i

DEDICATION

This work is dedicated to God Almighty who gives wisdom

and inspiration

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CHAPTER ONE

1.0. INTRODUCTION

This presentation is about one of the most famous methods for

making multi-criteria decisions called the Analytic Hierarchy

Process or AHP. AHP was developed to optimize decision making

when one is faced with a mix of qualitative, quantitative, and

sometimes conflicting factors that are taken into consideration.

AHP has been very effective in making complicated, often

irreversible decisions.

I intend to show how SAS/IML implements AHP to help decision

makers choose the best solution among several alternatives across

multiple criteria. With SAS/IML, I will build an AHP model using

the example of choosing a smart phone. Finally, I will describe

some recent uses and provide final notes.

Decision-making involves the use of intelligence, wisdom and

creativity in order for humans to satisfy basic needs or to

survive. Evaluating a decision requires several considerations

such as the benefits derived from making the right decision, the

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costs, the risks, and losses resulting from the actions (or non-

actions) taken if the wrong decision is made.

Decision-making methods range from reliance on chance (such as

flipping coins, reading tea leaves or tarot cards) to the use of

more structured decision-making tools. Sound decision-making

involves weighing all the factors that are important. Six sigma

belts must carefully weigh the advantages and disadvantages of

decision choices so that the future success and survival in

business or life can be optimized, nothing is guaranteed.

Modern Day decision-making has been inherently complex when many

factors have to be weighed against competing priorities. One of

the modern tools developed in the last 30 years used to assess,

prioritize, rank, and evaluate decision choices is the Analytic

Hierarchy Process (AHP) developed by Thomas Saaty [1-3, 5-7].

Thomas Saaty developed AHP in the 1970s as a way of dealing with

weapons tradeoffs, resource and asset allocation, and decision

making when he was a professor at the Wharton School of Business

and a consultant with the Arms Control Disarmament Agency. There

he was faced with the problem of dealing with high costs and a

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host of considerations with many factors that conflicted with

each other or were not easily specified.

1.1 HIERARCHIES DEFINED

A hierarchy is a stratified system of ranking and organizing

people, things, ideas, etc., where each element of the system,

except for the top one, is subordinate to one or more other

elements. Though the concept of hierarchy is easily grasped

intuitively, it can also be described mathematically. Diagrams of

hierarchies are often shaped roughly like pyramids, but other

than having a single element at the top, there is nothing

necessarily pyramid-shaped about a hierarchy. Human organizations

are often structured as hierarchies, where the hierarchical

system is used for assigning responsibilities, exercising

leadership, and facilitating communication.

1.2. THEORY ON HIERARCHICAL TEAMS

(1) The President of the United States is confronted with

information regarding a possible terrorist attack involving the

small pox disease originating from a foreign country. The

President is considering making a pre-emptive strike on the

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foreign country to thwart the attack. In his deliberations, he

calls in his National Security Advisor, the Secretary of State,

the Secretary of Defense, and the head of the Central

Intelligence Agency. Each member of the staff is presented with

the same information and asked to make a recommendation regarding

the appropriate response by the government. The president must

then make a final decision based on these recommendations.

(2) A position has opened in the management department at a

university. In an effort to decide which job candidate should be

hired, a team is constructed from departmental faculty. This team

is led by the department chair who has the final decision making

authority, but this person seeks advice from a three-person

committee that includes the top researcher, the top teacher, and

as well as an affirmative action officer. Each of these three

staff members are charged with rating the likelihood that the

candidate will make enough of a substantive contribution to the

department and university mission to get tenure at this

university in six years.

(3) A journal editor must decide whether to accept or reject a

manuscript. The study reported in the manuscript tests a

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controversial theory, and the editor solicits three

recommendations in an effort to determine whether the paper in

question will be an influential and well-cited article, or

ignored and considered trivial by the research community. One of

the reviewers is a firm proponent of the theory being tested, the

second is a well-known critic of this theory, and the third is a

trusted and long-time editorial board member who is not really an

expert in the area, but has no stake one way or the other

regarding the theory.

1.3 THE MULTILEVEL THEORY OF TEAM DECISION MAKING

Building off of these previous works on decision making,

Hollenbeck et al. (1995) developed the MLT of team decision

making as a conceptual framework for analyzing decision making in

these types of teams. This theory expands upon previous

literature by identifying four specific levels of analysis where

factors that affect hierarchical team decision making may reside.

Then, in an effort to promote theoretical parsimony, the theory

identifies the single most critical factor at each level of

analysis that determines accuracy. According to the MLT, the

lowest level of analysis that is relevant to hierarchical teams

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is the decision level. That is, decisions are nested under

individuals, in the sense that the individuals on the team each

make a number of judgments or decisions, and each of these

decision opportunities may vary in ways (e.g. time pressure or

novelty) that affect the accuracy of the team overall. The next

level is the individual level, where the focus is on a specific

staff member. Staff members are nested within teams, in the sense

that each team has multiple staff members, and variance in the

characteristics of the staff members (e.g. cognitive ability or

agreeableness) will be related to variance in team decision

making accuracy. Above this is the dyadic level, where the focus

is on the one-to-one relationships between team members. For

example, a four-person team can be thought of as containing six

unique dyadic relationships, three of which are vertical (i.e.

leader-staff) and three of which are horizontal (i.e. staff-

staff).

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CHAPTER TWO

2.0. CHARACTERISTICS OF THE MULTILEVEL THEORY: INFORMITY.

The lowest level of decision making is the decision level, and

any team or staff member may make multiple decisions. According

to this theory, the decision object manifests itself in the form

of a set of cue values relevant to the staff member. However, the

decision object may not provide complete information, in that it

generates levels on a subset of the cues, rather than all

possible cues. This means that some information presumed to be

relevant to the decision making process may not be available for

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a specific decision object. The amount of information available

about the focal decision object is known as decision informity.

Empirically, decision informity is the number of cue values known

about the object divided by the total number of cues that are

relevant for the decision. Each staff member defines what is a

relevant cue differently. Returning to our previous example, the

staff member on the academic job search team who is a research

expert may want to know five things about the candidate

including: (a) work habits; (b) theory development capabilities;

(c) methodological skills; (d) access to data; and (e) writing

ability.

2.1. INVESTIGATION OF THE CORE CONSTRUCTS

The literature examining the aggregation of advisor

judgments that we have already reviewed emerged from the

mathematical aggregation paradigm (e.g. Ashton, 1986). Brehmer

and Hagafors (1986) broadened this literature by examining team

decision making through the lens model framework. Brehmer and

Hagafors (1986) were interested in studying hierarchical teams

with distributed expertise. They were interested in the weighting

process undertaken by team leaders. Specifically, they were

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interested in determining whether team leaders would reduce their

cognitive load in the decision making process by utilizing only

the staff members’ recommendation, rather than relying on the

cues from the environment. Borrowing from social judgment theory

(Brehmer, 1986) and Brunswik’s (1955) lens model, the authors

built a model of hierarchical team decision making, and tested it

via a laboratory simulation. Thirty high school students were

paid to act as leaders of a hierarchical team in which three

experts analyzed two cues each in making a recommendation to the

leader. Similar to many of the other studies presented, the

authors simulated the experts rather than use actual people in

those roles. Each leader made 90 decisions and was provided with

feedback on their accuracy following each trial.

The participants were divided into three different conditions in

which the validity of the cues and the validity of the experts

varied. In the first condition (i.e. equal cues, equal validity),

each cue had the same correlation with the criterion and the

experts each provided recommendations that were based on the

optimal weights of the cues. In the second condition (i.e.

unequal cues, equal validity), the experts still optimally

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weighted the cues. However, the correlation between the cues and

the criterion differed across the three experts. In the final

condition (i.e. equal cues, unequal validity), the cues were

similar to the first condition, but the experts varied in their

utilization of the cues.

2.2. EXAMINATION OF NON-CORE CONSTRUCTS

A number of recent studies have examined the operation of the

non-core constructs identified earlier. These studies expand

previous work on the MLT of team decision making by investigating

some of the more distal non-core constructs that have an impact

on the decision making process. These studies examine the non-

core constructs of social environment (Hollenbeck, Ilgen et al.,

1998; LePine, Hollenbeck, Ilgen, Colquitt & Ellis, 2002), role

(Hollenbeck, Ilgen et al., 1998), and factors within the person

(Colquitt, Hollenbeck, Ilgen, LePine & Sheppard, 2002; Hollenbeck

et al., 1995; Hollenbeck, Ilgen et al., 1998; LePine, Hollenbeck,

Ilgen & Hedlund, 1997; Phillips, 2001; Phillips, Douthitt &

Hyland, 2001; Phillips, 2002). Both the Hollenbeck et al. (1995)

and the Hollenbeck, Ilgen et al. (1998) studies, which we

previously addressed, examined the effects that non-core

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constructs had upon decision making accuracy. In the Hollenbeck

et al. (1995) study, the authors examined three non-core

constructs: experience in the task, familiarity with the team

members, and team member replacement. These constructs were

hypothesized to influence decision making accuracy through their

effects on the lower-level core constructs. The results showed

that experience led to more accurate decisions, whereas

familiarity and attrition of team members did not have a direct

relationship with accuracy. Experience was also linked to dyadic

sensitivity (R2 = 0.03) and decision informity (R2 = 0.26),

whereas the three two-way interactions between the non-core

constructs explained 9% of the variance in individual validity.

These results implied that the benefits of experience were

highest for unfamiliar teams that did not experience attrition.

Familiarity and attrition both eroded the benefits of experience,

and attrition had especially pronounced negative effects on

familiar teams. Finally, the results demonstrated that the

experience-accuracy relationship was almost totally mediated by

the core constructs. In the Hollenbeck, Ilgen et al. (1998)

study, the authors also examined three additional non-core

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variables: informational redundancy (the overlap of information

between team members), staff member competence, and team

cohesiveness. In this study, the non-core constructs were shown

to have a significant effect on accuracy (R 2 = 0.17), with

cohesiveness and redundancy showing

particularly strong effects. In general, teams that were high in

informational redundancy and cohesiveness performed best,

although the effects for these two non-core variables were almost

completely mediated by the core constructs.

2.3. THE ANALYTIC HIERARCHY PROCESS (AHP)

The analytic hierarchy process (AHP) is a structured technique

for organizing and analyzing complex decisions, based on

mathematics and psychology. It was developed by Thomas L. Saaty

in the 1970s and has been extensively studied and refined since

then. It has particular application in group decision making, and

is used around the world in a wide variety of decision

situations, in fields such as government, business, industry,

healthcare, and education. Rather than prescribing a "correct"

decision, the AHP helps decision makers find one that best suits

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their goal and their understanding of the problem. It provides a

comprehensive and rational framework for structuring a decision

problem, for representing and quantifying its elements, for

relating those elements to overall goals, and for evaluating

alternative solutions.

Users of the AHP first decompose their decision problem into a

hierarchy of more easily comprehended sub-problems, each of which

can be analyzed independently. The elements of the hierarchy can

relate to any aspect of the decision problem—tangible or

intangible, carefully measured or roughly estimated, well or

poorly understood—anything at all that applies to the decision at

hand.

Once the hierarchy is built, the decision makers systematically

evaluate its various elements by comparing them to one another

two at a time, with respect to their impact on an element above

them in the hierarchy. In making the comparisons, the decision

makers can use concrete data about the elements, but they

typically use their judgments about the elements' relative

meaning and importance. It is the essence of the AHP that human

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judgments, and not just the underlying information, can be used

in performing the evaluations.

2.4. USES AND APPLICATIONS

While it can be used by individuals working on straightforward

decisions, the Analytic Hierarchy Process (AHP) is most useful

where teams of people are working on complex problems, especially

those with high stakes, involving human perceptions and

judgments, whose resolutions have long-term repercussions. It has

unique advantages when important elements of the decision are

difficult to quantify or compare, or where communication among

team members is impeded by their different specializations,

terminologies, or perspectives.

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CHAPTER THREE

3.0. DECISION SITUATIONS TO WHICH THE AHP CAN BE APPLIED INCLUDE:

Choice – The selection of one alternative from a given set of

alternatives, usually where there are multiple decision

criteria involved.

Ranking – Putting a set of alternatives in order from most to

least desirable

Prioritization – Determining the relative merit of members of

a set of alternatives, as opposed to selecting a single one or

merely ranking them

Resource allocation – Apportioning resources among a set of

alternatives

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Benchmarking – Comparing the processes in one's own

organization with those of other best-of-breed organizations

Quality management – Dealing with the multidimensional aspects

of quality and quality improvement

Conflict resolution – Settling disputes between parties with

apparently incompatible goals or positions

The applications of AHP to complex decision situations have

numbered in the thousands, and have produced extensive results in

problems involving planning, resource allocation, priority

setting, and selection among alternatives. Other areas have

included forecasting, total quality management, business process

re-engineering, quality function deployment, and the balanced

scorecard. Many AHP applications are never reported to the world

at large, because they take place at high levels of large

organizations where security and privacy considerations prohibit

their disclosure. But some uses of AHP are discussed in the

literature. Recently these have included:

Deciding how best to reduce the impact of global climate

change (Fondazione Eni Enrico Mattei)

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Quantifying the overall quality of software systems

(Microsoft Corporation)

Selecting university faculty (Bloomsburg University of

Pennsylvania)

Deciding where to locate offshore manufacturing plants

(University of Cambridge)

Assessing risk in operating cross-country petroleum

pipelines (American Society of Civil Engineers)

Deciding how best to manage U.S. watersheds (U.S. Department

of Agriculture)

AHP is sometimes used in designing highly specific procedures for

particular situations, such as the rating of buildings by

historic significance. It was recently applied to a project that

uses video footage to assess the condition of highways in

Virginia. Highway engineers first used it to determine the

optimum scope of the project, then to justify its budget to

lawmakers.

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3.1. EDUCATION AND SCHOLARLY RESEARCH

Though using the analytic hierarchy process requires no

specialized academic training, it is considered an important

subject in many institutions of higher learning, including

schools of engineering and graduate schools of business. It is a

particularly important subject in the quality field, and is

taught in many specialized courses including Six Sigma, Lean Six

Sigma, and QFD.

The value of the AHP is recognized in developed and developing

countries around the world. China is an example nearly a hundred

Chinese universities offer courses in AHP, and many doctoral

students choose AHP as the subject of their research and

dissertations. Over 900 papers have been published on the subject

in China, and there is at least one Chinese scholarly journal

devoted exclusively to AHP.

The International Symposium on the Analytic Hierarchy Process

(ISAHP) holds biennial meetings of academics and practitioners

interested in the field. A wide range of topics are covered.

Those in 2005 ranged from Establishing Payment Standards for

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Surgical Specialists, to Strategic Technology Roadmapping, to

Infrastructure Reconstruction in Devastated Countries. At the

2007 meeting in Valparaíso, Chile, over 90 papers were presented

from 19 countries, including the US, Germany, Japan, Chile,

Malaysia, and Nepal. A similar number of papers were presented at

the 2009 symposium in Pittsburgh, Pennsylvania, when 28 countries

were represented. Subjects of the papers included Economic

Stabilization in Latvia, Portfolio Selection in the Banking

Sector, Wildfire Management to Help Mitigate Global Warming, and

Rural Microprojects in Nepal.

3.2. USING THE ANALYTIC HIERARCHY PROCESS

As can be seen in the material that follows, using the AHP

involves the mathematical synthesis of numerous judgments about

the decision problem at hand. It is not uncommon for these

judgments to number in the dozens or even the hundreds. While the

math can be done by hand or with a calculator, it is far more

common to use one of several computerized methods for entering

and synthesizing the judgments. The simplest of these involve

standard spreadsheet software, while the most complex use custom

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software, often augmented by special devices for acquiring the

judgments of decision makers gathered in a meeting room.

3.3. THE PROCEDURE FOR USING THE AHP CAN BE SUMMARIZED AS:

1. Model the problem as a hierarchy containing the decision goal,

the alternatives for reaching it, and the criteria for

evaluating the alternatives.

2. Establish priorities among the elements of the hierarchy by

making a series of judgments based on pairwise comparisons of

the elements. For example, when comparing potential purchases

of commercial real estate, the investors might say they prefer

location over price and price over timing.

3. Synthesize these judgments to yield a set of overall

priorities for the hierarchy. This would combine the

investors' judgments about location, price and timing for

properties A, B, C, and D into overall priorities for each

property.

4. Check the consistency of the judgments.

5. Come to a final decision based on the results of this process.

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3.4. MODEL THE PROBLEM AS A HIERARCHY

The first step in the analytic hierarchy process is to model the

problem as a hierarchy. In doing this, participants explore the

aspects of the problem at levels from general to detailed, then

express it in the multileveled way that the AHP requires. As they

work to build the hierarchy, they increase their understanding of

the problem, of its context, and of each other's thoughts and

feelings about both.

CHAPTER FOUR

CONCLUSIONS

On October 7, 2001, after the ruling Taliban regime in

Afghanistan refused to hand over leaders of the terrorist group

al Qaeda to U.S. officials, a coalition of nations invaded

Afghanistan. The mission, code named Operation Enduring Freedom

was lead by General Tommy Franks. Both the mission itself, as

well as Franks approach to the mission, that relied almost

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exclusively on heavy bombing and surgical air strikes by the

U.S., combined with ground pressure from indigenous anti-Taliban

forces, received criticism from a number of sources. Many felt

that based upon the Soviet’s experience in Afghanistan years

earlier, the combination of rugged geography and intrepid warrior

culture of the Afghan people would make it impossible to dislodge

the Afghan government. Even among those who felt that an invasion

could be successful, few thought this could be achieved without

amassing a huge U.S. based ground force such as that employed in

Operation Desert Storm. The indigenous anti- Taliban forces were

viewed as untrustworthy and even cowardly. Even the Secretary of

Defense, Donald Rumsfelt was uncomfortable with Franks’ plan,

stating publicly in early November that it was “too conservative”

(Campbell, 2001). Despite advice to change his approach, Franks

persisted with his original plan, and in less than 60 days, a new

government was in place in Kabul, and Franks was being publicly

praised by many of his former detractors. In business, medical,

political and military contexts, a great deal of decision making

occurs in contexts where the decision maker is receiving advice

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from a number of different sources. The individual charged with

the authority to

make a decision does not have all the relevant knowledge for

rendering the judgment, and the outcomes of the eventual decision

will have far reaching implications beyond those for the decision

maker.

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