INTRODUCTION • The Analytic Hierarchy Process (AHP) is an alternate approach to expected utility. • AHP successfully addresses the limitations of expected utility. • AHP is implemented using the software package called Expert Choice.
INTRODUCTION • What is the Analytic Hierarchy Process (AHP)? • The AHP, developed by Tom Saaty, is a decision-making method for prioritizing alternatives when multi-criteria must be considered. • An approach for structuring a problem as a hierarchy or set of integrated levels.
INTRODUCTION • AHP problems are structured in at least three levels: • The goal, such as selecting the best car to purchase, • The criteria, such as cost, safety, and appearance, • The alternatives, namely the cars themselves.
INTRODUCTION • The decision-maker: • measures the extent to which each alternative achieves each criterion, and • determines the relative importance of the criteria in meeting the goal, and • synthesizes the results to determine the relative importance of the alternatives in meeting the goal.
APPROACH • How does AHP capture human judgments? • AHP never requires you to make an absolute judgment or assessment. You would never be asked to directly estimate the weight of a stone in kilograms. • AHP does require you to make a relative assessment between two items at a time. AHP uses a ratio scale of measurement.
APPROACH • Suppose the weights of two stones are being assessed. AHP would ask: How much heavier (or lighter) is stone A compared to stone B? • AHP might tell us that, of the total weight of stones A and B, stone A has 65% of the total weight, whereas, stone B has 35% of the total weight.
APPROACH • Individual AHP judgments are called pairwise comparisons. • These judgments can be based on objective or subjective information. • For example, smoothness might be a subjective criterion used to compare two stones. Pairwise comparisons could be based on touch.
APPROACH • However, suppose stone A is a diamond worth $1,000.00 and stone B is a ruby worth $300.00. • This objective information could be used as a basis for a pairwise comparison based on the value of the stones.
APPROACH • Consistency of judgments can also be measured. Consistency is important when three or more items are being compared. • Suppose we judge a basketball to be twice as large as a soccer ball and a soccer ball to be three times as large as a softball. To be perfectly consistent, a basketball must be six times as large as a softball.
APPROACH • AHP does not require perfect consistency, however, it does provide a measure of consistency. • We will discuss consistency in more detail later.
AHP APPLICATIONS • AHP has been successfully applied to a variety of problems. • 1. R&D projects and research papers; • 2. vendors, transport carriers, and site locations; • 3. employee appraisal and salary increases; • 4. product formulation and pharmaceutical licensing; • 5. capital budgeting and strategic planning; • 6. surgical residents, medical treatment, and diagnostic testing.
AHP APPLICATIONS • The product and service evaluations prepared by consumer testing services is another potential application. • Products and services, such as self propelled lawn mowers are evaluated. • Factors include: bagging, mulching, discharging, handling, and ease of use. • An overall score for each mower is determined.
AHP APPLICATIONS • Would you make your purchasing decision based solely on this score? • Probably not! Some of the information will be helpful. • Some additional questions are: • How important is each criterion? • Would you weigh the criteria the same way? • Are all of the criteria considered important to you? • Are there other criteria that are important to you? • Have you ever thought about these issues?
RANKING SPORTS RECORDS • The AHP has been used to rank outstanding season, career, and single event records across sports. • Season • 1. Babe Ruth, 1920: .847 slugging average • 2. Joe DiMaggio, 1944: 56 game hitting streak • 3. Wilt Chamberlain, 1961-62: 50.4 points per game scoring average
RANKING SPORTS RECORDS • Career • 1. Johnny Unitas, 1956-70: touchdown passes in 47 consecutive games • 2. Babe Ruth, 1914-35: .690 slugging average • 3. Walter Payton, 1975-86: 16,193 rushing yardage • Single event • 1. Wilt Chamberlain, 1962: 100 points scored • 2. Norm Van Brocklin, 1951: 554 passing yards • 3. Bob Beamon, 1968: 29' 2.5" long jump
RANKING SPORTS RECORDS • How do we compare records from different sports? • It all depends on the criteria that you select! • Golden and Wasil (1987) used the following criteria: • 1. Duration of record - years record has stood, years expected to stand • 2. Incremental improvement - % better than previous record • 3. Other record characteristics - glamour, purity (single person vs. team)
RANKING SPORTS RECORDS • Did this article end all arguments about sports records? • Absolutely not! • In bars and living rooms across the country, people still argue about sports. • AHP provides a methodology to structure the debate. • Different criteria and different judgments could produce different results.
A FINAL POINT ABOUT SPORTS • In reading the sports pages we often see discussion of how well teams match up across different positions. • These match-ups are often used to predict a winner. • Match-ups is a pairwise comparison concept!
AHP APPLICATIONS • Our culture is obsessed with quantitative rankings of all sorts of things. • There are many measurement problems associated with rankings of products, sports teams, universities, and the like. • Many of these issues are discussed on a web site at: • http://www.expertchoice.com/annie.person
APPLES AND ORANGES • The discussion of how to compare records from different sports recalls a saying from childhood:
APPLES AND ORANGES • The discussion of how to compare records from different sports recalls a saying from childhood: • You can’t compare apples and oranges. • All you get is mixed fruit!
APPLES AND ORANGES • The discussion of how to compare records from different sports recalls a saying from childhood: • You can’t compare apples and oranges. • All you get is mixed fruit! • After the discussion about sports, • do you still believe this statement?
APPLES AND ORANGES • The discussion of how to compare records from different sports recalls a saying from childhood: • You can’t compare apples and oranges. • All you get is mixed fruit! • After the discussion about sports, • do you still believe this statement? • We hope not!!!
APPLES AND ORANGES • What criteria might you use when comparing apples and oranges? • There are a vast set of criteria that may change depending upon time of day or season of year: • taste, texture, smell, • ripeness, juiciness, nutrition, • shape, weight, color, and • cost. • Can you think of others?
APPLES AND ORANGES • The point is that people are often confronted with the choice between apples and oranges. • Their choice is based on some psychological assessment of: • relevant criteria, • their importance, and • how well the alternatives achieve the criteria.