THE ANALYTIC HIERARCHY PROCESS 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. INTRODUCTION

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, and stone B is a ruby worth $ 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, : 50.4 points per game scoring average

RANKING SPORTS RECORDS Career 1.Johnny Unitas, : touchdown passes in 47 consecutive games 2.Babe Ruth, :.690 slugging average 3.Walter Payton, : 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:

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!!!

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. APPLES AND ORANGES