Chapter 15 Part 4 AHP

8/6/2019 Chapter 15 Part 4 AHP

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Agenda for This Week

Monday, April 25 AHP

Wednesday, April 27 AHP

Friday, April 29 AHP

Monday, May 2 Exam 2



Chapter 15

Analytical Hierarchy Process ±

Part 1



Analytical Hierarchy Process

Designed to solve multicriteria decision

problems

Model under conditions of certainty where weknow all of the info but we need to trade-off

many factors.

We are comparing several alternatives on the

basis of the same set of attributes.



Developing the Hierarchy

Develop a visual representation of the

problem in terms of the overall goal, the

criteria to be used and the decisionalternatives

Alternatives

Attributes

GOAL



AHP Example

Decision HierarchyDecision Hierarchy

Select Best ApartmentSelect Best Apartment

Criteria Rent Size ProximityCriteria Rent Size Proximity

Apt. 1Apt. 1

Apt. 2Apt. 2

Apt. 3Apt. 3

Apt. 1Apt. 1

Apt. 2Apt. 2

Apt. 3Apt. 3

Apt. 1Apt. 1

Apt. 2Apt. 2

Apt. 3Apt. 3

AlternativesAlternatives



AHP

Major question is how to assign relative

weights across alternatives, as well as for the

attributes (assigning weights is the crux of AHP).

People have been found to be more

consistent when they do pairwise

comparisons than when they just try to assignrelative weights.



AHP - Steps

1. Make pairwise comparisons

2. Synthesize judgments

3. Check for consistency



AHP ± Pairwise Comparison

Scale (Always Use)

Verbal Judgement of PreferencesVerbal Judgement of Preferences Numerical RatingNumerical Rating

Extremely preferredExtremely preferred 99

Very strongly to extremelyVery strongly to extremely 88

Very strongly preferredVery strongly preferred 77Strongly to very stronglyStrongly to very strongly 66

Strongly preferredStrongly preferred 55

Moderately to stronglyModerately to strongly 44

Moderately preferredModerately preferred 33Equally to moderatelyEqually to moderately 22

Equally preferredEqually preferred 11



Apt 1 Apt 2 Apt 3

Apt 1 1 4 1/3

Apt 2 ¼ 1 1/7

Apt 3 3 7 1

RENT

Step 1 ± Pairwise Comparison



Apt 1 Apt 2 Apt 3

Apt 1 1 1/6 1

Apt 2 6 1 6 Apt 3 1 1/6 1

SIZE

Step 1 ± Pairwise Comparison



AHP - Steps


2. Synthesize judgments

3. Check for consistency



AHP ± Step 2

Synthesization ± the process of calculating

the priority of each criterion in terms of its

contribution to the overall goal of achievingyour goal



Step 2 - Synthesization

Step 1: Sum values in each column of

pairwise comparison matrix

Step 2: Divide each element by its columntotal (gives normalized pairwise

comparison matrix)

Step 3: Compute average of elements in

each row (gives estimate of relative prioritiesof elements being compared)




Apt 1 Apt 2 Apt 3

Apt 1 1 4 1/3

Apt 2 ¼ 1 1/7

Apt 3 3 7 1

SUM 17/4 12 31/21

RENT

Next« divide each element by column total




Apt 1 Apt 2 Apt 3 Avg

Apt 1 .235 .334 .226 .266

Apt 2 .059 .083 .097 .080

Apt 3 .706 .583 .677 .654

RENT

Normalized pairwise comparison matrix

Relative prioritiesRelative priorities



AHP ± Relative Priorities

.266

.080

.654

What do

these mean?

Apt. 1

Apt. 2

Apt. 3

Relative Priorities for Rent



AHP ± Relative Priorities

.266

.080

.654

These mean that with

respect to Rent, Apt. 3 is

preferred first (65%), then

Apt. 1 (27%), then Apt. 2(8%)

Apt. 1

Apt. 2

Apt. 3

Relative Priorities for Rent




SIZE


Apt 1 Apt 2 Apt 3

Apt 1 1 1/6 1

Apt 2 6 1 6

Apt 3 1 1/6 1

SUM 8 8/6 8





Apt 1 .125 .125 .125 .125

Apt 2 .75 .75 .75 .75

Apt 3 .125 .125 .125 .125

SIZE






PROXIMITY


Apt 1 Apt 2 Apt 3

Apt 1 1 5 8

Apt 2 1/5 1 3

Apt 3 1/8 1/3 1

SUM 53/40 19/3 12





Apt 1 .755 .790 .667 .737

Apt 2 .151 .158 .25 .186

Apt 3 .094 .053 .083 .077

PROXIMITY





AHP - Steps


2. Synthesize judgments3. Check for consistency



AHP ± Step 3

A key step in the making of several pairwisecomparisons is considering the consistencyof the pairwise judgements.

Example: If A compared to B = 3 and Bcompared to C = 2 then A compared to C should= 3x2 = 6. If it wasn¶t, some inconsistency wouldoccur.

With AHP, we can measure the degree of consistency; and if unacceptable, we canrevise pairwise comparisons

Chapter 15 Part 4 AHP

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