BODIN & GASS - Exercises for Teaching the Analytic Hierarchy

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Exercises for Teaching the Analytic HierarchyProcess

Lawrence Bodin and Saul I. GassRobert H. Smith School of Business

University of Maryland

College Park, MD 20742

Abstract

In a related paper (Bodin and Gass, 2003), we described the basic concepts

that webelieve must becovered when teaching the Analytic Hierarchy Process(AHP) to MBA students and outlined six exercises that can be used as in-classexamples or homework problems. In this paper, we present the details of these

exercises and an example of an AHP analysis.

1. INTRODUCTION

When teaching the AHP to MBA students, the key points that should be coveredare: (a) the AHP fundamental pairwise comparison scale, (b) inconsistency and

sensitivity analysis, (c) ratio scales, (d) the ratings model, (e) the teamapproach for solving an AHP problem, (f) AHP and resource allocation, and (g) ifclass time is available, the notion of rank reversal although rank reversal is not

essential to a basic understanding of the AHP (Bodin and Gass, 2003). Details ofthe AHP are given in Saaty, 1980and Saaty, 1994.

Since the AHP has the proven ability to resolve (or assist in resolving) a wideclass of important decision problems, we believe that AHP must be part of the

common-knowledge base of an MBA. When faced with a multi-criteria decisionanalysis problem, an MBA graduate must have the background and experienceto ask the right questions of their staff and/or fellow workers and understand

how the AHP can be used to resolve multi-criteria decision analysis problems.The AHP is a decision-aid that can provide the decision maker (DM) withrelevant information to assist the DM in choosing the "best" alternative or to

rank a set of alternatives.

In the quantitative MBA class (Decision Analysis and Models) taught at theUniversity of Maryland, the AHP module was covered in about 2-2.5 weeks. Inthis module, we used the software package, Expert Choice. The trial version of

Expert Choice can be downloaded for free from the website . Other softwarepackages that contain an implementation of the AHP are HIPRE and Criterium.

We have not used HIPRE and Criterium and, hence, cannot comment on them.As an aid to the reader, the appendix describes the introductory operations

research and quantitative methods textbooks that discuss the AHP.

Given the ease of use of the Expert Choice software, we see no pedagogical

advantage in implementing the AHP in a spreadsheet program such as Excel byitself for carrying out the AHP analysis and computations. It must be noted,

Volume 4, Number 2, January 2004

mailto:[email protected]:[email protected]://www.expertchoice.com/http://www.expertchoice.com/http://-/?-http://-/?-http://-/?-http://-/?-mailto:[email protected]:[email protected]
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however, that the ratings version of the AHP in Expert Choice forms a tablecalled a ratings spreadsheet (called 'spreadsheet' in section 3 of this paper) fordetermining the weight for each alternative. The weight of the alternative in

this spreadsheet is a measure of how close that alternative is to the perfectalternative (weight = 1).

In Section 2 of this paper, six varied exercises that we found useful in theclassroom for conveying the essentials of an AHP analysis and the features of

the Expert Choice software are presented. As in Bodin and Gass, 2003, theseexercises are outlined as follow:

EX1 contains a simple direct comparison model for the purchase of a newautomobile. Variants of this example have appeared in numerouspublications including Saaty, 1990. The criteria and the alternatives arespecified.

EX2 and EX3 are problems involving the integration of the ratings modelversion of the AHP with a resource allocation problem.EX4 contains an analysis of alternative income tax structures. The criteria

to be used are not explicitly specified. The student must determine a setof criteria and alternative tax strategies (over and above the taxstrategies specified in the example). This problem works well for teams of

three to five students.EX5 is a problem of determining the best long distance telephone service.The student or team must collect data on each of these services

(generally from the Internet), determine a set of criteria, and develop aset of alternatives for the associated ratings model.

EX6 contains the analysis of the relative size of five geometric figures.EX6 is designed to validate the use of the 1-9 pairwise comparison scale.This validation example should be presented soon after AHP fundamentals

and examples of the AHP are discussed. The problem is due to Saaty,1994.

The availability of additional AHP examples that have appeared in the literatureor on the Internet are described in Bodin and Gass, 2003. As noted in Bodin and

Gass, 2003:

Our experience has shown that the AHP is a winning topic for MBA

students. The MBA students like the AHP, they easily learn how touse the AHP and, in many cases, they get very enthusiastic aboutthe AHP. We often have to "rein-in" the students because they getso excited about the material. AHP should be a required topic for any

introductory MBA course in decision making.

2. EXERCISES IN USING THE AHP

In this section, six exercises (called EX1-EX6) that can be used in class

problems or as homework problems on the AHP are presented.

2.1 EX1: Choosing the Best Automobile

This basic example illustrates the key aspects of the AHP and its implementat ion

by the Expert Choice software. The hierarchy is easy to build and the instructorcan demonstrate the replication command that simplifies the building of thehierarchy. The overall goal of the example is to choose the best automobile with

respect to the four criteria. Figure 2.1 gives the data for the problem. Thestudent can readily see that there is no one best alternative, as none of theautomobiles is best across all criteria (as indicated by the asterisks).

Alternatives Price Miles/Gallon (MPG) Prestige Comfort

Avalon \$15,000* 26 Low Good

Babylon \$18,000 28* Fair Fair

Carryon \$24,000 20 High* High*

Figure 2.1 Data for Automobile Purchase Example (* denotes best alternative)

The problem has both quantitative and qualitative data. The price data can beused directly in the EC comparison matrix by the data entry mode, but the dataentry has to be inverted (invert button) in that a low price is better than a

higher price (EC considers a higher number as being better than a lower number

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unless told otherwise). Note that the prices are of the same order of magnitude- we are not comparing a cheap Ford Falcon to a Jaguar. Comparing items of

the same "Order of Magnitude" is an axiom of the AHP. The price data can alsobe used indirectly by asking the usual pairwise comparison question, e.g., "IsAvalon preferred to Babylon with respect to price and how more is it preferred?"

Here the preference needs to be established using the 1-9 scale (or equivalentverbal scale) and the student has to decide how the \$15,000 compares to the

\$18,000. Using the 1-9 scale for the dollar figures tends to build a utilityevaluation on the dollars - the dollar spent for the cheaper auto has a greaterutility than a dollar spent on a more expensive auto. The data entry mode

treats all dollars as having the same utility. We suggest that the facultymember first illustrate the data entry mode and then illustrating the 1-9 pairwisecomparison mode. The final rankings will probably stay the same but the weights

assigned to the different elements will probably be different.

The MPG numbers are direct data entry; the weights obtained are just theindividual auto's MPG number divided by the sum of all the MPG numbers. For

prestige and comfort, the student must make pairwise comparisons that respectthe individual criterion transitivity relationship (High>Good>Fair>Low). The 1-9

scale does a very good job in capturing the preferences (e.g., High/Low = 7,High/Good = 5, High/Fair = 3, and so on).

2.2 EX2: Ratings/Resource Allocation-Case 1

EX2 and EX3 are take-home examples to be done by each student or a smallteam of students. They illustrate the use of the AHP ratings model to determineweights for competing projects, with the weights then used in a 0-1

optimization problem to select a subset of the projects subject to a budgetconstraint.

BMGT Industries has an internal Advanced Technology Project Committee (ATP)

responsible for selecting new projects for funding. The selection is made fromthose projects suggested by its division managers. The selection cycle is nowupon us. The ATP Committee feels that the time is right for it to restructure and

redirect its various R&D projects. BMGT wants to ensure that its divisions do notcontinue the status quo. It has instructed its division managers (Research andDevelopment, Manufacturing, Marketing, Logistics, Finance, Human Resources)

to come up with a set of new projects that addresses the future of eachdivision and BMGT.

The R&D and Manufacturing managers have joined forces and have agreed on

eleven new robotic manufacturing projects to go along with the other newproducts the R&D group expects to develop over the next two years. The staffshave

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