Selecting an Insurance Carrier Based on Geographic Coverage Using the

Spherical Law of Cosines

John ToczekDecision Support

Aramark

Background

180,000 Employees in the U.S.Thousands of injuries each year

State requirements for emergency care

Quiz

A

BlueCrossAetnaCigna

B C

Which insurance company should I choose for best coverage?

Quiz

A

BlueCrossAetnaCigna

B C

Which insurance company should I choose for best coverage?

ARAMARK and 'Provider A' Emergency Care Locations

Pairing Aramark locations to Emergency Care locations

4859 rows453 rows

Aramark locations 'Provider A' emergency locations

DATA COMBOS;set ARAMARK;if _N_ <=453; *Aramark locations (453max);

do i=1 to 4859; *Emergency locations (4859max);set EMERGENCY point=i nobs=n;output;

end;run;

Pairing Aramark locations to Emergency Care locations

DATA COMBOS;

2.5 million rows

arcos (sin(A-lat*0.0174)*sin(B-lat*0.0174)+cos(A-lat*0.0174)*cos(B-lat*0.0174)*cos(B-lon*0.0174-A-lon*0.0174))*3959;

Distance between two points on a sphere =

Spherical Law of Cosines

Calculating the distance between two points on a sphere in SAS

DATA DISTANCE;SET COMBOS;DIST = arcos(sin(A_Lat*0.017453)

*sin(E_Lat*0.017453)+cos(A_Lat*0.017453)*cos(E_Lat*0.017453)*cos(E_lon*0.017453-A_Lon*0.017453))*3959;

RUN;

Calculating the distance between two points on a sphere in SAS

Spherical Law of Cosines

DATA DISTANCE;

~2 million rows

(mi.)

DATA DISTANCE;

~2 million rows

(mi.)

DATA DISTANCE;

PROC REPORT DATA=DISTANCE out=FINAL;COLUMN DIST ARAMARK;DEFINE ARAMARK / GROUP;DEFINE DIST / MIN;

RUN;~2 million rows

(mi.)

DATA FINAL;

453 rows

PROC REPORT DATA=DISTANCE out=FINAL;COLUMN DIST ARAMARK;DEFINE ARAMARK / GROUP;DEFINE DIST / MIN;

RUN;

(mi.)

Questions?

Why not use Pythagorean?

• 3% error between SLOC and Pythagorean

• For 100 miles actual distance, Pythagorean would show 97 miles. Small but significant for this application

Abstract Selecting an Occupational Medicine Network Provider Based on Geographic Coverage Using the Spherical Law of Cosines ARAMARK corporation employs 200,000 people domestically and is a leading provider of food and facilities management services to Business, Education, Healthcare, and Sports and Entertainment clients in the US, generating $11.6 billion of sales in 2006. In order to provide timely and efficient medical treatment to its employees in the event of an injury, in certain states where permitted by law, ARAMARK selects an occupational medicine network provider who has Urgent Care Facilities (UCF) near ARAMARK locations of business.  In choosing an occupational medicine provider, ARAMARK must select one that provides the most comprehensive  geographic network of these UCFs so that response time and injury severity are minimized. SAS, in conjunction with the Spherical Law of Cosines, is used to calculate the distance between each ARAMARK location and each UCF. This amounts to over 2 million separate distance calculations for California alone. To find the nearest UCF, the data is collapsed using a DEFINE DISTANCE / MIN within a PROC REPORT.  The resulting table is a list of ARAMARK locations, the nearest UCF, and the distance to that UCF.  Runtime for the code is under 5 minutes. John Toczek is an Operations Research Analyst for ARAMARK Corporation in the Global Risk Management Division.  He earned his Bachelor of Science degree in Chemical Engineering at Drexel University (1996) and his Master of Science in Operations Research from Virginia Commonwealth University (2005).  He can be reached at toczek-john@aramark.com.