Transcript poster template - Rutgers University

Emergency Shelter Location and Resource Allocation
S. Ghorbani, M. Baykal-Gürsoy, P. Kazemian, E. Boros and N. Fefferman
Industrial & Systems Engineering Department
Rutgers, The State University of New Jersey
Rutgers University
Academic Excellence Fund
Extreme Weather Events
Assignment Policy
Any weather event that might lead to a
catastrophic situation affecting human life.
Research shows an increasing trend:
Triage
•Hurricane Floyd 1999, Katrina 2005, like 2008
•Heat wave in Chicago 1995 and France 2003
•Blackouts due to extreme heat or cold and
rising electricity consumption
•Result for Model
Mathematical Model I
Parameters
• popik : Number of type k people living in block-building i,
• capj : Number of patients that can be accommodated in center j,
(For potential locations, this capacity is the estimated capacity
if a new shelter is built at that place)
• dij : The transportation cost to go from block i to center j, j = 1,…, J
+ M,
• vkj : 0 If center j can provide the appropriate treatment for patient
type k & 1 Otherwise.
 Location/ Allocation problem of vulnerable
populations into health care centers in case of a
heat event in order to minimize the total distance
traveled subject to a constraint on the number of
possible deaths.
Literature Survey & Contribution

• Result for Model II
Mini 1


J M
j 1

K
k 1

j 1
x jik  1
i, k
The capacity constraint
 
I
K
i1
k1
popik x ijk  capj
j  1,...,J  M
The constraint on the average number of death

Vulnerable Population
K
J
I
K
J
 I



E   pop ik 1  x ijk     pop ikv kj x ikj  
j1
i1
k1
j1


 i1 k1

0  x ijk  1
i,k and j  1,...,J  M

Mathematical Model II

i = set of blocks = {1,2,…,100}
j = set of cooling centers = {1,2,…,10}
popi = population of block i
dij = distance between block i and cooling center j
xij  1 if block i is assigned to cooling center j
0 O.W.
u j  1 If cooling center is selected as a triage
0 O.W.
Min z =  popi .dij .x ij
Health Care Centers
Hospital
•Cardio Vascular people
•People with serious Respiratory problem
Acute Care Center(ACC)
•People with Respiratory problems
Cooling Center
•People who are suffering from Dehydration
x
ij
1
i, j
i
j
x ij  u j

u
j
4
j
Xij,uj binary

i, j
 75
 75
 75
 75
 75
 75
k 1
k 2
k 3
k 4
k 5
k 6
d ij popik xi jk
The coverage constraint
J M
•Cardio Vascular
•N/A
Subject to:
We consider an imaginary center with a very big numbers for
distance parameter and capacity which refers to people left
at home due to lack of enough capacity in the health centers.
We are going to present a model which assigns
people to the health centers based on their
medical needs associated with the demographic
data. We are going to estimate the number of
people in need by utilizing the mortality
information.
People are categorized to four groups based
on their health problems:
•Dehydration
Objective function
I
•Identification of areas as blocks
•Population size and age groups living in each
block
•Existing facilities: Hospitals, Acute Care
centers, and Cooling centers (Churches,
Schools, Libraries, …)
•Road maps with distances
•Respiratory
• xijk : The coverage percentage of people type k from block i
by center j, 0  x ijk  1,
Oh and Haghani, 1996
Yi and Ozdamar, 2006
Griffin et al., 2007
To design an efficient plan for the city of
Newark in the case of a heat event we utilize
the following data:
Health Groups
Decision Variables
Joint Location/Allocation and Supply
Management problem
• Elderly
• Morbidly obese with assistance needs
• Patients who are sustained at home using
medical equipments
ACC
Xpress-MP is utilized to solve these models for
100 blocks of population and 5 hospitals as well
as 10 candidates for cooling centers in Newark.
The results is as follows:
Cooling
Objective
Input data from GIS
Results
Hospital
People
Sara Ghorbani, [email protected]
Melike Baykal-Gursoy, [email protected]
Pooyan Kazemian, [email protected]
Heat Risk Index
Results show that bringing number of deaths to
attention significantly affects the problem
solution and results in setting up more cooling
center.
Conclusion
Two mathematical assignment models were
proposed for a heat wave problem with GIS
based data. Results show that mortality factor is
so important and affects the assignment results.
This issue is more highlighted when we want to
solve the problem for the entire city of Newark.
Risk index helps us to estimate the number of
people at risk for each group
Ik = Number of people in need of medical care
for group k
Bk= Baseline “bad outcome” for percent
change in death per 1˚C increase in
temperature taken from “normal” rates of
hospitalization during non-heat events
T = Increase in temperature (degrees of
Fahrenheit)
Ck = Number of deaths in the normal condition
in the hospitals for group k
I k  Bk Ck T
References for Heat Risk Index
• Conti et al., 2007, “General and specific
mortality among the elderly during the 2003
heat wave in Genoa (Italy)”
• Knowlton et al., 2009, “The 2006 California
Heat Wave: Impacts on Hospitalizations and
Emergency Department Visits”
• Basu & Ostro, 2009, “Multi-County Analysis
Identifying The Vulnerable Population for
Mortality Associated with High Ambient
Temperature in California”