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@jepson.gonzaga.edu

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.

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.

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

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 Structure of the Problem Satisfaction with a Job criteria; n=4 Starting Salary Nearness to Family Life Quality Interest Job A Job B Job C

Satisfaction with a Job Structure of the Problem Satisfaction with a Job Starting Salary Life Quality Interest Nearness to Family Job A Job B Job C Web site: http://www.hipre.hut.fi/

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

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.

A pairwise comparison matrix for the criteria level Satisfaction with a Job Web site: http://www.hipre.hut.fi/ Since n=4, there are 6 [n*(n-1)/2] judgments required to develop each matrix. Why?

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.

The next two pairwise matrices (for “Life Quality” and “Interest”) are as follows (see step#6 on the handout):

The last pairwise matrix (for “Nearness to family”) is listed below:

How to verify that the data entered in the comparison matrices is acceptable Consistency Index (C.I) is computed as follows (see handout, p.5) 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 2 3 4 5 6 7 8 9 10 R.I. .58 .90 1.12 1.24 1.32 1.41 1.45 1.51

Satisfaction with a Job

We will open an existing model http://www.hipre.hut.fi or http://hipre.aalto.fi/ File name: mbus673.jmd

Scroll down

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

(p.4 of Handout)

Result from double clicking “salary”

Result from double clicking “life quality”

Result from double clicking “interest”

Result from double clicking “nearness to family”

Perform Analysis click

Perform Analysis

Result from “Analysis of Composite Priorities … “ click According to the BAR chart, AHP suggests that Jane should take Job B. Why?

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)

Result as Text 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)

Your Turn -- Try It! http://www.hipre.hut.fi

How to create an AHP model for “a Job Selection.”

Double click a node (element) will appear Criteria level Enter a name Goal level

Edit the element’s Name (only if needed) Select this

Steps of creating “Links” 2. Right click 1. Left click Complete the remaining links

Complete the remaining links between “Criteria” and Alternatives” Steps of creating “Links” (cont.) Labels are changed 1. Left click 2. Right click Complete the remaining links between “Criteria” and Alternatives”

Steps of creating “Links” – Final Model (cont.) Labels are changed

Be sure that to save the model now (and periodically). Enter “filename”

Enter “filename” A “filename” is saved

Steps of assigning weights to different decision factors Goal level (satisfaction with job) Criteria level (salary, life quality, interest, and nearness to family)

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

Steps of assigning weights to different decision factors (cont.) Drag the bar or enter a number “Starting Salary” is strongly more important than “Life Quality”. That is why 5 is entered into the Salary row and Quality column.

Steps of assigning weights to different decision factors (cont.)

Steps of assigning weights to different decision factors (cont.)

Steps of assigning weights to different decision factors (cont.)

Steps of assigning weights to different decision factors (cont.)

Steps of assigning weights to different decision factors (cont.)

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

Steps of assigning weights to different decision factors (cont.) Next, to complete “pairwise comparison matrix” for the “Criteria” level of “Salary”) Double left click

Steps of assigning weights to different decision factors (cont.)

Steps of assigning weights to different decision factors (cont.)

Perform Analysis

Result from “Analysis of Composite Priorities … “ click According to the BAR chart, AHP suggests that Jane should take Job B

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)

Result as Text 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)

Save your work again click

Have a fun! http://www.hipre.hut.fi File name: mbus673.jmd

The following slides might be skipped.

Sensitivity Analysis