen – Business Intelligence AHP - 37

Double click a node (element) will appear Enter a name Dr. Chen – Business Intelligence Criteria level Goal level AHP - 38

Edit the element’s Name (only if needed) Select this Dr. Chen – Business Intelligence AHP - 39

Steps of creating “Links” The “Goal” and “Alternative” displayed on their “Level” respectively 2. Right click 1. Left click Dr. Chen – Business Intelligence Complete the remaining links AHP - 40

Steps of creating “Links” (cont. ) Labels are changed 1. Left click 2. Right click Complete the remaining links between “Criteria” and Alternatives” Dr. Chen – Business Intelligence AHP - 41

Steps of creating “Links” – Final Model (cont. ) Labels are changed Dr. Chen – Business Intelligence AHP - 42

Be sure that to save the model now (and periodically). Enter “filename” Dr. Chen – Business Intelligence AHP - 43

Enter “filename” A “filename” is saved Dr. Chen – Business Intelligence AHP - 44

Steps of assigning weights to different decision factors • Goal level (satisfaction with job) • Criteria level (salary, life quality, interest, and nearness to family) Dr. Chen – Business Intelligence AHP - 45

Steps of assigning weights to different decision factors We will first enter “pairwise comparison matrix” for the “Criteria” level Click on “AHP” Double Left click Dr. Chen – Business Intelligence AHP - 46

Steps of assigning weights to different decision factors (cont. ) Drag the bar or enter a number or click the bar to the “More Important” side “Starting Salary” is strongly more important than “Life Quality”. That is why 5 is entered into the Salary row and Quality column. Dr. Chen – Business Intelligence AHP - 47

Steps of assigning weights to different decision factors (cont. ) Dr. Chen – Business Intelligence AHP - 48

Steps of assigning weights to different decision factors (cont. ) Dr. Chen – Business Intelligence AHP - 49

Steps of assigning weights to different decision factors (cont. ) Dr. Chen – Business Intelligence AHP - 50

Steps of assigning weights to different decision factors (cont. ) Dr. Chen – Business Intelligence AHP - 51

Steps of assigning weights to different decision factors (cont. ) Dr. Chen – Business Intelligence AHP - 52

Steps of assigning weights to different decision factors (cont. ) This completes “pairwise comparison matrix” for the “Goal” level (i. e. , “Satisfaction with a Job”) Click OK when done Dr. Chen – Business Intelligence AHP - 53

Steps of assigning weights to different decision factors (cont. ) Next, to complete “pairwise comparison matrix” for the “Criteria” level of “Salary”) Double left click Dr. Chen – Business Intelligence AHP - 54

Steps of assigning weights to different decision factors (cont. ) Dr. Chen – Business Intelligence AHP - 55

Steps of assigning weights to different decision factors (cont. ) Dr. Chen – Business Intelligence AHP - 56

Perform Analysis Dr. Chen – Business Intelligence AHP - 57

Result from “Analysis of Composite Priorities … “ Better choice click According to the BAR chart, AHP suggests that Jane should take Job B Dr. Chen – Business Intelligence AHP - 58

Result from “Analysis of Composite Priorities … “ – with Values According to the “Values”, AHP suggests that Jane should take Job B (you need to “Add total” , see the next slide) Dr. Chen – Business Intelligence AHP - 59

Result as Text Dr. Chen – Business Intelligence Value Tree 0 satisfaction with a job 1 salary 0. 512 2 job A 0. 571 2 job B 0. 286 2 job C 0. 143 1 life quality 0. 098 2 job A 0. 163 2 job B 0. 540 2 job C 0. 297 1 interest 0. 244 2 job A 0. 088 2 job B 0. 669 2 job C 0. 243 1 nearness to family 0. 146 2 job A 0. 082 2 job B 0. 315 2 job C 0. 603 Better choice Composite Priorities job A job B job C salary 0. 293 0. 146 0. 073 life quali 0. 016 0. 053 0. 029 interest 0. 021 0. 163 0. 059 nearness t 0. 012 0. 046 0. 088 Overall 0. 342 0. 408 0. 249 step 7 (p. 5) AHP - 60

Save your work again click Dr. Chen – Business Intelligence AHP - 61

Add AHP software site to Java Site List Browser Required: Internet Explorer version 11 or older Dr. Chen – Business Intelligence AHP - 62

Windows 7: Step 1: Click on ( Dr. Chen – Business Intelligence ) and then select “Control Panel” AHP - 63

Windows 10: Step 1 b: Type “control panel” on the search box Step 1 c: Scroll down to and click “Java-(32/64) bit” Dr. Chen – Business Intelligence AHP - 64

Step 2: Click “Security” and Add the site (http: //hipre. aalto. fi) on the Java site list See detailed instruction on the following slides Dr. Chen – Business Intelligence AHP - 65

Step 3: Work on “Java Control Panel” Dr. Chen – Business Intelligence AHP - 66

Step 4: Click on “Edit Site List” and then Select “Add” Dr. Chen – Business Intelligence AHP - 67

Step 5: Enter http: //hipre. aalto. fi inside box of … Location and then click on “OK” Dr. Chen – Business Intelligence AHP - 68

Step 6: Click “Continue” on the Security Warning Menu Step 7: Complete the process a. You will see now that the AHP software site list (i. e. , http: //hipre. aalto. hi) has been added to “Exception Site List” b. Click “OK” to exit the “Security” option and Exit the “Java Control Panel” c. Re-activate the IE browser and enter the URL http: //hipre. aalto. fi Dr. Chen – Business Intelligence AHP - 69