Location of ems centers in indiana county
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Location of EMS Centers in Indiana County. By Paul Rossman And Jason Smith. Introduction. Optimize placement and minimize the number of EMS (Emergency Medical Service) centers in Indiana County so that the entire population is reached

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Location of EMS Centers in Indiana County

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Location of ems centers in indiana county

Location of EMS Centers in Indiana County

By Paul Rossman

And Jason Smith


Introduction

Introduction

  • Optimize placement and minimize the number of EMS (Emergency Medical Service) centers in Indiana County so that the entire population is reached

  • EMS Act of 1973: 95% of calls should be reached in 10 minutes


Introduction1

Introduction

  • Journal of Emergency Medical Services: 2007 survey of the 200 largest U.S. cities stated that 72.78% of EMS agencies use a target of 8:59 minutes or less

  • Fitch & Associates, 2005: Urban transport ambulance response time benchmarks ranging from 8:59 to 12:59 minutes


Research

Research

  • Toregas et al., 1971, pioneered binary integer programming and set covering to determine optimal EMS station placement

  • Eaton et al., 1985, similarly placed ambulance stations


Research1

Research

  • Batta and Mannur, 1990, similarly determined optimal placement of fire stations and ambulance stations

  • NUMB3RS season 4 opening episode “Trust Metric” (2007): Charlie Eppes uses set covering to optimize the position of police officers in downtown L.A.


Methodology

Methodology

  • Downloaded Pennsylvania map from U.S. Census Bureau website

  • Used ArcGIS to extract map of Indiana County


Methodology1

Methodology

  • Used ArcGIS to find centers of Indiana County municipalities

  • Mapped and labeled municipalities in alphabetical order from 1 to 38


Methodology2

Methodology

  • Imported Indiana County municipality central points into Google Earth

  • Used Google Earth to find distances in minutes between municipality centers


Distance matrix in minutes

Distance Matrix in Minutes


Distance matrix in miles

Distance Matrix in Miles


Populations

Populations

Inverse proportion = Total Population/ Population of Municipalities


Converting minutes to miles

Converting Minutes to Miles

Miles = -1.9998789 + 0.56322676 Minutes

Sample size: 1444

R (correlation coefficient) = 0.9486

R-sq = 0.8999157


Model

Model

  • = the set of all municipalities, 1 … 38

  • = the distance from node i to node j

  • T = the maximum predetermined time between municipalities


Model1

Model

s. t.

Z1 = the number of EMS centers required


Sample problem time 10 minutes

Sample Problem (Time <= 10 minutes)


Sample problem time 10 minutes1

Sample Problem (Time <= 10 minutes)


Technology

Technology

  • Generic Algebraic Modeling System

  • “a high-level modeling system for mathematical programming and optimization”


Technology1

Technology

option limcol=0;

set mun /1*38/;

alias (mun,i,j);

table travelTime(i,j) "travel time between municipalities in Indiana County"

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

1 0.00 42.00 84.00 26.00 20.00 12.00 13.00 11.00 73.00 29.00 35.00 53.00 42.00 38.00 47.00 59.00 5.00 43.00 71.00 68.00 55.00 25.00 32.00 52.00 68.00 63.00 30.00 37.00 48.00 40.00 42.00 71.00 59.00 52.00 75.00 14.00 32.00 47.00

2 42.00 0.00 73.00 34.00 37.00 28.00 37.00 32.00 58.00 21.00 27.00 56.00 34.00 35.00 20.00 44.00 45.00 25.00 73.00 54.00 51.00 20.00 21.00 37.00 61.00 48.00 36.00 17.00 33.00 48.00 10.00 47.00 39.00 24.00 51.00 46.00 21.00 20.00

3 84.00 73.00 0.00 82.00 84.00 76.00 80.00 79.00 18.00 69.00 61.00 34.00 55.00 93.00 62.00 40.00 87.00 61.00 22.00 33.00 47.00 68.00 60.00 41.00 26.00 31.00 67.00 63.00 51.00 104.00 74.00 46.00 51.00 62.00 44.00 94.00 60.00 89.00


Technology2

Technology

set cover(i,j) "Center at municipality i covers municipality j";

cover(i,j) = yes$(travelTime(i,j) <= 8.9333);

parameter popWeight(mun) population weight

/1 684.0076336

2 28.99838188

3 89.87462387

  • 68.03720577

    ...

    Binary Variables buildStation(mun);

    Variables totalStations;

    Equations coverConstraint(mun), objective;

    objective..

    totalStations =e= sum(mun, buildStation(mun)*popWeight(mun));

    coverConstraint(mun)..

    sum(j$cover(j,mun),buildStation(j)) =g= 1;

    model indiana /all/;

    * any optimum within <1 of the true optimum must BE the true optimum!

    indiana.optca = 0.999;

    solve indiana using rmip minimizing totalStations;


Analysis

Analysis

  • Fitch & Associates, 2005: Urban transport ambulance response time benchmarks ranging from 8:59 to 12:59 minutes

  • Using Uniform distribution, we picked 28 random numbers between 8:59 and 12:59

  • Similarly, we picked 28 random numbers between 3.01 and 5.31


Solutions

Solutions

* Changes were at 9 minutes, 10 minutes and 12 minutes


Solutions1

Solutions

* Changes are at 3.8 and at 4.0


Actual placement of centers

Actual Placement of Centers

  • According to model, it means a 23-minute response time.

  • Much lower because of IRPs and other factors


Conclusions

Conclusions

  • Model is sufficient, however leaves room for opportunities for improvement

  • Provides a snapshot of needs and thresholds for building EMS centers


Any questions

Any questions?


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