Post on 25-Feb-2023
1
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
2
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
3
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
4
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
5
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
6
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).
7
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
8
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
9
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
10
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
11
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
12
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
13
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
14
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.
15
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
16
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)
17
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.
18
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
19
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
20
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.
21
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
22
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
23
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.
REFERENCES
Saaty, Thomas L.; Peniwati, Kirti (2008). Group Decision Making: Drawing out
and Reconciling Differences. Pittsburgh, Pennsylvania: RWS Publications.
ISBN 978-1-888603-08-8.
Saaty, Thomas L. (June 2008). "Relative Measurement and its
Generalization in Decision Making: Why Pairwise Comparisons are
Central in Mathematics for the Measurement of Intangible Factors
– The Analytic Hierarchy/Network Process". Review of the Royal Academy
of Exact, Physical and Natural Sciences, Series A: Mathematics (RACSAM) 102 (2):
251–318. doi:10.1007/bf03191825. Retrieved 2008-12-22.
Bhushan, Navneet; Kanwal Rai (January 2004). Strategic Decision Making:
Applying the Analytic Hierarchy Process. London: Springer-Verlag. ISBN 1-
85233-756-7.
24
Forman, Ernest H.; Saul I. Gass (July 2001). "The analytical hierarchy
process—an exposition". Operations Research 49 (4): 469–487.
doi:10.1287/opre.49.4.469.11231.
de Steiguer, J.E.; Jennifer Duberstein; Vicente Lopes (October 2003).
"The Analytic Hierarchy Process as a Means for Integrated
Watershed Management". In Renard, Kenneth G. First Interagency
Conference on Research on the Watersheds. Benson, Arizona: U.S.
Department of Agriculture, Agricultural Research Service.
pp. 736–740.
Berrittella, M.; A. Certa; M. Enea; P. Zito (January 2007). "An
Analytic Hierarchy Process for the Evaluation of Transport
Policies to Reduce Climate Change Impacts". "Fondazione Eni
Enrico Mattei (Milano)".