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THE ANALYTIC THE ANALYTIC HIERARCHY HIERARCHY

PROCESSPROCESS

EXTENSIONSEXTENSIONS

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 percentage the areas of five shapes to find the percentage each shape contributes to the total area.each shape contributes to the total area.

The hierarchy has only two levels: the goal and the The hierarchy has only two levels: the goal and the five shapes.five shapes.


For example, the results might indicate that one For example, the results might indicate that one shape is 30% of the total areas of the five shape is 30% of the total areas of the five shapes.shapes.

We could use plane geometry to compute the We could use plane geometry to compute the exact areas. exact areas.

Using the AHP should provide estimates that are Using 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.


B

E

D

C

A

And now for the moment that you have all been And now for the moment that you have all been waiting for.........waiting for.........

The relative size of the five shapes are:The relative size of the five shapes are:

Circle A:Circle A: 0.4710.471

Triangle B:Triangle B: 0.0500.050

Square C:Square C: 0.2340.234

Diamond D:Diamond D: 0.1490.149

Rectangle E:Rectangle E:0.0960.096


MULTI-LEVEL HIERARCHIESMULTI-LEVEL HIERARCHIES

Tom Saaty suggests that hierarchies be limited to Tom 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 that This is based on the psychological result that people can consider 7 +/- 2 items people can consider 7 +/- 2 items simultaneously (Miller, 1956).simultaneously (Miller, 1956).

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

In this case, related items are grouped into In this case, related items are grouped into categories, creating additional levels in the categories, creating additional levels in the hierarchy.hierarchy.


The levels can be: goal, criteria, subcriteria, and The levels can be: goal, criteria, subcriteria, and alternatives. alternatives.

In Expert Choice, subcriteria are entered by In Expert Choice, subcriteria are entered by highlighting the desired criterion and highlighting the desired criterion and selecting the selecting the EEditdit and and Insert Insert CChild of Current hild of Current NodeNode commands. commands.

Alternatively, if many subcriteria are entered at Alternatively, if many subcriteria are entered at one time, they can be dragged and dropped one time, they can be dragged and dropped under the desired criteria.under the desired criteria.


Consider our car evaluation problem where ten Consider our car evaluation problem where ten evaluation factors have been identified.evaluation factors have been identified.

CARMULTI.AHP shows how these factors can CARMULTI.AHP shows how these factors can be grouped to form a four level hierarchy: goal, be grouped to form a four level hierarchy: goal, criteria, subcriteria, and alternatives.criteria, subcriteria, and alternatives.

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

Also, pairwise comparisons are needed for each Also, pairwise comparisons are needed for each set of subcriteria.set of subcriteria.


Another important point is that all items on the Another important point is that all items on the same 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 times more important than initial market size and more important than initial market size and appear 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 on might be comparable to NPV and appear on the same level.the same level.

We now display two additional examples of multi-We now display two additional examples of multi-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 and They appear in files VENDOR.AHP and SITE.AHP.SITE.AHP.

Others are found in the “samples” folder in Expert Others are found in the “samples” folder in Expert Choice.Choice.


RATINGS: BackgroundRATINGS: Background

Multilevel hierarchies are needed when there are Multilevel hierarchies are needed when there are many criteria - but what happens if we have many criteria - but what happens if we have many alternatives?many alternatives?

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

For example, if there are 50 employees to be For example, if there are 50 employees to be evaluated, then 1,225 (50(49)/2) pairwise evaluated, then 1,225 (50(49)/2) pairwise comparisons would be required for comparisons would be required for each each criterion!criterion!

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

The ratings approach requires setting up a The ratings approach requires setting up a ratings scale under each criterion. ratings scale under each criterion.

For example, in evaluating an employee’s For example, in evaluating an employee’s organizational skills, a manager could rate organizational skills, a manager could rate the employee as either Excellent, Very Good, the employee as either Excellent, Very Good, Good, Fair, or Poor.Good, Fair, or Poor.


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

Pairwise comparisons are needed to determine Pairwise comparisons are needed to determine the relative importance of each ratings scale the relative importance of each ratings scale category (intensity). category (intensity).

For example, with respect to the organizational For example, with respect to the organizational skills criterion, how much better is an skills criterion, how much better is an Excellent rating compared to a Very Good Excellent rating compared to a Very Good rating? rating?


The answer to this question might be different if The answer to this question might be different if we changed the criterion from organizational we changed the criterion from organizational skills to implementation skills. skills to implementation skills.

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

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


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

Assigning grades to any course is a ratings Assigning grades to any course is a ratings exercise. exercise.

Since an A is assigned a score of 4.00 and a C is Since an A is assigned a score of 4.00 and a C is assigned a score of 2.00, it follows that an A assigned a score of 2.00, it follows that an A is 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?


Consider the following example.Consider the following example.

Although a 91 is only two points higher than an Although a 91 is only two points higher than an 89, assigning an A to the 91 and a B to the 89 89, 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 the These and other problems are discussed at the Expert Choice web site Expert Choice web site (www.expertchoice.com) under Annie Person.(www.expertchoice.com) under Annie Person.


Many organizations use ratings or scoring Many organizations use ratings or scoring models for evaluation. models for evaluation.

For example, in evaluating carpet suppliers, a For example, in evaluating carpet suppliers, a company might assign the values 3, 1, 2 for company might assign the values 3, 1, 2 for cost, support, and quality, respectively. cost, support, and quality, respectively.

Typically, they assign 5, 4, 3, 2, and 1 to ratings Typically, they assign 5, 4, 3, 2, and 1 to ratings of excellent, very good, good, fair, and poor, of excellent, very good, good, fair, and poor, respectively.respectively.


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 A’s score would be 3*3+1*5+2*3=20.Supplier A’s score would be 3*3+1*5+2*3=20.

Assume that supplier B is judged to be excellent Assume that supplier B is judged to be excellent in cost, fair in support, and very good in in cost, fair in support, and very good in quality.quality.

Supplier B’s score would be: 3*5+1*2+2*4=25.Supplier B’s score would be: 3*5+1*2+2*4=25.


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

Absolutely not! The numbers assigned as Absolutely not! The numbers assigned as criteria weights and as intensity weights are criteria weights and as intensity weights are not necessarily ratio-scaled.not necessarily ratio-scaled.

Ratio-scaled comparisons, such as dividing Ratio-scaled comparisons, such as dividing supplier total scores are meaningless in such supplier total scores are meaningless in such cases. cases.


Ratio-scaled measurement assumes, for Ratio-scaled measurement assumes, for example, that cost is 3 times (3/1) more example, that cost is 3 times (3/1) more important than support, and that an excellent important than support, and that an excellent rating is 1.25 times (5/4) better than a very rating is 1.25 times (5/4) better than a very good rating for each criterion. good rating for each criterion.

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

The AHP is preferred because it applies ratio-The AHP is preferred because it applies ratio-scale measurement throughout the evaluation scale measurement throughout the evaluation process.process.


Goal and criteria (and possibly subcriteria) are Goal and criteria (and possibly subcriteria) are entered in a ratings model in the same fashion entered in a ratings model in the same fashion they were entered in standard AHP.they were entered in standard AHP.

Criteria (and possible subcriteria) pairwise Criteria (and possible subcriteria) pairwise comparisons are next performed. comparisons are next performed.

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

Highlight a cell in the first criteria column and Highlight a cell in the first criteria column and select the select the FFoormula Typermula Type and and RRatingsatings commands. commands.

EXPERT CHOICE: RatingsEXPERT CHOICE: Ratings

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

When finished select the When finished select the AAssessssess command. command.

You can now enter the pairwise comparisons You can now enter the pairwise comparisons for the rating scale intensities.for the rating scale intensities.

After recording judgments, select the After recording judgments, select the CCloselose command.command.


If the rating scale intensities and their pairwise If the rating scale intensities and their pairwise comparisons are not the same for all criteria, comparisons are not the same for all criteria, highlight a cell in the second criteria column highlight a cell in the second criteria column and repeat the process.and repeat the process.

If the intensities and pairwise comparisons are If the intensities and pairwise comparisons are the same for all criteria, then select the the same for all criteria, then select the Formulas Grid button (looks like Y=f(x)). Formulas Grid button (looks like Y=f(x)).

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


To copy the intensities and pairwise comparisons To copy the intensities and pairwise comparisons (from criterion 1) to other criteria (criteria 2 and (from criterion 1) to other criteria (criteria 2 and 3), highlight the Ratings cell in the Type column 3), highlight the Ratings cell in the Type column of criterion 1 and select the of criterion 1 and select the EEditdit and and CCopy opy FormulaFormula commands. commands.

Next, highlight the Ratings cells for criteria 2 and 3 Next, highlight the Ratings cells for criteria 2 and 3 and select the and select the EEditdit and and PPaste Formulaaste Formula commands. commands.

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


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

Remember that alternatives are Remember that alternatives are NOTNOT entered in entered in the hierarchy.the hierarchy.

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

When finished, highlight the cell corresponding When finished, highlight the cell corresponding to the first alternative (row 1) and the first to the first alternative (row 1) and the first criterion (column 1).criterion (column 1).


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.

For a given alternative (row), as the user highlights For a given alternative (row), as the user highlights each criterion (column), the appropriate intensities each criterion (column), the appropriate intensities appear and the user selects the desired one.appear and the user selects the desired one.

The final step is to select the The final step is to select the VViewiew and and TTotals columnotals column commands to see the final scores for each commands to see the final scores for each alternative.alternative.

To sort, highlight any final weight and select the To sort, highlight any final weight and select the EEditdit and and SSoortrt, , DDescendingescending commands. commands.


Criterion intensity scores are computed similarly Criterion intensity scores are computed similarly to ideal synthesis without the normalization to ideal synthesis without the normalization step.step.

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

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


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 intensity The 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.

For example, if we select a good rating for cost, For 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.


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

This model is based on a student project which This model is based on a student project which utilized the actual factors in an employee utilized the actual factors in an employee evaluation system.evaluation system.

Others are found in the “samples” folder in Others are found in the “samples” folder in Expert Choice.Expert Choice.


GROUP DECISION MAKINGGROUP DECISION MAKING

How did the couple arrive at their combined How 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 to There are many ways of applying AHP to support a group decision-making process. support a group decision-making process.

For example, all of the parties discuss, debate, For example, all of the parties discuss, debate, and eventually agree on each pairwise and eventually agree on each pairwise comparison entry.comparison entry.


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

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

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

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


One last approach is to achieve consensus One last approach is to achieve consensus mathematically.mathematically.

Each participant provides their own judgments Each participant provides their own judgments for each pairwise comparison and the results for each pairwise comparison and the results must be averaged.must be averaged.

For example, suppose two individuals compared For example, suppose two individuals compared cost to safety and provide judgments of 9 and cost to safety and provide judgments of 9 and 1/9.1/9.


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

Probably not! Since both judgments are at Probably not! Since both judgments are at opposite ends of scale, we would expect the opposite ends of scale, we would expect the combined judgment to be 1.00.combined judgment to be 1.00.

The The geometric meangeometric mean produces this result. produces this result.

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

As another example, in comparing cost to As another example, in comparing cost to safety suppose the judgments of three safety suppose the judgments of three individuals 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 group Expert Choice manages the entire group decision making process and achieves decision making process and achieves consensus mathematically by computing the consensus mathematically by computing the geometric mean. geometric mean.


First, create a hierarchy as described earlier.First, create a hierarchy as described earlier.

Tell Expert Choice that this is a group model by Tell Expert Choice that this is a group model by selecting the selecting the GGoo and and PParticipant Tablearticipant Table commands. commands.

Next, select Next, select EEditdit and and GGroup Enableroup Enable, followed by , followed by EEdit,dit, AAdd 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 any Click on a participant to change the name, enter any demographic data, and select demographic data, and select FFileile and and CCloselose..


At this point, there are N participants and a At this point, there are N participants and a facilitator.facilitator.

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

When a group model is opened, you must When a group model is opened, you must respond with either the facilitators name (you respond with either the facilitators name (you have access to all information) or the name of have access to all information) or the name of one of the participants (you only have access one of the participants (you only have access to that participant’s information).to that participant’s information).


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

Select a participant from the Participants drop-down Select a participant from the Participants drop-down list on the toolbar (under the list on the toolbar (under the GGoo command). command).

Choose a pairwise comparison mode and enter the Choose 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 parts of the hierarchy and for all participants.all parts of the hierarchy and for all participants.


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

This is accomplished by selecting Combined from This is accomplished by selecting Combined from the Participants drop-down list.the Participants drop-down list.

Next, select Next, select EEditdit, , CoCommbine Participants bine Participants Judgments/DataJudgments/Data, , EEntire Hierarchyntire Hierarchy, and , and BothBoth..

This will combine judgments by computing all This will combine judgments by computing all necessary geometric means.necessary geometric means.


Useful Expert Choice featuresUseful Expert Choice features• FFileile,, Print Pre Print Prevviewiew, , FFileile,, Save as Word Save as Word

DDocumentocument commands creates a Word file of the commands creates a Word file of the entire hierarchy. Use entire hierarchy. Use OOptionsptions and and PPrrintinginting commands to select desired output.commands to select desired output.

• Drop and drag features are useful when Drop and drag features are useful when developing the hierarchy.developing the hierarchy.

• To get information from Word to Expert Choice To get information from Word to Expert Choice use the use the EEditdit, , PPaste Children from Clipboardaste Children from Clipboard commands. This is useful if developing the commands. This is useful if developing the hierarchy while brainstorming in Word.hierarchy while brainstorming in Word.

BUILDING LARGER MODELSBUILDING LARGER MODELS

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 several Develop hierarchy iteratively over several

sessions.sessions.• An alternate approach is to only develop a An alternate approach is to only develop a

benefits hierarchy. The benefits alternative benefits hierarchy. The benefits alternative weights 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 a You could also have a benefits hierarchy and a cost hierarchy.cost hierarchy.


Lessons that we have learned about AHP.Lessons that we have learned about AHP.• Rank alternatives or criteria before performing Rank alternatives or criteria before performing

pairwise comparisons. This helps consistency.pairwise comparisons. This helps consistency.• Many people are comfortable with graphical Many people are comfortable with graphical

mode of pairwise comparison.mode of pairwise comparison.• After entering pairwise comparisons, Expert After entering pairwise comparisons, Expert

Choice displays a graphical representation of the Choice 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 the necessary. Expert Choice computes the corresponding pairwise comparisons that yield corresponding pairwise comparisons that yield these weights.these weights.


SUMMARYSUMMARY

In this module:In this module:

we provided an overview of classical decision we provided an overview of classical decision analysis; andanalysis; and

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

SUMMARYSUMMARY

AHP 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.

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