ahp process

8/2/2019 AHP Process

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THE ANALYTICTHE ANALYTICHIERARCHYHIERARCHY

PROCESSPROCESS

EXTENSIONSEXTENSIONS


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AHP VALIDATION EXERCISEAHP VALIDATION EXERCISE

This exercise helps to validate the AHP.This exercise helps to validate the AHP.

You will make judgments on the relative sizes of You will make judgments on the relative sizes of the areas of five shapes to find the percentagethe areas of five shapes to find the percentageeach shape contributes to the total area.each shape contributes to the total area.

The hierarchy has only two levels: the goal and theThe hierarchy has only two levels: the goal and the

five shapes.five shapes.


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AHP VALIDATION EXERCISEAHP VALIDATION EXERCISEF

or example, the results might indicate that oneF

or example, the results might indicate that oneshape is 30% of the total areas of the fiveshape is 30% of the total areas of the fiveshapes.shapes.

We could use plane geometry to compute theWe could use plane geometry to compute theexact areas.exact areas.

Using the AHP should provide estimates that areUsing the AHP should provide estimates that are

close to the actual values.close to the actual values.

The five shapes are on the next slide.The five shapes are on the next slide.


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B

E

D

C

A


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And now for the moment that you have all beenAnd now for the moment that you have all beenwaiting for.........waiting for.........

The relative size of the five shapes are:The relative size of the five shapes are:Circle A:Circle A: 0.4710.471Triangle B:Triangle B: 0.0500.050Square C:Square C: 0.2340.234Diamond D:Diamond D: 0.1490.149Rectangle E:Rectangle E: 0.0960.096



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MU LTIMU LTI- -LEVEL HIERARCHIESLEVEL HIERARCHIESTom Saaty suggests that hierarchies be limited toTom Saaty suggests that hierarchies be limited to

six levels and nine items per level.six levels and nine items per level.

This is based on the psychological result thatThis is based on the psychological result that people can consider 7 +/ people can consider 7 +/- - 2 items2 itemssimultaneously (Miller, 1956).simultaneously (Miller, 1956).

Brainstorming can identify several dozen criteria.Brainstorming can identify several dozen criteria.

In this case, related items are grouped intoIn this case, related items are grouped intocategories, creating additional levels in thecategories, creating additional levels in thehierarchy.hierarchy.


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MU LTIMU LTI- -LEVEL HIERARCHIESLEVEL HIERARCHIES

The levels can be: goal, criteria, subcriteria, andThe levels can be: goal, criteria, subcriteria, andalternatives.alternatives.

In Expert Choice, subcriteria are entered byIn Expert Choice, subcriteria are entered by

highlighting the desired criterion andhighlighting the desired criterion andselecting theselecting the E Edit dit andand Insert Insert C Child of Current hild of Current

Node Node commands.commands.

Alternatively, if many subcriteria are entered atAlternatively, if many subcriteria are entered atone time, they can be dragged and droppedone time, they can be dragged and droppedunder the desired criteria.under the desired criteria.


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Consider our car evaluation problem where tenConsider our car evaluation problem where tenevaluation factors have been identified.evaluation factors have been identified.

CARMULTI.AHP shows how these factors canCARMULTI.AHP shows how these factors can

be grouped to form a four level hierarchy: be grouped to form a four level hierarchy:goal, criteria, subcriteria, and alternatives.goal, criteria, subcriteria, and alternatives.

Notice that the Safety criterion has no Notice that the Safety criterion has nosubcriterion.subcriterion.

Also, pairwise comparisons are needed for eachAlso, pairwise comparisons are needed for each

set of subcriteria.set of subcriteria.


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Another important point is that all items on theAnother important point is that all items on thesame level should be within one order of same level should be within one order of magnitude of importance.magnitude of importance.

For example, NPV might be more than ten times

For example, NPV might be more than ten timesmore important than initial market size andmore important than initial market size andappear one level above initial market size.appear one level above initial market size.

However, all market criteria taken together However, all market criteria taken together might be comparable to NPV and appear onmight be comparable to NPV and appear onthe same level.the same level.


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We now display two additional examples of We now display two additional examples of multimulti--levels hierarchies using Expert Choice.levels hierarchies using Expert Choice.

Both are based on student projects.Both are based on student projects.

They appear in files VENDOR.AHP andThey appear in files VENDOR.AHP andSITE.AHP.SITE.AHP.

Others are found in the samples folder inOthers are found in the samples folder inExpert Choice.Expert Choice.



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RATINGS: BackgroundRATINGS: Background

Multilevel hierarchies are needed when thereMultilevel hierarchies are needed when thereare many criteriaare many criteria - - but what happens if we but what happens if wehave many alternatives?have many alternatives?

The ratings approach is used when there are aThe ratings approach is used when there are alarge number of alternatives to be evaluated.large number of alternatives to be evaluated.

F or example, if there are 50 employees to beF or example, if there are 50 employees to beevaluated, then 1,225 (50(49)/2) pairwiseevaluated, then 1,225 (50(49)/2) pairwisecomparisons would be required for comparisons would be required for eacheachcriterion!criterion!


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It is impractical to make that many alternativeIt is impractical to make that many alternative pairwise comparisons. pairwise comparisons.

The ratings approach requires setting up aThe ratings approach requires setting up a

ratings scale under each criterion.ratings scale under each criterion.

F or example, in evaluating an employeesF or example, in evaluating an employeesorganizational skills, a manager could rateorganizational skills, a manager could ratethe employee as either Excellent, Very Good,the employee as either Excellent, Very Good,Good, F air, or Poor.Good, F air, or Poor.



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It is crucial to define what Excellent means andIt is crucial to define what Excellent means andhow it is attained.how it is attained.

Pairwise comparisons are needed to determinePairwise comparisons are needed to determine

the relative importance of each ratings scalethe relative importance of each ratings scalecategory (intensity).category (intensity).

F or example, with respect to the organizationalF or example, with respect to the organizationalskills criterion, how much better is anskills criterion, how much better is anExcellent rating compared to a Very GoodExcellent rating compared to a Very Goodrating?rating?



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The answer to this question might be differentThe answer to this question might be differentif we changed the criterion fromif we changed the criterion fromorganizational skills to implementation skills.organizational skills to implementation skills.

In fact, you may decide to use differentIn fact, you may decide to use differentintensities for each criterion.intensities for each criterion.

It is important to understand that alternativesIt is important to understand that alternativesare not pairwise compared in a rating model,are not pairwise compared in a rating model,rather alternatives are rated for each criterion.rather alternatives are rated for each criterion.



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Ratings models are a part of everyday life.Ratings models are a part of everyday life.

Assigning grades to any course is a ratingsAssigning grades to any course is a ratingsexercise.exercise.

Since an A is assigned a score of 4.00 and a C isSince an A is assigned a score of 4.00 and a C isassigned a score of 2.00, it follows that an Aassigned a score of 2.00, it follows that an Ais twice as good as a C.is twice as good as a C.

We never met a student who agreed with this!We never met a student who agreed with this!Do you?Do you?



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Consider the following example.Consider the following example.

Although a 91 is only two points higher than anAlthough a 91 is only two points higher than an89, assigning an A to the 91 and a B to the 8989, assigning an A to the 91 and a B to the 89

means that the 91 is really 1.33 (4.00/3.00)means that the 91 is really 1.33 (4.00/3.00)times better than the 89.times better than the 89.

These and other problems are discussed at theThese and other problems are discussed at theExpert Choice web siteExpert Choice web site(www.expertchoice.com) under Annie Person.(www.expertchoice.com) under Annie Person.



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Suppose supplier A is judged to be good in cost,Suppose supplier A is judged to be good in cost,excellent is support, and good in quality.excellent is support, and good in quality.

Supplier As score would be 3*3+1*5+2*3=20.Supplier As score would be 3*3+1*5+2*3=20.

Assume that supplier B is judged to be excellentAssume that supplier B is judged to be excellentin cost, fair in support, and very good inin cost, fair in support, and very good in

quality.quality.

Supplier Bs score would be: 3*5+1*2+2*4=25.Supplier Bs score would be: 3*5+1*2+2*4=25.



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Can we say that supplier B is 25% better thanCan we say that supplier B is 25% better thansupplier A?supplier A?

Absolutely not! The numbers assigned asAbsolutely not! The numbers assigned ascriteria weights and as intensity weights arecriteria weights and as intensity weights arenot necessarily rationot necessarily ratio- -scaled.scaled.

RatioRatio--scaled comparisons, such as dividingscaled comparisons, such as dividingsupplier total scores are meaningless in suchsupplier total scores are meaningless in such

cases.cases.



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RatioRatio--scaled measurement assumes, for scaled measurement assumes, for example, that cost is 3 times (3/1) moreexample, that cost is 3 times (3/1) moreimportant than support, and that an excellentimportant than support, and that an excellentrating is 1.25 times (5/4) better than a veryrating is 1.25 times (5/4) better than a verygood rating for each criterion.good rating for each criterion.

This is rarely, if ever, the case for such scoringThis is rarely, if ever, the case for such scoringsystems!systems!

The AHP is preferred because it applies ratioThe AHP is preferred because it applies ratio- -scale measurement throughout the evaluationscale measurement throughout the evaluation

process. process.



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Goal and criteria (and possibly subcriteria) areGoal and criteria (and possibly subcriteria) areentered in a ratings model in the same fashionentered in a ratings model in the same fashionthey were entered in standard AHP.they were entered in standard AHP.

Criteria (and possible subcriteria) pairwiseCriteria (and possible subcriteria) pairwisecomparisons are next performed.comparisons are next performed.

Next, select the Data Grid button (looks like a Next, select the Data Grid button (looks like aspreadsheet).spreadsheet).

Highlight a cell in the first criteria column andHighlight a cell in the first criteria column and

select theselect the F F

oormula Typermula Type andand R Ratingsatings commands.commands.

EXPERT CHOICE: RatingsEXPERT CHOICE: Ratings


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Enter each rating scale intensity (for example,Enter each rating scale intensity (for example,excellent, very good, good, fair, and poor) inexcellent, very good, good, fair, and poor) inthe Intensity Name column.the Intensity Name column.

When finished select theWhen finished select the A A

ssess ssess command.command.

You can now enter the pairwise comparisonsYou can now enter the pairwise comparisonsfor the rating scale intensities.for the rating scale intensities.

After recording judgments, select theAfter recording judgments, select the C Closelosecommand.command.



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If the rating scale intensities and their pairwiseIf the rating scale intensities and their pairwisecomparisons are not the same for all criteria,comparisons are not the same for all criteria,highlight a cell in the second criteria columnhighlight a cell in the second criteria columnand repeat the process.and repeat the process.

If the intensities and pairwise comparisons areIf the intensities and pairwise comparisons arethe same for all criteria, then select thethe same for all criteria, then select theF ormulas Grid button (looks like Y=f(x)).F ormulas Grid button (looks like Y=f(x)).

(If this button does not appear, select the Model(If this button does not appear, select the ModelView button and then the Data Grid button.)View button and then the Data Grid button.)



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To copy the intensities and pairwise comparisonsTo copy the intensities and pairwise comparisons(from criterion 1) to other criteria (criteria 2 and(from criterion 1) to other criteria (criteria 2 and3), highlight the Ratings cell in the Type column3), highlight the Ratings cell in the Type columnof criterion 1 and select theof criterion 1 and select the E Edit dit andand C Copyopy F ormula F ormula commands.commands.

Next, highlight the Ratings cells for criteria 2 and 3 Next, highlight the Ratings cells for criteria 2 and 3and select theand select the E Edit dit andand P Paste F ormulaaste F ormula

commands.commands.

You have now copied all of the ratings intensitiesYou have now copied all of the ratings intensitiesand their pairwise comparisons from criterion 1and their pairwise comparisons from criterion 1to criteria 2 and 3.to criteria 2 and 3.



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Select the Data Grid button and you are ready toSelect the Data Grid button and you are ready toenter the alternatives.enter the alternatives.

Remember that alternatives areRemember that alternatives are NOT NOT entered inentered in

the hierarchy.the hierarchy.

Highlight the first cell in the Alternative columnHighlight the first cell in the Alternative columnand enter each alternative in turn.and enter each alternative in turn.

When finished, highlight the cell correspondingWhen finished, highlight the cell correspondingto the first alternative (row 1) and the firstto the first alternative (row 1) and the first

criterion (column 1).criterion (column 1).



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Select the desired rating scale intensity and repeat for Select the desired rating scale intensity and repeat for all criteria for all alternatives.all criteria for all alternatives.

F or a given alternative (row), as the user highlightsF or a given alternative (row), as the user highlightseach criterion (column), the appropriate intensitieseach criterion (column), the appropriate intensitiesappear and the user selects the desired one.appear and the user selects the desired one.

The final step is to select theThe final step is to select the V V iewiew andand T Totals columnotals column

commands to see the final scores for eachcommands to see the final scores for eachalternative.alternative.

To sort, highlight any final weight and select theTo sort, highlight any final weight and select the E Edit dit

andand S Soort rt ,, D Descending escending commands.commands.



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Criterion intensity scores are computed similarlyCriterion intensity scores are computed similarlyto ideal synthesis without the normalizationto ideal synthesis without the normalizationstep.step.

First, all intensity weights are divided by the

First, all intensity weights are divided by thelargest intensity weight.largest intensity weight.

Second, the adjusted intensity weight selected bySecond, the adjusted intensity weight selected bythe user is multiplied by the criteria weightthe user is multiplied by the criteria weightand the results added to the total score.and the results added to the total score.



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An AHP ratings model for our carpet supplier An AHP ratings model for our carpet supplier problem is in a file called CARPET.AHP. problem is in a file called CARPET.AHP.

The local weights for each rating scale intensityThe local weights for each rating scale intensity

are: 0.419, 0.263, 0.160, 0.097, and 0.062.are: 0.419, 0.263, 0.160, 0.097, and 0.062.

Dividing by 0.419 yields adjusted weights of:Dividing by 0.419 yields adjusted weights of:1.000, 0.627, 0.382, 0.232, and 0.148.1.000, 0.627, 0.382, 0.232, and 0.148.

F or example, if we select a good rating for cost,F or example, if we select a good rating for cost,then 0.382 times the cost weight of 0.558 or then 0.382 times the cost weight of 0.558 or

0.213 is added to the total score.0.213 is added to the total score.



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Another example of a ratings model withAnother example of a ratings model withsubcriteria appears in EMPEVAL.AHP.subcriteria appears in EMPEVAL.AHP.

This model is based on a student project whichThis model is based on a student project whichutilized the actual factors in an employeeutilized the actual factors in an employeeevaluation system.evaluation system.

Others are found in the samples folder inOthers are found in the samples folder inExpert Choice.Expert Choice.



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GRO U P DECISION M AKINGGRO U P DECISION M AKING

How did the couple arrive at their combinedHow did the couple arrive at their combined judgments in the original car evaluation judgments in the original car evaluation problem? problem?

There are many ways of applying AHP toThere are many ways of applying AHP tosupport a group decisionsupport a group decision- -making process.making process.

F or example, all of the parties discuss, debate,F or example, all of the parties discuss, debate,and eventually agree on each pairwiseand eventually agree on each pairwisecomparison entry.comparison entry.


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Alternatively, each individual provides their Alternatively, each individual provides their own judgments in separate copies of theown judgments in separate copies of themodel.model.

These results could be summarized and used asThese results could be summarized and used asa basis to reach consensus.a basis to reach consensus.

Another approach is to create a hierarchy withAnother approach is to create a hierarchy withgoal, participants, criteria, and alternatives.goal, participants, criteria, and alternatives.

Pairwise comparisons can determine eachPairwise comparisons can determine each participants weight in the process. participants weight in the process.


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One last approach is to achieve consensusOne last approach is to achieve consensusmathematically.mathematically.

Each participant provides their own judgmentsEach participant provides their own judgmentsfor each pairwise comparison and the resultsfor each pairwise comparison and the resultsmust be averaged.must be averaged.

F or example, suppose two individualsF or example, suppose two individualscompared cost to safety and providecompared cost to safety and provide judgments of 9 and 1/9. judgments of 9 and 1/9.


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The arithmetic mean is 4.56 ((9+(1/9))/2). DoThe arithmetic mean is 4.56 ((9+(1/9))/2). Doyou think this is the best estimate?you think this is the best estimate?

Probably not! Since both judgments are atProbably not! Since both judgments are atopposite ends of scale, we would expect theopposite ends of scale, we would expect the

combined judgment to be 1.00.combined judgment to be 1.00.

TheThe geometric meangeometric mean produces this result. produces this result.

In general, if there are n individuals that provideIn general, if there are n individuals that provide judgments, the geometric mean is defined as judgments, the geometric mean is defined asthe nth root of the product of the n judgments.the nth root of the product of the n judgments.


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As another example, in comparing cost toAs another example, in comparing cost tosafety suppose the judgments of threesafety suppose the judgments of threeindividuals are 2, 4, and 8.individuals are 2, 4, and 8.

The geometric mean is the cube root of their The geometric mean is the cube root of their product (64) which is 4. product (64) which is 4.

Expert Choice manages the entire groupExpert Choice manages the entire groupdecision making process and achievesdecision making process and achievesconsensus mathematically by computing theconsensus mathematically by computing thegeometric mean.geometric mean.



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First, create a hierarchy as described earlier.

First, create a hierarchy as described earlier.

Tell Expert Choice that this is a group model byTell Expert Choice that this is a group model byselecting theselecting the GG oo andand P Participant Tablearticipant Tablecommands.commands.

Next, select Next, select E Edit dit andand GG roup Enableroup Enable , followed by, followed by

E Edit,dit, A A

dd N Participantsdd N Participants , and enter the number of , and enter the number of participants. participants.

Click on a participant to change the name, enter anyClick on a participant to change the name, enter any

demographic data, and selectdemographic data, and select F F ileile andand C Closelose ..



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At this point, there are N participants and aAt this point, there are N participants and afacilitator.facilitator.

The facilitator acts as the leader and may alsoThe facilitator acts as the leader and may alsoenter judgments, if desired.enter judgments, if desired.

When a group model is opened, you mustWhen a group model is opened, you must

respond with either the facilitators name (yourespond with either the facilitators name (youhave access to all information) or the name of have access to all information) or the name of one of the participants (you only have accessone of the participants (you only have accessto that participants information).to that participants information).



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The facilitator can enter pairwise comparisons for The facilitator can enter pairwise comparisons for all participants.all participants.

Select a participant from the Participants dropSelect a participant from the Participants drop- -down list on the toolbar (under thedown list on the toolbar (under the GG oocommand).command).

Choose a pairwise comparison mode and enter theChoose a pairwise comparison mode and enter the judgments for the participant. judgments for the participant.

Record the judgments when finished and repeat for Record the judgments when finished and repeat for all arts of the hierarch and for all artici ants.all arts of the hierarch and for all artici ants.



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After all pairwise comparisons have been enteredAfter all pairwise comparisons have been enteredfor all participants, the judgments are combined.for all participants, the judgments are combined.

This is accomplished by selecting Combined fromThis is accomplished by selecting Combined fromthe Participants dropthe Participants drop- -down list.down list.

Next, select Next, select E Edit dit ,, CoCommbine Participantsbine Participants

Judgments/Data Judgments/Data ,, E Entire Hierarchyntire Hierarchy , and, and Both Both ..

This will combine judgments by computing allThis will combine judgments by computing allnecessary geometric means.necessary geometric means.



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Useful Expert Choice featuresUseful Expert Choice featuresF F ileile ,, Print Pre Print Prev viewiew ,, F F ileile ,, Save as Word Save as Word

D Document ocument commands creates a Word file of thecommands creates a Word file of theentire hierarchy. Useentire hierarchy. Use OOptions ptions andand P Pr rinting inting commands to select desired output.commands to select desired output.Drop and drag features are useful whenDrop and drag features are useful whendeveloping the hierarchy.developing the hierarchy.

To get information from Word to Expert ChoiceTo get information from Word to Expert Choiceuse theuse the E Edit dit ,, P Paste Children from Clipboard aste Children from Clipboard commands. This is useful if developing thecommands. This is useful if developing thehierarchy while brainstorming in Word.hierarchy while brainstorming in Word.

BU ILDING LARGER M ODELSBU ILDING LARGER M ODELS


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Lessons that we have learned about AHP.Lessons that we have learned about AHP.Have experts develop their part of the hierarchy.Have experts develop their part of the hierarchy.Develop hierarchy iteratively over severalDevelop hierarchy iteratively over severalsessions.sessions.An alternate approach is to only develop aAn alternate approach is to only develop a benefits hierarchy. The benefits alternative benefits hierarchy. The benefits alternativeweights could be used in a cost/benefit analysis.weights could be used in a cost/benefit analysis.

You could also have a benefits hierarchy and aYou could also have a benefits hierarchy and acost hierarchy.cost hierarchy.



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Lessons that we have learned about AHP.Lessons that we have learned about AHP.Rank alternatives or criteria before performingRank alternatives or criteria before performing pairwise comparisons. This helps consistency. pairwise comparisons. This helps consistency.Many people are comfortable with graphicalMany people are comfortable with graphicalmode of pairwise comparison.mode of pairwise comparison.After entering pairwise comparisons, ExpertAfter entering pairwise comparisons, ExpertChoice displays a graphical representation of theChoice displays a graphical representation of the

weights. The user can move these bars if weights. The user can move these bars if necessary. Expert Choice computes thenecessary. Expert Choice computes thecorresponding pairwise comparisons that yieldcorresponding pairwise comparisons that yieldthese weights.these weights.



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SUMM ARYSUMM ARYIn this module:In this module:

we provided an overview of classical decisionwe provided an overview of classical decisionanalysis; andanalysis; and

offered the AHP as an alternative decisionoffered the AHP as an alternative decision- -making process.making process.


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SUMM ARYSUMM ARYAHP benefits include:AHP benefits include:

natural way to elicit judgments;natural way to elicit judgments;

measure degree of inconsistency;measure degree of inconsistency;

easy to use;easy to use;

allows broad participation; andallows broad participation; and

fully supported by Expert Choice.fully supported by Expert Choice.

ahp process

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