1. Employing the Analytical Hierarchy Processin Graduate SchoolSelection
Shelisa M. Thomas, BS
Abstract
Selecting a graduate school amongst alternatives can be difficult for potential graduate students
for a number of reasons, including inconsistent preferences, personal biases towards specific
schools, and so on. This research examines the selection of graduate school for potential JD/PhD
students by using the Analytical Hierarchy Process (AHP) in order to select the best school to
attend. AHP is a technique that quantifies qualitative data by evaluating objective things and
assigning a quantitative value to them, which helps decision makers make the best decision that
fits the overall goal. A pairwise analysis will be developed in order to evaluate three potential
graduate schools based upon four primary factors, including: (1) proximity to home; (2) job
attainment post-graduation; (3) financial aid package; and (4) prestige. The paper will conclude
with an evaluation of the AHP approach as a viable selection tool for selecting the best school
for a JD/PhD bound student.
Keywords: Analytical Hierarchy Process (AHP), graduate school selection, spreadsheet
modeling
Introduction
Choosing which graduate schools to apply to
and which offers to accept are crucial yet
challenging tasks that all graduate-school
bound students face. Many different factors
exist throughout this particular decision
making process, such as location, climate,
financial aid, safety, family, friends, and so
on. Because there is no one right or wrong
way to proceed through this decision making
process, there is a demand for assistance in
this selection process.
The most common difficulties in the graduate
school selection process can abundantly be
categorized into competing interests (e.g.
location, tuition, financial aid, campus
resources, etc.) and maintaining an objective
view of how each potential school meets the
potential student’s preferences. Although
objectivity is the goal, individual judgments
have “been considered to be a questionable
practice when objectivity is the norm”
(Saaty: 85, 2008). As a result, AHP is an
appropriate selection tool to employ during
this particular decision making process. AHP
is designed in such a way that qualitative data
can be quantified and then evaluation criteria
and alternative options can be considered to
yield the best decision. AHP allows for the
comparing of various competing criteria such
as proximity to home, job attainment, and
financial aid by assigning a scaled,
quantitative value to the preference; this aids
in maintaining an objective perspective. The
AHP model results in numerical values for
each school, with the highest representing the
option that best fits the decision maker’s
preferences. AHP is “one of the most widely
used multiple criteria decision-making tools”
for many different decisions, for example
(Vaidya & Kumar: 1, 2004; Saaty: 95-96,
2008):
 Xerox Corporation employed AHP to
allocate nearly $1 billion to research
projects
 British Airways used it to choose the
entertainment system vendor for its
entire fleet of airplanes
 The U.S. Nuclear Regulatory
Commission used AHP to allocate
more $100 million in resources to IT
projects, which helped reduced
significantly reduce decision time

2. Employing the Analytical Hierarchy Process in Graduate School Selection
Shelisa Thomas 2015: Page 2 of 4
Methods
This research was created using the analytical
hierarchy process, Microsoft Excel, and a
self-developed case. The following steps
were followed to develop the model: (1) state
objective, (2) define criteria, (3) select
alternatives, (4) determine relative
importance of criteria to develop a pairwise
comparison, (5) develop a normalized matrix,
and (6) calculate weights to determine
relative ranking of criteria and scores for the
ranking of alternatives under each criterion.
The goal of the case was to determine which
school to apply to for a JD/PhD in
Management program of three alternatives:
Northwestern, University of Chicago, or
Harvard. The potential student chose three
criteria to use in helping make the decision:
proximity to home (Northwest Indiana), job
attainment post-graduation, financial aid
package, and prestige.
To determine the relative importance of
criteria, the information in Table 1 was used.
Based on the information in Table 1, pairwise
comparison matrices were developed for
ranking of criteria and ranking of alternatives
amongst each criterion, where the rankings
range from 1/9 (absolutely less important) to
9 (absolutely more important) with 1 being of
equal importance. Pairwise comparison
matrices are paired comparisons that can
address a decision from four different
standpoints: benefits of the decision,
opportunities created by the decision, costs
incurred by the decision, and potential risks
to be faced (Saaty: 94, 2008).
A normalized matrix for each pairwise
comparison was developed by taking the
relative ranking of each cell and dividing it
by the sum of the rankings for each column
of criteria or alternatives, which allows for
each criterion and alternative to be assigned a
weighted value for each pairwise comparison
by taking the average of the rows in the
normalized matrices. These weights
represent the level of importance of each
criteria and how well each alternative scores
on that criteria as it pertains to the decision
maker’s preferences.
To ensure that rankings were consistent, a
consistency check was conducted by
comparing the consistency index to the
random index, which represents the average
consistency index for a “huge number of
randomly generated matrices of the same
TABLE 1

3. Employing the Analytical Hierarchy Process in Graduate School Selection
Shelisa Thomas 2015: Page 3 of 4
order” (Sego, 2013). The consistency check
of each matrix was less than .1, which means
that the comparisons are consistent enough to
be useful.
Finally, a final matrix was developed to
compare each alternative’s performance
under each criterion. By taking the average of
the weights/scores for each alternative, the
result determined which alternative best met
the decision maker’s preference.
Discussion of Results
The weighted scores indicate which
alternative is the best under the criteria set
forth by the decision maker. It can be seen
from the results below in Table 2 which is
reflective of the information detailed in Table
1 that Northwestern is the university that best
meets the criteria that was set forth since it
has the highest weighted score.
Using AHP to make this decision helps
maintain consistency throughout the decision
making process. For example, Harvard has an
excellent reputation and may be perceived to
be the best school no matter what because of
its reputation, but AHP surpasses that
personal bias by maintaining objectivity of
preferences. It can be seen from Table 2 that
Harvard is the least appropriate school based
on the personal preferences that were used. It
is this level of objectivity that makes AHP an
excellent selection tool.
Conclusion
The analytical hierarchy process is a viable
selection tool for selecting the best school for
a JD/PhD in Management bound student.
Although AHP doesn’t optimize each
criterion, it can be employed to help
determine which schools align best with the
prospective student’s interests collectively
for both choosing schools to apply to and also
to determine which offer to accept. AHP is a
globally used decision-making tool that can
be used for making many decisions whether
it be at the personal level, corporate level, or
in academe. This new application of AHP
shows that simple spreadsheet modeling can
in fact be used to lessen the stress and
difficulties associated with selection graduate
schools to apply to and which offers to
accept.
Author’s Note:
Shelisa M. Thomas, College of Business,
Purdue University Calumet.
Mentor: Raida Abuizam, PhD
Contact: shelisa_t@live.com
TABLE 2.
Determining the Best Graduate School
Matrix of Scores Weighted Scores
Proximity Job Attainment Financial Aid Prestige
Northwestern 0.3025 0.1038 0.7235 0.0796 0.4222
University of Chicago 0.6366 0.6651 0.1932 0.2648 0.4023
Harvard 0.0609 0.2311 0.0833 0.6555 0.1756

4. Employing the Analytical Hierarchy Process in Graduate School Selection
Shelisa Thomas 2015: Page 4 of 4
Works Cited
Saaty, T. L. (2008). Decision making with the
analytical hierarchy process. International
Journal of Services Sciences, 1(1), 83-98.
Retrieved from
http://www.colorado.edu/geography/leyk/ge
og_5113/readings/saaty_2008.pdf
Sego, V. (2013, July 31). How to compute the
consistency index in Analytic Hierarchy
Process? Retrieved from
http://math.stackexchange.com/questions/45
5973/how-to-compute-the-consistency-
index-in-analytic-hierarchy-process
Vaidya, O.S. & Kumar, S. (2004). Analytic
Hierarchy Process: An Overview of
Applications. European Journal of
Operational Research, 169(2006), 1-29.
DOI: 10.1016/j.ejor.2004.04.028. Retrieved
from
http://www.fcmfmpep.org.br/disciplinas/tur
ma1/MB-
721/Aula03/AHP%20an%20overview%20of
%20applications.pdf