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

Emergency Shelter Location and Resource Allocation

S. Ghorbani, M. Baykal-Gürsoy, P. Kazemian, E. Boros and N. FeffermanIndustrial & Systems Engineering DepartmentRutgers, The State University of New Jersey

Sara Ghorbani, ghorbani@eden.rutgers.eduMelike Baykal-Gursoy, gursoy@rci.rutgers.eduPooyan Kazemian, kazemian@eden.rutgers.edu

Extreme Weather EventsExtreme Weather Events

Any weather event that might lead to a catastrophic situation affecting human life.Research shows an increasing trend:

•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

References for Heat Risk IndexReferences for Heat Risk Index

To design an efficient plan for the city of Newark in the case of a heat event we utilize the following data:

•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

Results

Mathematical Model I

• Elderly• Morbidly obese with assistance needs• Patients who are sustained at home using

medical equipments

Input data from GISInput data from GIS

Joint Location/Allocation and Supply Management problem

Oh and Haghani, 1996Yi and Ozdamar, 2006Griffin et al., 2007

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.

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:

•Result for Model

• Result for Model II

Results show that bringing number of deaths to attention significantly affects the problem solution and results in setting up more cooling center.

Vulnerable PopulationVulnerable Population

People are categorized to four groups based on their health problems:

•Cardio Vascular

•Respiratory

•Dehydration

•N/A

Health GroupsHealth Groups

75

75

75

75

75

2k

1k

3k4k

5k

6k

Heat Risk IndexHeat Risk Index

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 kBk= Baseline “bad outcome” for percent change in death per 1˚C increase in temperature taken from “normal” rates of hospitalization during non-heat events = Increase in temperature (degrees of Fahrenheit)Ck = Number of deaths in the normal condition in the hospitals for group k

T

75

TCBI kkk

ObjectiveObjective

Assignment Policy

Mathematical Model II

Literature Survey & ContributionLiterature Survey & Contribution

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.

Conclusion

• 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”

Rutgers UniversityAcademic Excellence Fund

Health Care CentersHealth Care Centers

People Triage

Hospital

ACC

Cooling

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.

• xijk : The coverage percentage of people type k from block i by center j,

0 x ijk 1,

• 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.

Parameters

Decision Variables

Objective function

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.

The coverage constraint

The capacity constraint

The constraint on the average number of death

jkikij

K

k

MJ

j

I

ixipopdMin

111

popik x ijkk1

Ki1

I cap j j 1,...,J M

E popik 1 x ijkj1

J

k1

Ki1

I popikj1

Jk1

Ki1

I vkj x ikj

0 x ijk 1 i,k and j 1,...,J M

kixMJ

j jik ,11

i = set of blocks = {1,2,…,100}j = set of cooling centers = {1,2,…,10}popi = population of block idij = distance between block i and cooling center j 1 if block i is assigned to cooling center j 0 O.W. 1 If cooling center is selected as a triage 0 O.W.

Min z =

Xij,uj binary

ijx

ju

x ij

j

1 i

x ij u j i, j

u j

j

4

popi .dij

i, j

.x ij