THE THE AANALYTIC NALYTIC HIERARCHY HIERARCHY

PROCESSPROCESS

INTRODUCTIONINTRODUCTION

The Analytic Hierarchy Process (AHP) is an The Analytic Hierarchy Process (AHP) is an alternate approach to expected utility. alternate approach to expected utility.

AHP successfully addresses the limitations of AHP successfully addresses the limitations of expected utility. expected utility.

AHP is implemented using the software AHP is implemented using the software package called package called Expert ChoiceExpert Choice..

INTRODUCTIONINTRODUCTION

What is the Analytic Hierarchy Process (AHP)?What is the Analytic Hierarchy Process (AHP)?

The AHP, developed by Tom Saaty, is a The AHP, developed by Tom Saaty, is a decision-making method for prioritizing decision-making method for prioritizing alternatives when multi-criteria must be alternatives when multi-criteria must be considered.considered.

An approach for structuring a problem as a An approach for structuring a problem as a hierarchy or set of integrated levels.hierarchy or set of integrated levels.

INTRODUCTIONINTRODUCTION

AHP problems are structured in at least three AHP problems are structured in at least three levels:levels:

The goalThe goal, such as selecting the best car to , such as selecting the best car to purchase,purchase,

The criteriaThe criteria, such as cost, safety, and appearance,, such as cost, safety, and appearance,

The alternativesThe alternatives, namely the cars themselves., namely the cars themselves.

INTRODUCTIONINTRODUCTION

The decision-maker:The decision-maker:

measures the extent to which each measures the extent to which each alternative achieves each criterion, and alternative achieves each criterion, and

determines the relative importance of determines the relative importance of the criteria in meeting the goal, and the criteria in meeting the goal, and

synthesizes the results to determine the synthesizes the results to determine the relative importance of the alternatives relative importance of the alternatives in meeting the goal.in meeting the goal.

INTRODUCTIONINTRODUCTION

APPROACHAPPROACH

How does AHP capture human judgments?How does AHP capture human judgments?

AHP AHP nevernever requires you to make an absolute requires you to make an absolute judgment or assessment. You would never judgment or assessment. You would never be asked to directly estimate the weight of a be asked to directly estimate the weight of a stone in kilograms.stone in kilograms.

AHP AHP doesdoes require you to make a relative require you to make a relative assessment between assessment between twotwo items at a time. items at a time. AHP uses a ratio scale of measurement. AHP uses a ratio scale of measurement.

APPROACHAPPROACHSuppose the weights of two stones are being Suppose the weights of two stones are being

assessed. AHP would ask: How much heavier assessed. AHP would ask: How much heavier (or lighter) is stone A compared to stone B?(or lighter) is stone A compared to stone B?

AHP might tell us that, of the total weight of AHP might tell us that, of the total weight of stones A and B, stone A has 65% of the total stones A and B, stone A has 65% of the total weight, whereas, stone B has 35% of the total weight, whereas, stone B has 35% of the total weight.weight.

APPROACHAPPROACHIndividual AHP judgments are called Individual AHP judgments are called pairwise pairwise

comparisonscomparisons..

These judgments can be based on objective or These judgments can be based on objective or subjective information.subjective information.

For example, smoothness might be a subjective For example, smoothness might be a subjective criterion used to compare two stones. criterion used to compare two stones. Pairwise comparisons could be based on Pairwise comparisons could be based on touch. touch.

APPROACHAPPROACHHowever, suppose stone A is a diamond worth However, suppose stone A is a diamond worth

$1,000.00 and stone B is a ruby worth $1,000.00 and stone B is a ruby worth $300.00.$300.00.

This objective information could be used as a This objective information could be used as a basis for a pairwise comparison based on the basis for a pairwise comparison based on the value of the stones.value of the stones.

APPROACHAPPROACHConsistency of judgments can also be measured. Consistency of judgments can also be measured.

Consistency is important when three or more Consistency is important when three or more items are being compared. items are being compared.

Suppose we judge a basketball to be twice as Suppose we judge a basketball to be twice as large as a soccer ball and a soccer ball to large as a soccer ball and a soccer ball to be three times as large as a softball. be three times as large as a softball.

To be perfectly consistent, a basketball must be To be perfectly consistent, a basketball must be six times as large as a softball. six times as large as a softball.

APPROACHAPPROACH

AHP does not require perfect consistency, AHP does not require perfect consistency, however, it does provide a measure of however, it does provide a measure of consistency. consistency.

We will discuss consistency in more detail later.We will discuss consistency in more detail later.

AHP APPLICATIONSAHP APPLICATIONS

AHP has been successfully applied to a variety AHP has been successfully applied to a variety of problems.of problems.

1.1. R&D projects and research papers;R&D projects and research papers;

2.2. vendors, transport carriers, and site locations;vendors, transport carriers, and site locations;

3.3. employee appraisal and salary increases;employee appraisal and salary increases;

4.4. product formulation and pharmaceutical product formulation and pharmaceutical licensing;licensing;

5.5. capital budgeting and strategic planning;capital budgeting and strategic planning;

6.6. surgical residents, medical treatment, and surgical residents, medical treatment, and diagnostic testing.diagnostic testing.

AHP APPLICATIONSAHP APPLICATIONS

The product and service evaluations prepared by The product and service evaluations prepared by consumer testing services is another potential consumer testing services is another potential application.application.

Products and services, such as self propelled Products and services, such as self propelled lawn mowers are evaluated. lawn mowers are evaluated.

Factors include: bagging, mulching, discharging, Factors include: bagging, mulching, discharging, handling, and ease of use.handling, and ease of use.

An overall score for each mower is determined.An overall score for each mower is determined.

AHP APPLICATIONSAHP APPLICATIONSWould you make your purchasing decision based Would you make your purchasing decision based

solely on this score?solely on this score?Probably not! Some of the information will be Probably not! Some of the information will be

helpful. helpful.

Some additional questions are:Some additional questions are:How important is each criterion?How important is each criterion?Would you weigh the criteria the same way?Would you weigh the criteria the same way?Are all of the criteria considered important to you?Are all of the criteria considered important to you?Are there other criteria that are important to you?Are there other criteria that are important to you?Have you ever thought about these issues?Have you ever thought about these issues?

RANKING SPORTS RECORDSRANKING SPORTS RECORDS

The AHP has been used to rank outstanding The AHP has been used to rank outstanding season, career, and single event records across season, career, and single event records across sports.sports.

SeasonSeason

1.1. Babe Ruth, 1920: .847 slugging averageBabe Ruth, 1920: .847 slugging average

2.2. Joe DiMaggio, 1944: 56 game hitting streakJoe DiMaggio, 1944: 56 game hitting streak

3.3. Wilt Chamberlain, 1961-62: 50.4 points per Wilt Chamberlain, 1961-62: 50.4 points per game scoring averagegame scoring average

RANKING SPORTS RECORDSRANKING SPORTS RECORDSCareerCareer

1.1. Johnny Unitas, 1956-70: touchdown passes in Johnny Unitas, 1956-70: touchdown passes in 47 consecutive games47 consecutive games

2.2. Babe Ruth, 1914-35: .690 slugging averageBabe Ruth, 1914-35: .690 slugging average

3.3. Walter Payton, 1975-86: 16,193 rushing yardageWalter Payton, 1975-86: 16,193 rushing yardage

Single eventSingle event

1.1. Wilt Chamberlain, 1962: 100 points scoredWilt Chamberlain, 1962: 100 points scored

2.2. Norm Van Brocklin, 1951: 554 passing yardsNorm Van Brocklin, 1951: 554 passing yards

3.3. Bob Beamon, 1968: 29' 2.5" long jumpBob Beamon, 1968: 29' 2.5" long jump

RANKING SPORTS RECORDSRANKING SPORTS RECORDSHow do we compare records from different How do we compare records from different

sports?sports?It all depends on the criteria that you select!It all depends on the criteria that you select!

Golden and Wasil (1987) used the following Golden and Wasil (1987) used the following criteria:criteria:

1.1. Duration of record - years record has stood, Duration of record - years record has stood, years expected to standyears expected to stand

2.2. Incremental improvement - % better than Incremental improvement - % better than previous recordprevious record

3.3. Other record characteristics - glamour, purity Other record characteristics - glamour, purity (single person vs. team)(single person vs. team)

RANKING SPORTS RECORDSRANKING SPORTS RECORDSDid this article end all arguments about sports Did this article end all arguments about sports

records?records?Absolutely not! Absolutely not!

In bars and living rooms across the country, In bars and living rooms across the country, people still argue about sports. people still argue about sports.

AHP provides a methodology to structure the AHP provides a methodology to structure the debate. debate.

Different criteria and different judgments could Different criteria and different judgments could produce different results.produce different results.

A FINAL POINT ABOUT SPORTSA FINAL POINT ABOUT SPORTS

In reading the sports pages we often see In reading the sports pages we often see discussion of how well teams match up across discussion of how well teams match up across different positions. different positions.

These match-ups are often used to predict a These match-ups are often used to predict a winner. winner.

Match-ups is a pairwise comparison concept!Match-ups is a pairwise comparison concept!

AHP APPLICATIONSAHP APPLICATIONS

Our culture is obsessed with quantitative Our culture is obsessed with quantitative rankings of all sorts of things.rankings of all sorts of things.

There are many measurement problems There are many measurement problems associated with rankings of products, sports associated with rankings of products, sports teams, universities, and the like.teams, universities, and the like.

Many of these issues are discussed on a web site Many of these issues are discussed on a web site at:at:

http://www.expertchoice.com/annie.personhttp://www.expertchoice.com/annie.person

The discussion of how to compare records from The discussion of how to compare records from different sports recalls a saying from different sports recalls a saying from childhood:childhood:

APPLES AND ORANGESAPPLES AND ORANGES

The discussion of how to compare records from The discussion of how to compare records from different sports recalls a saying from different sports recalls a saying from childhood:childhood:

You can’t compare apples and oranges. You can’t compare apples and oranges.

All you get is mixed fruit!All you get is mixed fruit!

APPLES AND ORANGESAPPLES AND ORANGES

The discussion of how to compare records from The discussion of how to compare records from different sports recalls a saying from different sports recalls a saying from childhood:childhood:

You can’t compare apples and oranges. You can’t compare apples and oranges.

All you get is mixed fruit!All you get is mixed fruit!

After the discussion about sports, After the discussion about sports,

do you still believe this statement?do you still believe this statement?

APPLES AND ORANGESAPPLES AND ORANGES

APPLES AND ORANGESAPPLES AND ORANGESThe discussion of how to compare records from The discussion of how to compare records from

different sports recalls a saying from different sports recalls a saying from childhood:childhood:

You can’t compare apples and oranges. You can’t compare apples and oranges.

All you get is mixed fruit!All you get is mixed fruit!

After the discussion about sports, After the discussion about sports,

do you still believe this statement?do you still believe this statement?

We hope not!!!We hope not!!!

What criteria might What criteria might youyou use when comparing use when comparing apples and oranges?apples and oranges?There are a vast set of criteria that may change There are a vast set of criteria that may change depending upon time of day or season of year:depending upon time of day or season of year:

taste,taste, texture,texture, smell,smell,ripeness,ripeness, juiciness,juiciness, nutrition,nutrition,shape,shape, weight,weight, color, andcolor, andcost.cost.

Can you think of others?Can you think of others?

APPLES AND ORANGESAPPLES AND ORANGES

The point is that people are often confronted with The point is that people are often confronted with the choice between apples and oranges. the choice between apples and oranges.

Their choice is based on some psychological Their choice is based on some psychological assessment of: assessment of:

relevant criteria, relevant criteria,

their importance, and their importance, and

how well the alternatives achieve the how well the alternatives achieve the criteria.criteria.

APPLES AND ORANGESAPPLES AND ORANGES