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IEEE TRANSACTIONS ON SYSTEM, MAN, AND CYBERNETICS PART A, VOL. X, NO. X, MARCH 2011
A Novel Space Partitioning Algorithm to Improve
Current Practices in Facility Placement
Tamara Jimenez, Armin R Mikler and Chetan Tiwari
Abstract-In the presence of naturally occurring and man-
made public health threats, the feasibility of regional bio-
emergency contingency plans plays a crucial role in the mitigation
of such emergencies. While the analysis of in-place response
scenarios provides a measure of quality for a given plan, it
involves human judgment to identify improvements in plans
that are otherwise likely to fail. Since resource constraints and
government mandates limit the availability of service provided in
case of an emergency, computational techniques can determine
optimal locations for providing emergency response assuming
that the uniform distribution of demand across homogeneous
resources will yield and optimal service outcome. This paper
presents an algorithm that recursively partitions the geographic
space into sub-regions while equally distributing the population
across the partitions. For this method, we have proven the
existence of an upper bound on the deviation from the optimal
population size for sub-regions.
Index Terms-Epidemics, Pandemics and Biological Threats,
Public Health Preparedness, Response Analysis, Optimization,
Algorithm, Algorithmic Optimization.
RECENT events have emphasized the necessity of emer-
gency response plans for natural as well as man-made
disasters. Naturally occurring disasters can be caused by
diseases, such as H1N1 or Cholera, as well as environ-
mental events, including earthquakes and hurricanes. Man-
made emergencies include those caused by acts of terror
and might involve the spread of biological agents, such as
anthrax. Emergency preparedness coordinators must therefore
devise contingency plans for different types of emergencies.
In particular, regional public health departments must address
public health threats, such as epidemics caused by seasonal
influenza, or the release of anthrax. Many of the resulting
emergency response scenarios involve the placement of points
of dispensing (PODs) throughout the geographic region, at
which the general public is provided prophylactic medications
or vaccines in a timely manner . It is crucial to analyze if an
underlying response plan will succeed in case of an emergency,
i.e. meet mandated time-frames. We have developed the com-
putational framework RE-PLAN (REsponse PLan ANalayzer),
which aids public health experts to determine optimal POD
placement and facilitate analysis of existing response scenario.
While RE-PLAN's analysis module is tailored to design and
improve POD-based mitigation, related work compares dif-
ferent mediation strategies for specific public health events.
The analysis of response plans for attacks with aerosolized
smallpox is discussed by Miller et al. , comparing dif-
ferent vaccination strategies. Similarly, different emergency
This research has been funded by NIH grant NIH 1R15LM010804-01.
responses for airborne anthrax attacks are compared by Wein
et al. . Research presented by Kaplan et al.  primarily
focuses on modeling general vaccination policies of large U.S.
cities and estimating the number of deaths. The comparison
determines mass vaccination as the most successful vacci-
nation strategy. The success of a response scenario cannot
be guaranteed if the POD operation itself is not thoroughly
planned. The simulation and decision support system RealOpt
focuses on POD layout design, staffing, and clinic design
 . Standards for mass antibiotic dispensing specifically
for POD-based response scenarios have been recommended
by RAND . These standards comprise guidelines for the
number and locations of PODs, internal POD operation, PODs
staffing, as well as POD security. The recommendations have
been implemented by various U.S. counties and represent the
modus operandi. Implicitly, equal capacity PODs are assumed
when generating the number of PODs. For the placement
of disaster recovery centers in Florida a two-stage process
has been proposed . After suitable locations have been
found, realistic locations nearby are identified that satisfy
additional criteria. However, the underlying system limits the
problem size, which restricts the number of demand points
and therefore its granularity. Different aspects of disaster
response planning take into account the supply chains of global
humanitarian relief organizations . Problems posed by such
global scenarios include stocking/inventory, as well as the
placement of distribution centers in the relief network.
For the design and analysis of bio-emergency contingency
plans underlying geographic information, as well as resource
constraints and assumptions by public health experts have
to be taken into account. Geographic information is derived
from census blocks and the corresponding road infrastructure.
Census block data from the Census 2000 can be obtained for
all U.S. counties on the U.S. Census website . Detailed
road information along with corresponding traffic counts and
road capacities may be available from local authorities. If
limited data are available, road capacities and traffic counts
can be estimated as described in . Constraints include
available resources, such as medical staff at the POD locations,
as well as Centers for Disease Control and Prevention (CDC)
mandated time-frames. In the event of an anthrax attack, the
population in the affected geographic region must be supplied
with prophylactic medication within 48 hours ,  after
an initial setup phase of 12 hours . This timeline is
illustrated in Figure 1. Similarly, in the event of a smallpox
outbreak the population has to be vaccinated within 72 hours
, , . Note, that for a vaccination scenario the
serving time per person at a POD location is longer than
for a scenario involving the distribution of medication. This
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Jimenez, Tamara; Mikler, Armin R. & Tiwari, Chetan. A Novel Space Partitioning Algorithm to Improve Current Practices in Facility Placement, article, March 2011; [New York, New York]. (digital.library.unt.edu/ark:/67531/metadc132975/m1/3/: accessed March 30, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Engineering.