Journal of the Operational Research Society (2009) 60, 869--872  2009 Operational Research Society Ltd. All rights reserved. 0160-5682/09
www.palgrave-journals.com/jors/
Locating automated external defibrillators in
a university community
DC Myers and M Mohite
Bowling Green State University, Bowling Green, OH, USA
Automated external defibrillators (AEDs) use smart technology to determine whether a victim of cardiac arrest
requires defibrillation and will deliver a shock only if one is needed. These portable devices are becoming
increasingly more available in such places as airports, shopping malls, and sports facilities. This article reports
on a model for determining appropriate locations for AEDs in a university community. Additionally, we
describe difficulties encountered when attempting to implement the results obtained from the model.
Journal of the Operational Research Society (2009) 60, 869­872. doi:10.1057/palgrave.jors.2602615
Published online 28 May 2008
Keywords: risk management; covering; location problems; health
Introduction
Cardiovascular disease is a major public health problem and
is the leading cause of death in the United States. Between
300 000 and 400 000 Americans die each year due to cardiac
arrest, a sudden and unexpected loss of heart function. When
cardiac arrest occurs inside a hospital, medical personnel
administer an electric shock to the patient in an attempt to
restore the heart to a normal rhythm. If this is done early
enough, there is a high probability (50­90%) that the patient
will survive. The survival probability shrinks quickly with
the passing of time (about 10% per minute) (Toeppen-Sprigg
et al, 2003).
Automated external defibrillators (AEDs) are portable
devices designed to use smart technology that automatically
determines whether a victim's heart requires a shock and
will only deliver a shock if one is needed. Voice instructions
guide the user throughout the procedure. For ease of access,
these devices are usually located in a wall cabinet similar to
those housing fire extinguishers (see Figure 1). AEDs have
been shown to be a safe and effective method of defibrillating
a victim even when used by children (Gundry et al, 1999).
In June of 1999, Chicago's O'Hare and Midway Airports
installed AEDs in sufficient numbers so that the response time
to reach the victim is 1 min (Chicago HeartSaveTM Program
(Bond, 1999)). As of 11 April, 2004, a Federal Aviation
Administration (FAA) rule went into effect requiring every
big jet in the US fleet to have a defibrillator on board (Davis,
2004). The FAA had been debating the rule for 4 years.
Correspondence: DC Myers, Department of Applied Statistics and
Operations Research, Bowling Green State University, Bowling Green,
OH 43403, USA.
E-mail: myers@bgsu.edu
The cost of AEDs has reached a level where these devices
are affordable even for home use. One manufacturer offers a
home defibrillator with `technology identical to those in use
on airplanes and in airports, workplaces, and communities
around the world' (http://www.heartstarthome.com). While
individual purchases for home use require a prescription in
most states, thousands of the devices have been purchased by
shopping malls, golf courses, and, more recently, universities.
Problem description
This article reports on a model developed at a mid-western
United States university for locating AEDs obtained from a
grant. The Director of Risk Management was given the task
of determining appropriate locations for the AEDs to provide
timely response capability for medical emergencies requiring
defibrillation. Medical authorities report that a victim of
cardiac arrest has the best chance of survival without neurological
damage if care is received within 3­5 min of occurrence
(American Heart Association, 2001). (Actually, this
time is a source of contention. Various sources use anywhere
from 3 to 8 min, although shorter times are clearly better for
the victim.) Thus, the goal of our analysis was to determine
the location of the AEDs so that every member of the university
community would be within 4 min of one of the devices.
Certain of the locations were easy to determine since those
areas were either isolated from other areas of the university
(greater than 4 min from the nearest other facility) or was
an area with an increased likelihood of having a need for
these devices (such as the golf course, recreation centre, and
football stadium complex).
Related research
The mathematical model developed is known in the literature
as a covering model. We wanted to provide `coverage'
870 Journal of the Operational Research Society Vol. 60, No. 6
Figure 1 AED in wall-mounted storage cabinet.
to all university areas with the available AEDs. The covering
problem is a well-known problem in management science
and numerous practical applications of set covering methodology
have been documented. Plane and Hendrick (1977)
used a set covering model to locate fire companies in Denver.
Current and O'Kelly (1992) developed set covering models
for locating emergency sirens to warn citizens of approaching
severe weather. In 1979, Sweeney et al used a similar model to
determine the number of banking facilities required to permit
a regional banking firm to do business in all counties of a midwestern
state. Brotcorne et al (2003) recently reviewed 30
years of ambulance location and re-location model research.
Previous research in the management science literature
involving AEDs includes determining the cost effectiveness
of the units and equitable allocations of AED units. Rauner
and Bajmoczy (2003) investigate cost effectiveness of AEDs
for the Austrian Red Cross. Mandell and Becker (1996) use a
multi-objective integer programming model to assist decision
makers in determining which basic life support companies to
equip with AEDs in order to achieve an equitable survival
rate.
Model
Prior to model construction, data had to be collected regarding
the estimated travel times between pairs of buildings. Student
teams from the first author's management science class were
assigned the duty of determining these times. The times were
obtained by actually walking (at a hurried pace) from building
to adjacent building. The collected times were then used to
estimate times between non-adjacent buildings. For some of
the buildings, this was essentially an additive process. For
other pairs of buildings, the actual walking distance was used.
These times were then used to create a coverage matrix.
A Microsoft
Excel spreadsheet was set up with one array
containing the actual building-to-building time estimates and
another array containing binary values indicating whether the
buildings are `reachable' within the desired 4 min time limit.
Using the binary coverage matrix, a spreadsheet model was
constructed with a cell allocated for each campus building in
which AEDs could be located. These cells would eventually
contain a binary value indicating whether the building was
selected or not. Dormitories, fraternities, and sororities were
not considered as acceptable locations for AEDs due to the
potential for misuse by building occupants. (These facilities
were included as buildings that must be reachable within the
time limit.)
In the initial model, xi is a binary variable which will have
a value of 1 if an AED is located in area i and a value of
0 otherwise. Also, yi is a binary variable which will have a
value of 1 if university area i is covered by an AED (within
the required time limit) and a value of 0 otherwise. The model
is given as
Max
B
i=1
yi (1)
s.t.
B
j=1
xj = D (2)
jCi
xj yi , i = 1, . . . , B (3)
x, y binary (4)
where B is the number of buildings on campus, D is the
number of defibrillating devices available, and Ci is an index
set indicating that areas are within the maximum time limit
of area i. The Director of Risk Management identified 107
university facilities that were to be covered by the AEDs and
58 viable locations for the units. Thus, the model had 165
binary variables and 107 constraints.
Grant funds were considered sufficient for the purchase
of nine additional AEDs to go with the three the university
already had (thus, D = 12). The initial model above
involved maximizing the number of facilities reachable within
the desired time limit by appropriate placement of the 12
AEDs. The results indicated that the entire campus community
could, indeed, be covered with these 12 AEDs. However,
campus security officials felt that, instead of locating each of
the AED units in a specific building, the campus community
would be better served by reserving three of the units for use
in campus police patrol cars. This led to the consideration of
DC Myers and M Mohite--Locating AEDs 871
Table 1 Maximum coverage with fixed number of AEDs
# of AEDs # Campus locations covered
(within 4 min)
1 64
2 84
3 94
4 99
5 102
6 104
7 106
8 107
9 107
10 107
11 107
12 107
a variation of the original model to determine the minimum
number of AEDs needed to provide timely coverage for all
campus facilities. This model is shown below:
Min
B
j=1
xj (5)
s.t.
jCi
xj 1, i = 1, . . . , B (6)
x binary (7)
Since some campus buildings are open for longer periods of
time and/or may serve a larger part of the campus community
(eg student union, recreation centre), a third model variant
was constructed to allow consideration of such issues. This
involved attaching weights to each building variable to reflect
the relative size and composition of the campus population
served by the building. This did not affect the number of AEDs
needed, but it did generate AED placements more acceptable
to the Director of Risk Management.
Discussion of results
The solution to the initial model indicated that, given the
freedom to objectively determine the AED locations, the
entire campus community could be covered within the
desired 4 min with 12 AEDs. In fact, Table 1 shows that this
coverage is achievable with as few as eight units. However,
as mentioned earlier, the university already had three of
these devices. These had been provisionally placed and the
university was reluctant to move them. One of these had
been purchased with non-university funds for placement in
a specific location and its removal would be particularly
problematic. Further, the Director of Risk Management had
previously been advised by an oversight committee where
six of the soon to be purchased AEDs should be placed. This
was determined by identifying campus locations frequented
by relatively large numbers of people, in particular, athletic
facilities. Added to this was the insistence by campus security
officials that three of the devices be earmarked for installaTable
2 Coverage provided by preliminary AED locations
# of Minutes # locations covered
4 84
5 91
6 92
7 93
8 99
9 104
10 106
11 107
tion in campus security cruisers. Thus, it seems that all of
the locations for the AEDs had been pre-determined.
Running the covering model with these restrictions showed
that this configuration would provide 4 min coverage for only
84 of the 107 campus facilities. Some campus facilities would
require as long as 9­11 min to be reached from this predetermined
placement of the AEDs. Table 2 summarizes this
analysis. It was further determined that to reach the entire
university community within 4 min while maintaining these
pre-determined placements would require the acquisition of
five more AEDs beyond those currently approved. Additional
runs of the model showed that moving just one of the AEDs
would increase the coverage from 84 to 96, and placing only
two AEDs (instead of the three requested) in campus security
cruisers would provide an identical improvement in coverage.
Making both of these changes simultaneously would provide
coverage to 101 of the 107 campus facilities. After some
discussion with the oversight committee, it was decided to
re-locate these two devices. Campus coverage thus increased
from 78.5 to 94.4%. However, the committee could not be
convinced to rearrange other AEDs in order to reach 100%
coverage. Re-solving the model with the re-located devices
indicated that two additional devices would be necessary to
provide complete campus coverage (instead of the five originally
thought to be needed). The committee agreed to place
subsequently obtained devices in the locations determined by
the computer model.
In addition to determining the AED locations, the oversight
committee has established guidelines for their use. An area
coordinator assigned to each AED location is responsible for
maintaining sufficient personnel trained in their use. At least
two certified employees (certified in AED usage as well as
cardio-pulmonary resuscitation (CPR)) are to be available at
each AED site whenever the facility is open.
We (the authors) were somewhat disappointed at our
inability to convince the oversight committee to adopt the
AED placements that achieve 100% campus coverage. This
unfortunate outcome is due mostly to the lateness of our
participation in the decision-making process. Our involvement
began after reading in the campus newspaper about the
receipt of the grant for obtaining the AEDs. Apparently, this
was already too late. The university already had three AEDs
in place around campus. No consideration was seriously
872 Journal of the Operational Research Society Vol. 60, No. 6
given to the possibility of re-locating these. Also, the oversight
committee had already met to discuss the placement of
the incoming devices. Some locations were chosen due to
some committee members' perception of them as `high-risk'
areas. They deemed it more important to have an AED in
each of these critical areas than to have one in a nearby
facility even though some of the critical areas could be easily
reached from a nearby facility within the time limit. While
the committee was impressed by the model(s) later presented
by the authors (and some members expressed surprise that
such models are available), it should come as no surprise to
OR/MS practitioners that it is very difficult to change decisions
once they are already made. The good news, however,
is that this project started a dialogue between the authors and
campus security officials regarding other campus situations
that may benefit from an OR/MS approach. On a higher
level, even better news is that the availability of the AEDs
on campus has already resulted in one life being saved.
Summary
This article describes a model (and several variations) for
determining appropriate locations for AEDs in a campus
community. The appropriateness of a location depends on
several factors, which include time and population considerations.
Solutions obtained for each model varied and
disagreed with some of the pre-determined locations identified
by an oversight committee. While the models identified
locations that assure 100% coverage within the desired time,
the pre-determined locations had been selected due to some
committee members' perception of them as `high-risk' areas
and there was some reluctance by these members to consider
alternative sites. After an extended discussion of the model
results, the committee agreed to re-locate two of the devices
to locations identified by the model. This increased campus
coverage from 78% to nearly 95% with the further benefit
of reducing the need for additional AEDs (to achieve 100%
coverage) from five to two.
With the prices of the devices decreasing and liability suits
becoming more prevalent, more university communities may
consider purchasing AEDs for their campuses as part of their
risk management strategy. Models such as those described
herein can be useful in guiding them on purchase and location
issues. Given the authors' experience, it is important
that campus officials be made aware of the potential for such
models early in the decision-making process.
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Received May 2007;
accepted February 2008 one revision